text
stringlengths 0
190k
|
|---|
quant-ph9611023.txt |@word logarithms:1 code:2 partial:1 consider:2 tamagawa:1 results:1 entropy:8 grateful:1 consists:1 maxπ:2 λij:2 inverse:1 finally:1 tr1:1 tr2:1 conjecture:1 choice:2 mpu:1 matrices:1 trk:1 large:2 math:2 small:2 eigenvalues:1 trs:3 optics:1 upper:1 estimates:1 rate:1 peredachi:3 spectral:6 index:1 what:2 sj2:4 diag:1 decoding:1 subspaces:1 sup:1 new:1 consisting:1 contrast:1 3d:1 full:1 equals:2 here:2 reported:1 deduced:1 property:3 institute:1 drs:1 trial:1 schumacher:4 hospitality:1 projection:1 family:2 marginal:1 outcomes:1 decrease:1 unit:3 use:1 projector:2 prove:2 probabilities:1 positive:5 msu:1 next:1 call:1 πi2:4 more:2 introducing:1 operators:4 appendix:2 particular:1 hold:1 account:3 word:4 work:2 mi:1 modified:1 westmoreland:3 following:3 stimulating:1 proof:2 states:12 minimum:2 numbers:3 sense:2 sharp:1 information:8 holds:2 whence:1 write:1 xxxi:1 pure:3 sik:1 sin:2 product:2 max:8 wiley:1 mapping:1 demonstrating:1 law:2 si1:6 light:1 sp:1 acknowledged:1 su:7 inform:3 si:9 definitions:1 typical:5 september:1 indeed:2 interpreted:1 course:1 paper:1 through:1 omitting:1 existence:1 steklov:1 its:1 euj:16 chosen:1 suboptimal:1 choose:1 mail:1 main:2 defining:2 maximal:1 spλ:4 school:1 introduce:3 nov:1 yu:1 easily:1 term:1 equality:2 university:2 inequality:5 transmitted:3 each:2 repeating:1 traces:1 side:1 osaki:1 financial:1 ej:7 sition:1 ed:1 idea:2 measurement:1 quantum:18 our:1 shannon:2 ru:1 ejn:1 matrix:3 space:2 rep:1 since:3 rev:1 holevo:3 denotes:1 formula:2 electronics:1 xu:5 independence:1 probl:4 theory:4 diagonal:1 possibility:1 complicated:1 trp:3 put:3 estimate:5 jozsa:5 definition:4 length:3 gordon:1 hence:2 onto:3 ej1:1 xj:5 xk:2 already:1 xn:1 probability:16 nc1:1 coding:4 channels:2 enlarged:1 another:1 precisely:1 open:1 size:2 given:4 start:1 πk:1 πi:12 least:1 their:2 confirming:1 bits:1 grant:1 moscow:1 wisdom:1 manifestation:1 alphabets:1 x0:1 x1:1 than:2 second:1 outcome:1 russia:1 developement:1 modern:1 kitaev:1 ras:1 apparently:1 any:2 evasion:1 lim:1 latter:1 generalized:1 channel:13 towards:1 trace:5 who:1 simplify:1 acknowledgements:1 class:1 average:2 cover:1 points:1 fact:4 quantity:2 thomas:1 nonpositive:1 random:2 notations:1 implying:2 spaces:1 apriori:3 written:1 completes:1 araki:1 dn:8 means:1 words:8 during:1 runs:1 arxiv:1 miles:1 gram:1 fixed:3 set:2 exists:1 correlations:1 j1:1 see:3 result:4 japan:1 discussions:2 recently:1 subject:1 satisfying:2 capacity:9 inequalities:1 state:2 fermi:1 justified:1 knowing:1 terms:1 restricting:1 jl:1 jn:1 key:1 distribution:8 last:1 2n:5 similar:2 taking:3 equal:4 profs:1 cn:6 cm:1 simple:1 asymptotically:1 dimensional:1 respect:4 conference:1 pu:14 due:3 int:1 combined:1 ph:1 ak:2 define:1 corresponding:4 subspace:3 coherent:1 c1:3 general:2 present:1 case:3 ap:1 might:1 value:1 will:1 while:2 replaced:1 error:8 situation:1 eij:2 πi1:6 von:1 thus:4 according:3 ij:3 properties:1 il:1 dual:1 rfbr:1 binary:1 author:1 alphabet:5 same:2 stimulated:1 quant:1 finite:2 transm:1 independent:1 used:1 i1:4 hand:1 πij:11 enrico:1 πin:1 identity:3 recent:1 lower:1 maximizing:1 epr:1 left:1 just:1 less:1 obtain:2 λj:6 density:2 superadditivity:3 theorem:4 input:5 evaluate:1 additivity:2 possibly:2 entangled:2 presume:1 using:1 necessary:1 follows:6 signal:2 wooters:3 arbitrary:3 output:4 terminology:1 mathematical:3 right:1 old:1 neumann:1 classical:6 sequence:5 conditional:1 some:4 decision:3 measurements:2 per:7 does:1 decomposition:3 tends:2 prof:1 proc:1 bu:19 step:1 nonseparability:1 rus:3 hilbert:3 about:1 actual:1 commun:1 o:11 distinct:1 range:2 mixed:4 lieb:1 raised:1 h2:1 communication:7 into:3 h1:1 disentangled:2 bound:7 ussr:1 references:1 operator:5 λj1:1 log:1 support:1 initial:1 u1:3 strict:1 jsps:1 way:1 was:8 vanishing:1 converse:2 denoting:2 hk:2 made:1 wish:1 maximum:1 us:5 un:3 limit:1 uk:2 uj:1 problem:2 λjn:1 called:1 proved:4 defined:2 abstract:1 denote:6 substantially:1 families:1 inf:1 distributions:2 sasaki:1 physical:1 noiseless:1 codes:1 trials:1 ny:2 elements:1 calculating:1 symbol:1 problems:1 shown:1 πj2:1 a1:1 a2:1 independently:1 implies:2 assume:1 rule:1 hirota:1 n1:2 n2:2 resolution:3
|
quant-ph9611024.txt |@word concept:1 sci:1 consider:1 switched:1 rev:5 separates:1 results:1 eds:3 computation:1 consists:1 landau:1 whose:2 inverse:1 bˆ:1 concerned:1 deterministic:8 answered:1 finally:2 does:3 must:1 eikonal:1 ionizing:1 protective:19 very:6 frequencies:1 tends:1 wave:37 electron:23 p1:1 stays:2 difference:2 exact:1 condition:3 treating:1 school:1 tokyo:1 level:1 suffices:1 having:2 applicable:2 large:11 convenience:3 vector:1 science:1 small:11 equation:1 smaller:3 tel:2 grateful:1 consistent:1 measurable:1 maintain:1 approximation:19 fold:1 second:3 evaluated:1 picked:2 further:2 estimated:2 zq:4 even:3 transverse:1 plays:1 apparatus:1 section:12 localization:1 contributed:1 find:3 diagrammatic:1 version:2 en:1 above:6 lifshitz:1 expresses:1 net:1 ever:1 acknowledgments:1 satisfy:1 full:2 ǫu:1 exchange:5 respectively:2 never:2 component:1 equals:1 here:1 atoms:4 drei:2 believed:1 protection:1 them:1 possibility:1 separation:1 address:1 path:1 along:3 standard:2 implicit:1 change:2 obtained:1 publisher:2 hamiltonian:2 wesley:2 shift:3 popescu:1 larger:3 allows:2 leaving:1 p2:3 simultaneous:1 implement:2 fourier:3 der:1 uniquely:1 via:5 figure:1 ions:1 neutrons:2 weaker:1 issue:1 should:2 readily:3 use:3 proceed:1 would:5 massar:1 probabilities:1 positive:1 contains:1 charge:6 next:4 classically:1 ψn:2 therefore:3 type:3 von:5 more:5 beyond:1 israel:2 sharing:1 relax:1 initial:12 operators:3 odinger:1 validity:2 berlin:1 rigid:1 normalized:1 verlag:1 particular:2 foundations:1 cases:1 iii:2 carried:3 states:1 springer:1 collision:3 deformed:2 recall:1 originally:1 work:2 easier:1 mv:25 indicating:1 following:1 scatter:2 mechanik:1 control:1 ma0:1 impose:1 indicated:1 process:2 relativistic:1 appreciable:1 suggestions:1 generically:1 sample:1 indicates:2 protects:1 numbers:1 want:1 yet:1 axis:1 information:1 end:1 sphere:1 hinders:1 rather:6 hydrogen:4 discussion:4 σel:1 feature:2 regions:1 far:2 traversal:1 significance:1 centimeters:1 absolute:2 parameter:3 ensemble:3 exponentially:3 profile:1 map:3 staying:2 description:1 rearrangement:1 after:3 impulsive:8 fb:1 δvi:3 physik:1 faculty:1 parallel:2 types:1 short:3 decaying:1 effective:3 light:1 spectra:1 lines:1 packets:1 element:1 destroying:1 ionized:1 so:10 allow:3 insofar:1 order:9 typical:4 interpretation:2 indeed:3 pointed:1 facilitated:1 utilize:1 experiments:14 differs:1 kinetic:6 still:2 pointer:15 its:4 before:2 mµ:2 sinθ:1 how:2 energies:1 lateral:1 translation:2 actually:1 aviv:2 absence:1 systems:4 constitutes:1 main:1 h0:4 maximal:2 non:3 weakness:2 practice:1 fig:3 nodeless:1 projectiles:14 break:1 framework:1 example:1 effects:2 they:1 eµ:1 1b:1 nov:1 speculate:1 discuss:2 eigenvalue:4 february:1 several:1 electrostatic:1 goldstein:1 explains:1 university:3 presented:1 realistic:1 magnitude:1 conflict:1 each:3 found:4 difficult:2 mean:2 heavy:8 reactions:1 differential:1 ei:2 significantly:1 fairly:1 energy:12 idea:1 related:1 eb:1 involve:1 measurement:13 quantum:19 our:6 happen:1 differ:1 eq:11 event:1 out:6 projections:1 leave:1 shown:3 collimated:1 unbound:1 space:5 furthermore:1 since:6 crucial:2 semi:6 particles:2 collisions:1 hill:1 conjectured:1 ref:2 ri:2 foundation:1 turning:2 theory:2 interactions:3 maintains:1 transfer:9 free:1 quite:1 completely:2 york:2 ask:1 detecting:1 predicated:1 e0:6 interaction:23 r2:1 could:7 transition:1 days:1 used:2 ups:1 motion:2 length:2 massive:5 assumed:3 hence:2 onto:1 neglect:1 south:2 first:11 origin:2 xi:1 features:1 probability:11 38a:1 subtlety:1 ez:1 number:5 hearing:1 phil:1 done:2 long:3 directly:1 force:1 precisely:1 angular:1 aharonov:13 size:1 given:7 perturbation:4 guaranteeing:1 needed:1 introduction:1 mcgraw:1 eqs:1 sackler:1 system:14 approximately:1 unruh:2 1a:2 their:3 assumption:3 just:2 statement:2 realization:1 scheme:1 final:1 shifted:1 elaboration:1 hypothetical:1 centered:2 completed:1 continuous:1 proving:1 direct:3 task:1 somewhat:1 authors:1 schr:1 anandan:7 sign:1 peculiar:1 specify:1 distance:1 target:3 parenthetically:1 princeton:2 fundamental:2 require:2 dtg:1 namely:4 murayama:1 a47:1 aav:3 coulombic:2 publ:1 were:3 radius:1 outcome:2 treated:2 inferring:1 explicit:1 ann:2 turned:1 say:9 alike:1 distorted:2 need:9 seen:1 projectile:26 any:5 ray:1 implemented:1 angle:4 built:1 zero:1 latter:6 able:1 ideas:1 vint:2 note:3 sciences:1 potential:4 take:3 measurability:1 finding:2 destroy:2 switching:1 accuracy:2 displacement:1 multiple:1 electric:1 opposite:1 simplify:1 pexc:2 involving:3 propagate:1 plan:1 device:2 zeits:1 nussinov:1 measured:5 why:1 idealized:1 ke:2 considered:2 average:5 later:1 stronger:2 feynman:1 points:3 electrons:2 principle:2 exp:3 nuclear:2 velocity:6 physics:1 review:2 fact:3 quantity:1 axes:2 particularly:1 show:2 probe:1 scattered:3 purely:2 calculable:1 thickness:1 requisite:1 ground:11 impact:3 q0:3 slow:6 ratio:2 knowledge:1 parameters:1 rovelli:1 state:33 negligible:1 than:11 only:10 experiment:2 factor:9 acknowledge:1 over:3 carolina:2 exchanged:3 do:2 get:1 dependent:1 beams:1 expectation:1 satisfied:1 beam:3 cannot:2 dz:2 closely:1 new:2 dv:2 during:2 dt:5 dr:2 justified:1 dq:1 qq:7 adiabatically:1 evolution:3 4πq:1 arxiv:1 fixes:1 summary:2 paper:3 though:1 contain:1 fixed:1 approximations:1 transforms:1 monochromatic:1 rms:1 requirement:3 set:1 computed:1 lifetimes:1 exerted:1 packet:6 depends:1 individual:1 sec:1 result:5 close:1 satisfies:3 acquires:1 suffer:1 interacting:2 dn:1 subsequent:2 away:2 tend:1 symmetric:1 enough:5 determined:3 various:2 amusingly:1 between:6 conceptual:1 geometric:1 conditions:1 available:2 eˆz:1 recently:3 parallels:1 nature:2 initially:4 screen:1 weak:6 however:11 incident:2 cut:1 wimp:1 recent:1 probing:1 virial:1 eˆb:2 configuration:1 suggested:3 providing:1 last:2 many:7 taking:1 density:5 comment:1 ln:1 connection:1 context:1 contribution:1 whole:2 masses:1 experimental:1 arbitrarily:2 strongly:2 jammer:1 relevant:1 cn:2 point:4 simple:1 corresponds:1 proton:3 sampling:1 simply:2 respect:1 destroyed:1 strong:2 described:1 basis:2 due:3 been:1 defined:1 much:2 pf:1 treat:1 interest:3 basic:5 expected:1 transformed:1 ph:1 pi:5 pn:1 choose:1 addison:2 generating:1 lived:1 corresponding:3 concerning:1 excite:1 precision:3 gap:1 zeilinger:2 determination:1 general:4 present:2 case:13 novel:2 straight:1 value:2 transformation:1 will:10 while:3 100kev:1 evaluating:1 involved:1 grundlagen:1 real:4 vb:6 uncertainty:1 ve:1 almost:2 vi:6 refs:3 thus:9 vm:1 iv:2 ii:7 δe0:3 sudden:3 im:1 against:1 dual:1 elsevier:1 nγ:2 eigenfunction:1 10ev:2 different:2 moves:1 excludes:1 author:1 suggest:3 make:4 cross:3 same:5 clearly:2 beside:1 shifts:1 unity:1 parts:2 quant:1 arguments:1 gets:1 infer:2 neutron:2 higher:1 development:1 independent:1 literature:1 columbia:1 raymond:1 see:4 upon:1 effect:1 hand:2 effectively:1 devoid:1 levels:1 moving:2 purpose:2 potentials:1 muons:4 interested:1 normalization:1 destruction:1 deflects:1 lower:1 weakly:2 off:3 charges:1 expression:1 modeled:1 vaidman:12 concrete:2 mathematische:1 without:1 solve:1 english:1 coordinate:4 position:4 whereas:1 usual:2 muon:2 dickson:1 proposed:1 being:4 when:6 obtain:2 rest:1 underlying:1 atomic:4 spherically:1 scattering:49 eigenstates:2 captured:1 previous:1 letting:1 inelastic:1 infinitely:1 photons:3 seems:1 avignone:1 valid:1 extends:1 treatment:2 av3:1 wimps:2 heavier:1 excited:6 momentum:18 amusing:2 identical:1 aspects:1 around:6 putative:1 decomposed:1 period:2 early:1 lett:3 vη:1 press:1 using:5 formal:1 desire:1 appearing:1 like:5 particle:14 alternatively:1 δt:1 adiabatic:6 disallows:1 specific:3 flux:2 nv:1 always:1 beverly:1 recalls:1 stationary:2 reduced:1 mathematical:2 pertaining:1 exceed:2 neumann:5 classical:12 some:3 deflection:8 born:12 b2:2 duration:1 home:1 total:2 sufficiently:1 demonstrates:1 avoid:1 measurements:22 extensively:1 comments:1 instantaneous:1 critical:1 provides:1 assuming:2 greenberger:2 minimal:2 measuring:8 seconds:1 problems:2 uniform:2 200gev:2 translated:1 conveyed:1 2m:2 concreteness:1 exciting:2 super:1 intense:1 comparison:2 about:2 usa:2 extending:1 slightly:2 discussed:1 factors:1 o:3 range:1 insufficient:1 consequently:1 complementing:1 considerations:1 follows:1 into:4 within:3 definitely:1 bound:8 phase:3 appropriate:2 square:1 references:1 tiny:1 operator:6 proportional:2 binding:3 often:1 elastic:6 few:1 probabilistic:6 there:5 question:1 specifically:2 class:1 width:2 exchanging:1 trigger:1 quanta:4 low:1 was:6 function:31 complete:5 form:12 collapsed:1 but:2 gaussian:4 volume:1 repeated:3 hi:9 recoil:2 repeatedly:1 atom:12 line:1 considerable:1 made:2 applying:1 rate:1 inside:1 dω:4 smooth:1 up:3 us:5 below:1 limit:2 sum:2 continuously:1 distribution:2 similar:3 mechanics:8 interval:1 ai:4 stripped:1 abstract:1 measure:6 am:1 textbook:1 resultant:1 tˆ:1 single:9 periods:1 av:3 lifetime:1 formalism:1 200mev:1 ew:1 physical:2 radically:1 compared:1 completeness:1 ideally:1 no:5 discerned:1 generally:1 na0:1 virtual:1 other:4 role:1 ezawa:1 papers:1 benefited:1 finite:2 really:3 arithmetic:1 conclusion:1 briefly:2 repeat:1 conveys:1 excitation:8 photon:3 symbol:1 mechanical:1 αem:1 a0:10 meaning:1 a2:1 nucleus:8 allowing:1 transfers:1 astronomy:1 structure:1 max:1 implies:6 coupling:1 coulomb:3 practically:1 assume:6 required:3 mask:1 dσ:4 dρ:1 ghose:1 factorizes:1 mass:6 time:12 nuclei:1 requires:1 original:6 once:1
|
quant-ph9611025.txt |@word neighbors:3 gv:2 logarithms:1 code:62 consider:15 pointing:1 induces:1 dynamic:2 resistance:2 roy:3 gt:2 subclass:1 computation:95 ρt1:4 consists:2 rectangles:32 causes:1 duplicated:3 devoted:1 particles:4 terms:1 leung:1 knill:4 subjected:7 tr:1 factoring:2 environment:3 finally:1 asking:1 those:3 th:12 under:1 multilinear:1 swap:1 third:4 alternating:4 case:13 wb:1 string:12 g1:2 orthogonal:1 far:1 frequencies:1 deviates:2 induce:2 results:8 every:2 decide:1 entries:1 associated:5 difference:1 logarithmically:2 generalised:1 entire:1 randomness:1 unlike:1 presented:1 did:1 turns:1 rectangle:24 list:1 devided:3 t1:3 try:1 discrete:1 vector:6 minimal:1 recall:2 small:15 syndrome:9 refer:1 straight:1 20th:1 upper:3 smaller:16 α2d:3 grateful:2 tolerate:1 coefficient:5 past:1 rate:18 cost:6 dissipation:1 interpolation:4 initialized:4 defines:1 theory:3 even:2 what:1 errors:21 adds:1 appear:2 richard:2 chicago:1 giving:1 section:11 celebrated:1 shares:1 find:1 current:1 sequential:1 above:9 bm:5 new:4 order:7 preserved:1 ρt:2 satisfy:1 full:1 ρw:2 degree:7 d1:1 respectively:1 realizations:1 abstractly:1 here:1 understanding:1 following:9 protection:1 operating:1 represented:3 path:19 along:1 change:1 obtained:1 search:1 institute:1 larger:6 doria:1 φr:27 ab0:1 g2d:2 resulting:5 pick:2 tolerantly:2 proof:18 makes:1 involves:1 conditioning:1 via:1 followed:3 secure:1 extra:2 tensored:1 initializing:2 merely:2 explained:1 compare:1 logical:2 replace:2 initialize:1 apply:19 unit:2 solovay:1 use:25 takes:3 working:17 prove:17 distinct:1 positive:2 motivate:1 toffoli:6 induction:19 hilbert:4 few:4 bases:1 m1:19 m0:19 m3:1 memory:1 taken:2 themselves:1 stage:36 theoretical:1 minor:2 more:21 israel:2 sharing:2 strange:1 becomes:2 potentially:1 corrected:7 occurred:5 duplicating:1 permit:1 appendix:8 normalized:1 known:1 foundations:4 cases:4 hold:2 must:4 high:3 account:3 claims:7 word:16 ρi:1 science:9 work:3 modified:1 mk:1 cat:14 labeled:2 ρr:2 polylogarithmic:5 hope:1 ms:1 mr:22 believed:1 im:2 example:3 initial:3 nearest:5 f2:2 transition:1 give:7 process:6 share:1 states:39 indicates:1 minimum:1 performed:1 want:6 allowed:2 times:11 occur:6 g2:1 information:3 end:23 recovery:1 thing:1 provide:2 s1:6 s0:14 damage:7 faults:37 vancouver:1 pure:11 answer:7 gate:38 axis:8 fp:14 inputs:3 product:4 blocks:47 description:2 transforming:2 ancilla:15 after:15 different:7 hence:6 wrong:6 designed:1 improving:2 requirements:2 unencoded:1 types:2 recursive:2 acyclic:1 imply:1 sets:5 computations:4 maybe:4 explicit:7 correspond:2 su:1 fpm:4 complexity:1 so:29 automatically:1 allow:4 sc:1 definitions:2 sa:26 operate:6 divided:3 sd:1 operations:3 restriction:4 holds:1 indeed:6 over:16 mainly:1 choose:1 course:1 paper:11 london:1 graph:2 differs:1 existence:1 satisfies:7 still:7 before:5 thomas:1 remark:1 thank:3 fit:1 how:11 chosen:2 matrices:10 succeeds:1 coordinates:3 actually:5 better:2 according:2 systems:4 annual:4 mail:2 main:3 might:6 setting:1 happened:2 maximal:3 them:4 good:3 combination:2 dim:1 functional:1 p10:1 steane:1 motivates:1 effects:1 they:5 instead:2 accumulate:2 nov:1 now:18 developments:1 suppose:1 eigenvalue:1 2v:2 gets:3 2k:2 always:2 university:3 level:18 alternately:4 appropriate:1 possibilities:1 into:3 inequality:1 l2:9 nisan:3 reasonable:1 each:89 2l:19 found:1 entirely:1 polynomially:2 2i:1 referred:1 subsystem:1 el:2 weighted:1 ei:2 significantly:1 weight:1 independent:2 t2:3 hard:1 reduce:3 idea:5 faulttolerant:1 carry:1 wires:1 ex:1 b1:5 year:1 quantum:151 our:3 operation:11 2πi:1 special:1 out:3 divincenzo:1 shown:8 reducing:2 matrix:81 space:21 since:28 crucial:1 semi:1 wab:2 research:1 looking:2 replacing:1 meaning:2 denoted:4 get:7 cause:2 correct:42 shows:1 i2:4 linear:17 written:2 diagonal:1 standard:1 corrects:11 besides:1 put:1 estimate:1 e1:1 finite:1 repeat:1 log:13 definition:13 pairs:1 fixed:2 starts:1 computers:5 success:1 tolerant:16 turn:1 length:1 place:1 exponentially:2 circuit:46 leading:1 corrections:33 today:1 approaching:1 generalizations:1 support:1 frequent:2 first:31 already:2 probability:35 encoding:3 relate:2 powerful:1 number:27 xd:1 lond:2 multiplication:1 done:7 long:1 degf:1 blank:1 vote:2 array:1 unruh:1 open:3 aharonov:4 size:18 1p:2 given:10 likely:1 their:2 introduction:1 data:3 participates:1 system:13 construct:1 πm:2 needed:1 assumption:6 rates:2 too:10 realization:1 scheme:8 bits:4 final:13 recovered:6 gives:13 relies:1 collapse:1 coef:1 recursively:1 exactly:3 mn:2 simulate:5 preparata:1 classically:1 copy:4 maintaining:1 than:51 coefficients:1 begins:1 distance:1 develop:1 ben:4 effective:6 showed:2 1m:1 require:2 measured:1 namely:2 submitted:1 claim:7 classes:3 amplitude:1 represents:1 naturally:2 meets:1 descriptions:1 sb:9 correction:41 modern:1 measure:1 generalization:1 summing:1 miquel:1 say:4 contains:1 conjugate:1 need:9 recover:1 seek:1 any:19 viewed:3 paths:1 generalizes:4 angle:2 zero:6 check:1 self:1 able:4 isolated:2 note:3 majority:11 potential:1 generalized:1 micali:1 essential:1 wcl:1 accuracy:1 added:1 multiple:1 trace:1 opposite:1 outcome:5 sequence:5 most:13 connected:1 encodes:1 decohered:1 representation:2 pair:1 sa2:2 sa1:2 beth:1 probabilistic:4 class:3 undamaged:1 understands:1 average:3 adopt:1 stronger:1 km:1 blowup:2 points:11 principle:1 inaccuracies:1 duplication:1 physics:2 sum:7 fact:5 shor:9 show:8 checks:1 random:5 impagliazzo:1 discovered:1 solving:1 spaces:1 chuang:3 lloyd:1 βk:2 participate:1 threshold:11 algorithms:1 uniform:1 trivial:1 indicate:1 calderbank:1 copies:2 simulating:10 parameters:6 ruin:1 less:3 distributed:2 state:60 topological:1 should:9 values:1 failed:1 only:30 version:1 factor:2 thresholds:1 achieve:3 ser:1 do:5 dl:1 mixture:4 dj:1 goes:1 quantph:1 means:2 closeness:1 zurek:5 hopefully:1 satisfied:2 next:1 coset:1 damping:1 words:2 report:1 during:9 procedures:28 stoc:1 prime:1 acm:2 αj:1 consist:1 twice:1 c2n:1 goldwasser:1 arxiv:1 consisting:1 circuits:16 physicists:1 contain:1 through:1 counted:1 limitations:1 interference:1 view:1 fault:60 set:48 computed:2 exists:4 achieved:2 physically:1 undergoes:1 achieves:1 correlations:3 ends:1 operates:5 observed:1 edition:1 depends:3 computer:8 result:21 discussions:1 close:3 institutes:1 analog:4 techniques:3 preparation:1 a400:1 said:8 tensor:2 definite:1 originated:1 behind:1 correctly:2 between:8 αi:4 probably:2 αk:5 reading:11 tolerance:2 αl:12 preserve:1 perfect:1 notice:1 wl:1 recently:2 creating:1 wa:2 adding:1 qubits:107 notion:1 however:4 equals:1 succeed:2 wr:2 jk:1 distinguish:1 group:3 picking:1 problem:1 improve:4 assumptions:3 restrictions:3 protect:4 realizable:2 improved:2 zoller:3 refinement:1 resistant:3 many:7 taking:14 density:72 equal:6 against:4 improves:1 qubit:41 whole:4 comes:1 otherwise:1 mechanics:1 ci:11 unclear:1 afterwards:1 point:8 seems:1 ca:1 corresponds:4 dimensional:3 2kl:3 cirac:3 simply:5 assertions:3 cs:3 respect:6 wel:1 pr:1 wigderson:1 described:5 second:8 basis:11 addition:1 trajectory:6 create:4 due:3 quickly:1 secret:4 much:2 pg:1 basic:10 applying:19 ph:6 universal:12 pl:5 define:13 addison:1 direction:1 enable:1 corresponding:9 both:4 coherence:1 subspace:6 convert:5 gap:1 bitwise:5 demand:1 c2:12 c1:13 denote:3 present:3 applied:10 p0:1 replaces:1 critical:1 exponential:4 raw:1 reliable:1 f2d:1 harder:1 value:2 will:47 technical:1 while:3 proves:3 replaced:3 rotating:1 error:45 property:1 35th:1 procedure:61 interpolating:1 correspondence:2 generate:2 unitary:8 hoping:1 laflamme:4 almost:1 metric:6 thus:3 non:5 conditioned:2 ik:1 ij:4 converts:1 il:2 hebrew:2 parity:3 alone:1 rotated:2 binary:3 damaged:9 lemma:14 perform:9 acknowledgments:1 paz:1 same:15 clearly:2 complex:4 quant:6 copying:1 mixtures:3 helpful:2 several:2 higher:2 development:1 evolve:1 used:9 revised:1 see:1 i1:3 initialization:15 yao:3 effect:12 v1:3 v2:2 levels:15 uses:3 infinite:1 interested:1 identity:2 keep:2 simulates:9 lower:4 fourier:5 proceed:1 well:3 without:3 simulated:7 very:3 organization:1 model:8 0m:1 dimension:2 polynomial:14 recoverable:3 gates:30 noam:1 37th:2 just:2 heavily:1 half:1 networks:1 obtain:2 preperation:1 deviated:47 transforms:12 questions:1 using:15 protecting:1 yamamoto:1 yet:1 divide:1 blow:1 wca:2 unique:1 integer:1 conclusions:1 cl:3 had:2 except:4 xr:1 improvement:5 imitate:1 add:7 spread:29 ρu:1 lett:1 cosets:1 theorem:8 input:10 mod:1 suominen:1 transformation:3 take:2 around:6 last:2 rules:2 big:1 desired:4 measurement:4 possible:6 spanned:2 period:16 vα:5 vβ:2 confined:1 immediately:1 bit:11 outcomes:2 correcting:9 apart:1 generated:5 rotate:2 imposed:3 like:2 particle:2 follows:5 piece:1 specific:5 arrays:1 steps:7 sparse:51 arbitrary:1 multiplicative:1 output:12 works:2 reduced:5 deviation:9 because:4 peter:2 often:1 classical:15 smoothly:2 polylog:4 some:29 back:2 alive:2 understood:1 growth:2 b0:1 examples:3 b2:2 table:1 proper:27 extended:1 proofs:2 generates:1 happens:2 2d:8 vol:2 dense:1 dimensions:1 measurements:6 per:4 does:5 connecting:1 provides:2 assuming:1 rotation:6 proc:4 o1:1 o0:2 measuring:16 noise:42 run:3 pdim:1 power:1 bc:1 bl:4 selecting:2 equivalent:1 l1:9 wesley:1 step:14 symp:1 br:3 2m:1 occured:4 adversary:1 2n:10 noisy:10 about:1 actual:1 would:1 extension:2 og:1 theorems:1 assertion:1 o:11 simulation:12 practical:3 remains:1 a2:1 extensions:1 neighbor:2 brings:1 mixed:12 palma:1 suggestions:1 discusses:1 slightly:1 block:64 em:1 soc:3 rev:3 computes:4 presence:4 image:1 rotations:2 bound:3 three:7 remarks:1 hermitian:1 schemes:1 references:1 determine:1 strip:5 elementary:1 accumulated:2 jerusalem:2 bosonic:1 rows:1 deal:2 area:1 assumed:2 suffice:1 there:26 question:2 transform:11 fast:1 pages:8 editor:2 start:3 perp:4 inner:1 way:7 series:1 forward:1 call:1 was:3 therefore:9 function:7 medium:3 increase:1 enough:8 concatenated:5 huji:2 deviations:1 but:9 volume:2 encode:2 repeated:1 34th:1 pk:5 encoded:21 highest:1 true:7 he:1 directed:1 made:2 compute:13 appendixes:5 places:3 whether:6 wish:2 inside:1 up:5 us:17 αm:12 empty:4 theoreticians:1 distribution:7 stages:15 similar:3 called:8 expect:1 detailed:1 ac:5 ab:7 constant:19 coordinate:3 computing:7 defined:9 cki:2 abstract:1 describe:6 linearity:1 general:14 cbr:2 single:1 reliability:5 exist:5 simulations:9 controlled:12 kl:29 happen:1 union:4 physical:5 effected:5 again:8 functions:1 codes:64 completeness:1 ideally:1 no:8 ekert:1 when:23 vanishes:2 field:3 other:12 dm:1 details:2 outputs:9 x2d:5 nice:1 node:1 symposium:4 elements:3 superposition:2 modg:1 problems:1 polynomials:2 includes:2 a1:1 cleve:2 develops:2 important:2 bounded:2 advances:1 dimentional:2 4d:4 structure:1 independently:5 implies:1 longer:1 algorithm:1 assume:8 starting:1 columns:1 together:4 strings:3 ga:1 depth:6 reversible:2 deg:9 time:38 push:1 decoherence:4 requires:3 original:4 once:1
|
quant-ph9611026.txt |@word represent:1 consider:14 lack:1 brownian:2 results:6 leads:2 obstruction:1 comments:1 eiλ:4 edu:1 go:1 follow:1 disk:1 reparameterization:10 discern:1 regularize:2 certainly:2 depend:2 calculate:2 irrelevant:1 segments:1 pˆj:5 corrections:1 tn:2 under:1 include:7 carried:1 p2:12 global:3 amplitudes:1 easier:1 returning:1 very:1 rise:1 harmonics:2 wave:3 witten:1 difference:4 condition:2 steve:1 annihilated:2 went:1 hamiltonian:18 did:4 t2:19 solution:6 t1:17 try:1 discrete:2 convenience:2 vector:14 math:2 small:2 relation:1 equation:13 configurations:1 upper:1 approximately:2 haar:1 consistent:2 direct:1 approximation:1 across:1 second:5 further:1 dynamics:5 correspond:1 canonical:2 even:1 appear:5 richard:1 clock:3 dr1:2 section:2 dr2:1 both:4 agrees:1 above:14 unpinned:1 new:8 ˆk:1 method:2 satisfy:2 compact:4 full:20 integrated:1 degree:7 placing:1 preserves:1 here:1 understanding:1 mev:2 possibility:2 groups:2 meet:2 path:61 november:1 quite:1 equations:14 appears:5 change:1 patches:1 pˆ1:3 study:5 vectors:2 approaches:1 aω:3 resulting:17 poisson:2 pick:1 action:5 advantages:3 york:1 useful:2 projection:30 extra:1 λdt:1 extending:1 explained:1 replace:4 scaled:1 apply:1 total:13 linearly:1 derivatives:1 conventional:1 proceed:1 usa:1 h0:2 etc:1 properties:4 comparing:1 therefore:5 ip:24 taken:1 tell:1 more:12 flat:3 formally:5 continue:1 furthermore:1 becomes:6 operators:26 odinger:2 curvature:1 ip2:2 ol:1 normalized:5 cases:2 iτ:2 must:6 quantized:6 integrating:2 science:1 originally:1 work:12 oscillator:32 modified:1 quantizes:1 labeled:3 mechanic:1 following:7 cab:1 example:10 compare:3 give:4 process:1 expanding:2 sˆ3:2 dependence:4 states:37 sphere:5 minimum:2 want:1 normalizations:1 tan:3 rescaling:2 normalize:1 information:1 regularization:1 redundancy:1 end:2 s3:4 s2:7 s1:6 get:2 schiff:1 write:3 maps:2 lawrie:2 instead:1 ordinary:4 sin:8 map:2 product:7 undergoing:1 algebra:9 may:5 oscillators:7 after:6 derived:1 orbits:11 davis:1 choice:7 ambiguous:2 natural:9 chern:1 ordinarily:1 element:9 sk:2 rather:1 switch:1 so:26 fundamental:3 correlation:4 representation:5 order:3 transformation:5 restriction:1 least:1 help:1 essence:1 over:18 insight:1 dα:4 choose:7 years:1 symbols:1 paper:3 including:2 looks:1 motions:1 differs:1 still:6 its:3 before:1 superior:1 group:5 symmetry:1 how:4 energies:3 interesting:2 fix:5 φb:3 coordinates:14 writing:2 forms:1 complex:1 degrees:3 systems:12 derivative:1 secondary:1 defining:2 spreading:1 non:4 good:1 teitelboim:1 etotal:2 introduce:2 landau:1 break:2 hamilton:1 they:8 front:3 skagerstam:1 nov:1 now:11 s0:1 nor:2 possess:1 easily:2 term:21 dirac:11 2r:1 university:2 identified:1 orthonormal:1 2e:2 theory:1 each:10 2m:4 2n:2 higher:1 2j:5 constraints:15 lie:2 lifted:1 weyl:4 ei:1 weight:1 evolve:2 doing:2 series:1 energy:15 gaussian:1 semiclassical:1 t3:6 frequency:2 grav:2 measure:43 quantum:13 our:11 eigenstates:1 special:1 out:5 contend:1 large:2 matrix:9 3rd:1 space:78 integrates:2 since:1 rev:3 looking:1 replacing:1 acting:1 hca:1 mα:2 hill:1 induced:3 occurs:1 independence:1 foundation:1 earlier:2 linear:1 ucdavis:1 mapped:2 free:3 standard:8 admits:1 quick:2 reason:1 necessarily:1 california:2 φdt:5 e1:1 e2:1 definition:1 pairs:1 r1:6 r2:4 geometry:5 ds2:1 phy:1 noted:2 motion:14 place:4 δij:1 enough:1 hence:2 needs:1 onto:11 first:14 initial:4 probability:2 consideration:1 number:4 twisted:2 restrict:2 done:2 relations:2 another:3 angular:6 idea:1 given:12 toy:1 bracket:1 width:1 introduction:1 together:1 eqs:4 system:47 construct:13 pinned:5 πs:1 statement:1 eqn:3 1i:4 john:1 final:2 gives:4 grant:2 discussion:2 square:1 centered:1 tool:1 continuous:1 artifact:1 regards:1 hδ:1 fuzzy:1 whiting:1 sˆ:5 intrinsically:1 diffusion:3 determines:2 princeton:2 double:10 see:32 normalizing:2 project:3 amplitude:1 were:1 descriptions:1 lowest:1 fashion:2 rewrite:2 calculation:1 ann:1 dθ2:1 dθ1:1 dq1:4 already:4 mcgraw:1 epp:3 close:2 need:3 seen:4 seem:1 constrained:10 any:12 paths:3 relationship:1 zero:5 depending:1 εt:1 able:1 gravity:5 note:11 jersey:1 potential:3 absorbed:1 generalized:1 obviously:1 finding:2 heisenberg:6 begin:8 2πn:1 unless:2 normal:4 most:2 but:6 phase:74 inserted:1 class:11 probable:1 takes:1 considered:1 clear:1 later:1 oscillated:1 dimension:2 feynman:1 quotienting:1 points:1 exp:15 effect:1 normally:2 sum:1 fact:6 applied:1 ambiguities:1 show:3 absorbing:1 supported:1 gauge:55 solutions:3 carefully:1 substituting:1 trivial:4 find:10 ground:4 q1:11 q0:2 sj:2 q2:11 based:1 dp2:1 dp1:2 aφ:4 rovelli:5 commutators:1 state:61 should:8 only:8 explicitly:1 factor:8 integrate:5 circle:1 local:4 lapse:1 do:5 his:3 handle:2 viewpoint:1 means:3 dependent:7 sˆ0:1 de:1 overall:1 expectation:2 combinations:1 reconstruct:2 dt:22 geometric:1 dp:5 dq:9 normalizable:1 evolution:14 determinants:1 continuum:3 covering:1 αm:5 arxiv:1 remove:3 patch:2 e1i:1 bad:1 clocks:2 limits:1 gribov:8 qi:4 through:4 fixed:1 dpj:4 dpi:1 qn:11 kernel:2 set:20 constructing:1 imposing:1 national:1 correlations:4 j0:1 j1:1 packet:2 up:5 shabanov:2 radius:1 result:7 domain:1 discussions:1 recently:1 dµ:26 quantizing:1 commutation:2 review:3 yet:1 written:8 various:1 closed:3 between:8 si:4 invariant:16 boundary:4 approach:12 email:1 αn:4 ends:1 terms:31 ability:1 extend:2 importance:1 however:12 vanishing:1 comm:1 multiplier:14 configuration:1 come:1 remaining:3 thank:2 suggested:1 observable:1 cos:7 0t:2 many:3 ill:4 uncertainty:2 pdq:4 quantization:21 chosen:2 admit:1 hω:2 symplectic:4 expression:1 comes:2 otherwise:1 arbitrarily:3 detailed:1 point:5 simple:5 jk:1 harmonic:26 dimensional:3 ucd:1 simply:2 lagrange:16 moreover:1 along:1 considering:3 pp:1 pq:6 described:2 transformations:3 basis:3 addition:8 locally:1 three:3 been:3 treat:1 interest:2 likewise:1 ph:7 pi:6 pn:11 define:5 determinant:1 arises:1 corresponding:2 commutes:3 zumino:1 coherent:48 understand:4 spin:7 case:10 dξ:1 p0:2 p1:14 look:2 unlike:2 developing:1 might:1 bω:2 value:3 choices:1 will:28 daubechies:1 near:1 replaced:2 fiducial:5 behavior:1 eim:1 dλ:5 inherits:1 eimθ:3 aa:1 unitary:1 simons:1 averaging:3 metric:14 thus:3 surface:9 reads:1 im:1 df:3 trival:1 different:2 null:2 author:2 acknowledgments:1 renormalize:2 same:9 clearly:1 φa:20 unity:8 φc:2 quant:8 units:1 physical:34 naive:1 difficult:2 independent:8 ds1:1 used:2 solved:2 forced:1 appearances:1 published:1 dξdξ:1 iǫijk:1 hand:2 suggestive:1 arose:1 infinite:3 changing:2 ab:2 normalization:1 recent:2 deduced:1 lower:2 weakly:1 schr:2 center:1 well:6 remain:1 deal:1 picks:1 thought:1 s20:2 without:3 solve:1 encounter:2 coordinate:9 position:8 model:2 possesses:1 left:4 spherical:1 manifold:2 aborted:1 just:16 being:2 actions:1 λb:1 λa:9 underlying:1 identify:1 questions:1 klauder:18 eiσ:1 λn:2 integer:4 density:1 ipe:2 seems:1 appeared:1 interested:2 easy:3 constant:2 iσ:1 dq2:2 dqi:1 momentum:13 take:4 identical:1 iλ:1 orbit:2 depends:2 eigenvalue:1 henneaux:1 cargese:1 iε:3 possible:7 know:2 press:2 using:5 bit:2 dφa:1 projects:2 formal:3 insert:1 like:13 semi:3 loses:1 imposes:2 steps:2 either:3 integrals:3 arbitrary:1 δf:1 become:1 weiner:14 stationary:1 reduced:34 because:19 methods:2 classical:20 ashworth:2 quantizations:1 some:5 play:1 regularized:3 repeat:2 examples:2 proper:3 dimensions:1 lead:1 eiθ:3 avoid:1 though:1 integration:3 overlap:4 does:1 eliminate:1 inserting:1 peek:1 obey:2 2q1:1 rescale:3 equivalent:7 use:10 broken:2 step:4 inherently:1 although:2 eiφ:1 hilbert:6 dpdq:5 about:7 kinematical:4 would:15 world:2 constraint:41 freedom:10 discussed:3 meaning:1 o:11 topologically:2 dependency:1 obeys:1 act:1 ωt:1 reproducing:2 slightly:1 perelomov:1 own:1 into:15 within:1 integral:58 functional:3 j2:1 carlip:1 variable:3 hermitian:1 right:1 references:1 wess:1 determine:1 operator:47 ǫijk:1 next:1 unambiguous:1 additional:2 area:2 probabilistic:1 support:1 there:12 transform:1 start:2 low:1 way:5 cartesian:1 scientific:2 was:5 propagator:4 naturally:2 function:14 complete:3 form:16 offer:1 precise:1 ht:11 back:3 volume:4 construction:10 repeatedly:1 fg03:1 removed:1 raising:5 applying:3 embedded:1 understood:1 wish:3 brackets:1 2πm:2 particle:2 us:26 relabeling:1 limit:10 ωn:1 problem:9 similar:6 mechanics:1 interval:1 intersects:1 lowering:4 defined:19 cover:1 abstract:1 describe:2 direction:3 general:5 globally:1 single:14 pˆ:3 rule:6 formulation:5 eigenstate:2 constructed:3 again:5 functions:9 differentiable:1 no:4 amounts:1 fixing:17 wavefunction:3 when:7 proceedings:1 multipliers:2 field:2 other:7 details:8 papers:1 department:2 roll:1 govaerts:2 polar:1 elements:1 symbol:2 setting:1 problems:4 bundle:3 includes:1 helping:1 commutator:1 generated:7 important:2 peak:4 included:2 ξdξ:1 structure:6 implies:2 longer:1 assume:2 physics:2 dτ:2 required:3 sˆ2:1 dσ:6 governed:1 sˆ1:2 time:38 observables:2 resolution:7 original:1 once:3
|
quant-ph9611027.txt |@word concept:2 consider:2 caused:1 keep:1 amplifier:2 results:1 illustrated:2 eds:1 code:9 computation:9 go:2 follow:1 amplified:1 causes:2 row:1 amplification:1 knill:4 technique:2 extraneous:1 environment:3 finally:1 indicate:1 those:2 stable:2 eprint:5 applied:7 supported:2 orthogonal:1 very:5 paz:1 level:2 schumacher:1 solution:2 correct:7 leave:1 minimal:1 small:1 enhance:1 barbara:1 prevent:1 10n:2 foundation:1 elegant:1 likely:2 design:3 value:1 qeccs:2 further:4 repetition:2 rectangular:1 remarkably:1 even:2 what:1 errors:20 xor:4 appear:2 organisms:1 giving:1 sum:2 expressed:1 decoding:3 3n:3 above:1 new:1 poorly:1 method:6 relaxation:1 coefficient:1 evolving:1 measurements:3 degree:1 desired:2 iσy:1 others:1 active:15 consideration:1 november:1 equations:1 change:1 obtained:3 great:2 institute:1 involved:3 popescu:2 larger:1 allows:4 completely:1 published:1 suggests:2 accomplished:1 symp:1 products:1 permit:1 action:1 adopting:1 pathological:1 involves:4 plotted:1 depart:1 extra:1 merely:1 plenum:1 replace:1 iz:2 sloane:1 opportunities:5 apply:1 use:3 identifies:1 would:3 probabilities:1 beginning:1 next:1 comparing:1 therefore:1 lond:1 taken:3 type:3 theoretical:1 more:11 main:1 relax:1 successful:1 becomes:1 operators:4 under:2 corrected:1 tested:1 carrying:2 degrade:1 known:1 foundations:1 must:4 entangle:1 states:2 account:1 permits:1 science:2 equation:3 work:3 glauber:1 values:2 following:1 making:2 example:4 mnemonic:1 figure:4 give:1 process:1 discussed:2 bennett:2 purposes:1 high:1 minimum:2 performed:3 allowed:1 times:2 occur:2 information:5 redundancy:1 soc:1 recovery:14 defective:3 ie:3 discussion:1 37th:1 algorithms:1 far:1 frontiers:1 answer:1 instead:1 roy:1 brassard:1 r2n:2 product:1 may:1 ancilla:14 after:6 lab:1 diagram:1 wrong:3 designed:1 gottesman:1 horizontal:1 parallel:2 man:1 introduced:2 natural:1 computations:2 grant:1 yielding:1 redundant:1 purification:1 so:8 allow:1 order:5 operations:2 exclusive:1 feedback:2 minimising:1 over:3 undetected:1 feature:1 stability:1 course:1 paper:1 through:1 r2493:1 its:3 tendency:1 before:4 how:2 xors:2 systems:5 freely:1 might:1 syndromes:4 gate:6 designs:1 good:1 affected:1 widely:1 reveal:1 propose:1 processes:3 introduce:1 break:1 steane:4 effects:3 they:2 half:4 oxford:1 stabilise:2 nov:1 now:4 nor:1 2t:3 represents:2 term:1 university:1 identified:1 realistic:1 magnitude:2 transmitted:2 arrow:2 each:10 2n:5 macchiavello:2 mean:2 weighted:1 england:1 stabiliser:4 reduce:2 idea:1 related:1 elementary:3 encodings:1 quantum:41 laboratory:1 operation:10 summary:1 stabilised:2 out:4 living:1 shown:7 network:20 space:5 open:1 furthermore:3 since:5 rev:13 research:1 re:1 acting:1 dominated:1 cause:1 resistor:2 shows:1 occurs:1 theory:1 interactions:3 possibility:2 weakly:1 reason:1 california:1 corrects:1 estimate:2 jozsa:1 additional:1 interaction:7 dubbed:1 optics:1 could:1 tolerant:8 place:2 onto:2 support:2 first:6 there:5 features:1 probability:8 encoding:2 powerful:4 number:2 transform:2 set:3 defects:1 directly:3 carry:2 impossible:2 electronic:1 passes:2 given:3 necessarily:1 their:3 unknown:3 interact:2 deutsch:1 system:13 needed:1 assumption:2 wootters:1 bits:2 final:4 store:4 gives:1 servo:2 exactly:1 part:3 than:9 relative:1 isolation:1 require:1 zero:2 submitted:2 preparation:9 actively:1 supposed:2 were:3 rate:1 cloning:1 function:3 correction:8 modern:1 curves:1 already:1 substantial:2 manner:1 seem:1 recover:1 any:4 built:1 convenient:1 latter:2 propagation:1 ideas:1 parks:1 note:1 emphasis:1 causing:1 take:3 performance:1 many:4 channel:3 removes:1 who:1 techniques:1 most:4 involving:4 amongst:1 letter:1 measured:1 ekert:2 interacting:1 kc:1 constructed:1 cover:1 typically:1 fact:1 precise:1 shor:10 particularly:1 thorough:1 show:1 chances:1 random:2 rth:1 merit:1 discovered:1 subtle:1 trivial:2 networks:1 based:4 just:2 situations:1 distributed:1 ox1:1 should:1 failed:2 only:8 bases:1 circle:1 achieve:1 handle:1 notation:2 means:2 occuring:1 zurek:2 overall:1 preferred:1 cannot:1 preparing:2 during:6 interpreted:1 produced:1 evolution:3 arxiv:1 yield:1 consisting:1 twice:1 qc:28 common:1 prevents:2 including:1 steam:1 pioneering:1 erroneous:2 constructing:1 reference:2 achieved:2 national:1 testing:1 deemed:1 detection:1 see:4 computer:3 devices:2 discussions:1 terms:2 best:1 subject:3 fails:3 satisfying:1 tensor:1 inappropriate:1 halves:1 state:27 future:1 various:2 correctly:1 between:8 αi:1 probably:2 checks:5 questionable:1 recently:1 vertical:2 nature:1 qubits:22 however:3 consists:1 suppressed:1 essentially:3 recovered:1 last:2 reported:1 reinterpreted:1 fault:8 taking:1 acknowledge:1 correctable:1 against:1 σz:5 σx:5 bristol:1 0e:2 qubit:13 whole:5 solving:1 author:1 prepared:3 point:1 simple:3 2kc:1 cf:2 alone:1 written:1 throughout:2 uncorrected:2 described:2 syndrome:12 been:3 phy94:1 combined:1 minimise:1 ph:5 universal:1 fig:13 engine:1 box:1 enable:1 corresponding:2 suppress:2 sufficient:4 σi:1 careful:1 spin:2 present:3 case:4 myself:2 p1:5 miquel:1 ǫn:1 governor:1 transformation:1 will:21 p2:4 suppose:1 error:25 procedure:1 unlikely:1 ix:2 unitary:6 laflamme:5 refs:1 thus:3 non:2 equal:1 itself:1 dual:1 interacts:1 result:5 different:1 qecc:2 satisfy:1 perform:1 large:1 make:1 lett:7 same:2 quant:5 φe:11 pauli:2 mixtures:1 resulting:1 several:1 higher:1 used:4 reinterpretation:1 logic:1 effect:1 possible:4 uses:1 purpose:2 entanglement:2 identity:1 cycle:3 relies:1 task:1 nevertheless:1 well:1 analysis:5 without:2 sets:1 arising:1 self:1 left:1 gates:5 calderbank:3 proposed:3 less:2 being:1 when:2 kinks:1 rest:2 detail:1 accumulate:2 stored:2 identify:1 voltage:1 using:4 followed:2 yet:1 previous:1 heuristic:1 nǫ:2 density:2 royal:1 except:1 improvement:3 passive:5 source:1 add:2 treatment:1 theorem:1 save:1 remaining:2 details:1 identical:1 tests:3 insensitive:1 increased:1 depends:1 replaced:3 showing:2 3pu:1 early:1 test:2 five:1 sanpera:1 world:1 bit:1 correcting:4 helpful:1 necessary:2 like:1 identifying:1 follows:2 unnecessary:1 separately:2 wooters:2 steps:3 either:1 arbitrary:1 become:1 summarise:1 preskill:1 parity:6 qec:9 because:2 deal:1 some:3 understood:1 deduce:1 examples:1 choosing:1 disrupting:1 dimensions:1 sufficiently:1 affects:1 sarker:1 unavoidable:1 per:2 does:2 assuming:1 yields:2 propagating:1 proc:2 restoring:1 noise:34 communicate:1 analysed:1 clarendon:1 step:6 binomial:1 santa:1 hadamard:2 transported:1 hilbert:4 noisy:1 pike:1 actual:1 carried:3 getting:1 introduces:3 o:5 reduced:2 range:1 interpret:1 insufficient:1 referred:1 road:1 22n:2 equally:1 computational:3 presence:5 previously:2 communication:2 into:7 within:1 rotations:1 appropriate:1 references:1 primarily:1 stabilisation:21 operator:1 reducing:1 signifies:1 classical:5 assumed:1 suffice:1 initial:2 question:2 approximate:2 long:4 generation:3 low:1 way:2 was:5 synthesis:7 hz:1 hx:1 complete:3 form:2 enough:2 positioned:1 smolin:2 analyse:2 but:12 failure:1 repeated:2 construction:2 encoded:11 line:3 dissipative:3 longer:1 made:3 applying:1 consist:1 society:1 whether:2 wish:2 correctors:1 up:2 us:1 achieving:1 below:1 problem:3 similar:1 called:1 strongly:1 proved:1 corrective:6 computing:2 defined:2 certain:1 abstract:1 measurement:7 general:6 peres:1 dashed:1 single:9 exist:1 controlled:1 quantph:1 check:1 physical:2 again:1 functions:1 codes:5 no:7 rains:1 na:5 whereas:2 storage:1 inset:2 started:1 other:3 es:10 department:1 conclusion:1 elements:1 superposition:2 hilger:1 divincenzo:3 symbol:1 includes:3 generated:2 important:2 allowing:1 suppression:1 dissipation:2 matrix:3 independently:2 implies:1 coupling:1 physics:3 lanl:5 4r:2 together:1 impossibility:1 adam:1 time:4 decoherence:2 requires:1 original:1 once:1
|
quant-ph9611028.txt |@word logarithm:1 gv:2 logarithms:1 measurements:4 consider:4 induces:2 reversibility:6 results:8 roy:1 proposition:1 generalize:1 computation:43 foundations:1 consists:1 gk:2 issues:1 whose:1 damaged:1 graph:2 subjected:1 tr:1 environment:6 quasi:2 uniquely:1 preserved:1 th:5 under:2 dramatically:1 norm:1 applied:5 string:7 takes:2 orthogonal:1 very:2 desirable:1 ρr:5 connects:2 choice:2 corollary:2 every:3 cellular:1 entries:1 exact:3 condition:2 ibm:2 subsets:1 level:2 turns:3 michael:1 t1:1 vector:6 recall:1 small:4 entropy:27 upper:7 averaged:1 hk2:1 matrices:15 rate:1 cost:3 design:1 equal:2 initialized:4 implemented:3 theory:3 even:6 will:26 what:3 errors:3 organisms:1 section:4 uniform:1 current:2 version:1 causes:1 above:2 resilient:1 values:3 unrestricted:4 method:1 3d:5 y2:1 full:1 2kp:1 degree:2 respectively:5 applies:1 here:2 desired:1 operating:2 alone:1 november:1 appears:1 logarithmic:1 obtained:1 convert:2 study:6 studied:3 allows:3 reason:1 amount:1 ρin:1 resulting:3 permutation:1 correct:1 dorit:1 proof:19 changes:1 composed:3 offs:1 useful:2 projection:1 family:1 extra:1 problematic:2 logical:1 replace:1 boolean:11 decrease:2 outcomes:2 apply:6 unit:8 presents:1 use:7 russell:1 prove:13 probabilities:3 positive:1 toffoli:1 negative:4 next:2 scenarios:1 automata:2 call:2 opposed:1 taken:2 simpler:1 type:3 until:1 more:7 zeroes:1 formally:1 outputs:8 gi:4 corrected:1 reversible:57 controlling:1 known:4 applying:3 cases:2 hold:1 negativity:1 must:5 fan:2 high:4 keeping:1 works:1 oi:4 err:2 ρi:10 science:5 work:3 ρm:2 labeled:2 ij:2 obvious:1 three:6 concepts:1 following:8 making:2 example:3 numbers:1 control:2 claim:2 weaker:3 corrupted:1 give:9 process:3 ak:20 bennett:4 states:16 indicates:2 performed:1 want:2 allowed:2 simulation:3 g2:1 information:26 soc:1 g1:2 rather:2 discussion:1 holds:1 damage:3 entangled:2 write:9 how:2 pure:8 instead:3 inputs:10 product:8 may:5 after:10 variant:2 long:3 wrong:1 studies:1 times:2 λ2j:4 acyclic:1 natural:2 third:1 λ2m:2 computations:1 lemmas:5 correspond:1 complexity:6 so:7 allow:3 definitions:5 operate:5 order:13 operations:2 a400:1 diagonalizes:2 indeed:3 over:9 flips:2 trade:1 paper:5 left:1 y1:1 satisfies:2 still:2 its:13 before:1 measuring:4 faults:2 ln:3 interesting:1 decreases:3 writing:1 concavity:2 systems:1 ours:3 main:2 might:2 split:2 yi:5 non:11 good:6 motivated:1 combination:3 yn:2 flipping:1 p10:1 they:5 gate:28 determines:1 nov:1 now:10 eigenvalue:5 term:1 gets:1 2p:10 always:3 university:3 alternately:2 asher:1 reasonable:1 each:42 disregard:1 2m:1 2n:13 2o:5 2i:1 mean:1 subsystem:2 schemes:1 series:1 energy:1 revised:1 reduce:2 logx:1 used:8 knill:1 measurement:11 quantum:97 our:8 operation:5 beyond:1 extract:1 shannon:6 out:8 divincenzo:1 shown:3 matrix:48 factors:1 res:2 λ1i:4 since:8 operates:2 λ1n:1 λ1m:7 mccarthy:1 particles:1 tolerant:1 adapt:1 reader:2 denoted:3 formula:1 get:10 induction:3 occurs:1 shows:2 log2:6 linear:1 found:1 diagonal:6 possibility:1 vazirani:1 qi:1 completely:1 base:2 conditioning:1 eigenvalues:10 put:1 definition:7 qj:7 could:1 keep:1 turn:2 exponentially:2 circuit:68 twenty:1 hence:3 view:2 first:20 there:4 xn:10 probability:43 feel:1 relate:2 variables:3 powerful:2 number:13 lond:1 smaller:6 done:2 least:5 another:3 open:3 aharonov:3 size:34 given:3 necessarily:1 needed:1 introduction:1 unknown:1 di2:1 system:18 construct:2 1a:1 indicate:1 too:1 convention:1 bits:17 final:4 gives:2 eigenvectors:7 collapse:2 exactly:2 proving:1 padding:1 simulate:4 consult:1 x2:1 λ2n:3 x0:2 resistance:2 than:20 relative:9 kind:1 ben:2 edition:1 require:1 computes:8 submitted:1 preparation:1 matter:1 fanout:2 synthesis:1 outcome:6 powers:1 descriptions:1 correction:1 modern:1 generalization:1 randomly:2 say:5 vn2:8 vn1:1 conjugate:1 need:2 seem:3 any:19 viewed:2 forced:1 subsystems:1 zero:3 isolated:2 note:5 majority:14 analog:4 xi:11 accuracy:1 play:1 trace:2 though:1 price:1 sets:1 satisfy:1 gt:2 most:4 connected:3 representation:2 device:1 probabilistic:4 class:4 volume:1 constructed:1 especially:1 average:3 later:1 stronger:1 blowup:1 proceedings:1 ρvi:1 usual:3 physics:1 notion:2 fact:10 quantity:1 show:14 random:8 impagliazzo:1 spaces:1 relation:1 newmann:1 threshold:5 subtle:1 3t:5 agrees:1 fifth:1 pick:1 cell:1 x1:2 written:4 topological:1 lemma:22 only:10 subsection:1 factor:4 bernstein:1 columns:1 do:6 mixture:3 establishes:1 quantph:1 means:5 zurek:1 space1:1 ones:2 new:3 during:3 stoc:1 acm:1 regarding:2 arxiv:1 circuits:65 34th:1 avoidable:1 contain:1 worries:1 fixed:7 qn:4 preserve:1 requirement:2 set:4 computed:10 exists:2 achieved:3 undergoes:1 up:5 observed:1 differs:1 depends:5 computer:5 result:14 fail:1 triples:4 best:1 subject:2 closes:1 wire:8 tensor:8 ways:1 review:1 definite:1 πak:1 λn:1 state:30 un:1 chosen:2 between:2 invariant:1 αk:2 diagonalized:1 c2n:1 αl:6 available:2 letting:1 terms:5 extend:3 qubits:59 jn:1 add:1 jk:1 suggested:1 both:4 last:3 resistant:6 many:2 taking:2 annual:2 space:8 flipped:3 sensitive:1 connection:1 eigenvector:1 logic:1 qubit:26 argue:1 whole:1 ci:9 characterization:2 unitary:12 corresponds:3 poly:1 dimensional:2 represented:2 simply:2 polynomial:7 associated:2 throughout:1 considering:1 worthless:7 described:2 transformations:1 second:1 basis:16 due:6 been:4 t2:1 yao:1 much:2 oλ:1 combined:4 interest:1 basic:9 pj:1 pk:3 ph:1 pi:20 pn:4 abstract:1 pl:5 define:1 addison:1 corresponding:4 observable:7 subspace:1 whatever:1 observe:1 bitwise:2 c2:1 c1:1 present:3 case:14 p0:4 p1:2 exponential:11 developing:1 reliable:1 value:8 aim:1 dept:1 while:1 replaced:4 behavior:1 error:13 di:5 landauer:2 correspondence:1 vectors:2 laflamme:1 vol:1 vi:3 von:8 vk:1 thus:4 vm:14 according:2 hardware:1 ik:1 itself:2 triple:3 hebrew:3 binary:2 different:7 develop:3 perform:1 make:1 belong:2 same:9 complex:6 quant:1 emphasize:2 mixtures:3 units:1 products:3 proved:1 finite:2 difficult:1 development:1 independent:6 wires:7 eds:1 imply:1 see:4 i1:1 i2:1 upon:1 effect:1 hand:1 levels:2 identity:1 implements:1 lower:14 makes:1 page:2 well:3 deal:2 without:1 components:1 simulated:1 coordinate:1 model:22 latest:1 gates:24 noam:1 just:5 less:5 being:3 networks:1 transforms:2 λk:1 λj:2 λi:1 yet:1 λm:1 divide:1 blow:5 kluwer:1 density:46 seems:1 except:1 thermodynamics:1 ρu:1 other:3 transformed:1 easy:1 theorem:12 input:18 transformation:1 divided:3 sponding:1 rules:2 evaluate:1 possible:4 vα:5 vβ:2 know:2 background:1 using:6 bit:15 progresses:1 advanced:1 meaning:2 naturally:1 semi:1 follows:5 reduces:2 separately:2 steps:8 arbitrary:6 output:16 fault:3 reduced:6 because:1 neumann:7 classical:8 sequence:1 concave:1 polylog:9 some:19 begin:1 understood:1 respect:4 proofs:2 ourselves:2 superposition:2 specific:2 unavoidable:1 per:1 everything:1 does:6 ucsd:1 proc:1 limitations:1 pr:1 noise:39 power:14 slight:1 equivalent:6 wesley:1 step:22 although:1 putting:1 occured:1 adversary:5 hilbert:5 noisy:60 about:3 polynomially:1 anything:3 polylogarithmic:3 favorite:1 develops:3 o:29 surge:1 extension:3 carries:2 plus:1 mixed:9 renormalizing:1 2k:17 slightly:1 book:1 converging:1 raised:1 computational:2 presence:1 h2:1 into:2 bound:16 copies:4 equality:2 hermitian:3 references:1 methods:1 rows:1 log:35 her:1 suffice:1 initial:3 question:3 transform:2 specifically:1 pages:2 start:1 inner:2 way:1 was:1 therefore:2 function:25 invite:1 enough:2 but:5 change:6 larger:1 unreliable:1 true:2 directed:1 made:1 compute:5 nisan:2 whether:1 wish:2 bounds:7 us:10 theoretical:1 international:1 converted:2 limit:3 sum:7 highlight:1 distribution:11 called:2 entropies:2 mechanics:1 constant:16 computing:1 defined:10 universal:5 general:8 peres:2 single:3 journal:1 controlled:3 distributions:1 physical:5 again:1 functions:3 nk:5 ideally:1 no:1 index:2 when:7 tight:4 hn2:2 role:1 normal:3 department:3 ns:1 node:1 symposium:2 elements:2 topic:1 conditioned:1 models:2 generated:2 important:3 variable:3 assume:4 required:1 together:2 depth:37 appendix:3 time:41 far:2 failures:2 starting:2 strings:2
|
quant-ph9611029.txt |@word neighbors:2 gv:2 positions:1 gt:12 partial:1 consider:5 limited:2 caused:1 informally:1 dynamic:1 results:19 leads:1 roy:3 computation:34 battle:1 gl:5 c1:1 causes:1 duplicated:1 devoted:1 depend:2 analytic:5 graph:3 subjected:18 deterministic:1 tr:1 factoring:3 environment:9 finally:1 tj:2 preserved:1 th:6 under:1 tb:1 norm:1 ta:2 case:9 supported:1 string:8 g1:2 orthogonal:1 very:4 continues:1 p0:1 geometrical:2 replaces:2 every:4 decide:1 entries:10 experimentally:1 ga:1 difference:1 matrices:20 fan:9 condition:3 quantumly:2 issue:1 list:5 solution:2 occurs:2 large:2 discrete:1 vector:4 recall:4 small:4 eigenvalues:5 unconditioned:3 equation:4 configurations:2 multiplies:1 upper:8 smaller:10 force:1 version:1 deutsch:1 consistent:2 coefficient:1 initializes:1 rate:29 cost:19 dissipation:1 equal:1 initialized:1 machines:4 shma:1 even:6 what:3 errors:2 adds:1 appear:3 clock:2 section:11 associate:2 remain:2 reasoning:1 sequential:9 above:5 fe2:1 method:2 contrast:1 satisfy:3 margolus:1 notions:1 degree:2 respectively:1 applies:3 equals:2 here:3 understanding:2 desired:1 operating:2 represented:2 path:14 strong:1 equations:1 appears:1 logarithmic:1 simulating:6 obtained:1 property:1 remarks:1 institute:1 involved:1 study:3 studied:1 doria:1 eiσ:2 timings:1 p2:2 amount:3 resulting:4 permit:1 tolerantly:1 proof:13 makes:1 helps:1 conditioning:1 uniquely:1 equivalence:2 divide:1 win:1 namely:1 private:1 outcomes:3 ask:1 apply:6 glance:1 rarely:1 ρq1:1 unit:2 presents:2 use:8 takes:2 would:2 prove:5 probabilities:3 positive:2 chooses:3 induction:8 fei:1 classically:1 live:2 call:1 therefore:6 themselves:1 e2:3 type:4 theoretical:1 today:1 more:9 separated:1 israel:2 initiated:1 started:1 outputs:9 ti:3 site:1 normalized:1 particular:1 known:3 foundations:3 cases:1 hold:3 must:2 entangle:2 high:9 berth:1 oi:4 ρi:3 science:8 challenge:2 work:4 ρq:6 labeled:2 bias:1 ρu:1 hope:1 fe1:2 following:5 closing:1 mediums:21 root:1 initial:2 nearest:3 compare:1 transition:12 triple:1 give:6 process:15 bennett:1 purposes:1 implementations:1 states:24 indicates:2 assumptions:2 t1j:1 want:2 allowed:3 sharp:2 keep:1 occur:5 g2:1 end:1 decaying:5 turn:1 discussion:2 holds:1 37th:1 isi:1 cites:1 machine:5 faults:31 pair:1 pure:13 significance:1 answer:1 instead:2 ignore:1 inputs:2 product:9 description:6 may:2 turing:9 after:8 connects:1 corrections:1 tries:1 fi:2 choice:1 fm:1 types:2 efficiently:5 short:2 imply:4 maybe:3 children:1 correspond:2 complexity:2 sons:6 algorithms:3 realizes:1 asserts:1 keeps:1 representation:2 operate:8 pulled:1 order:6 turns:1 operations:1 torino:1 help:1 demand:1 indeed:1 over:9 insight:1 soon:1 stability:1 report:1 experiments:4 decays:1 thesis:2 during:8 differs:2 conclusions:2 satisfies:3 still:3 before:2 planning:1 write:4 position:2 treat:1 how:7 chosen:1 exact:1 gtk:2 smolin:1 expectations:1 exhibits:1 actually:2 feel:1 systems:4 annual:4 mail:2 might:8 outside:1 correspondence:1 non:9 good:2 combination:1 conversations:1 evolution:3 elementary:1 xg:1 p10:1 framework:2 effects:5 they:2 gate:17 nov:1 now:4 bigger:4 matched:2 eigenvalue:4 term:2 finite:1 always:1 university:3 alternately:1 hermitian:3 theory:3 inequality:1 reasonable:2 each:40 found:3 2n:13 2i:1 referred:2 subsystem:1 weighted:3 ei:2 weight:3 t2:3 frequency:2 reduce:3 staying:1 slowdown:6 deterministically:1 extended:3 connect:1 measurement:19 quantum:92 our:16 operation:2 transitions:4 special:2 out:4 divincenzo:5 matrix:53 space:6 quantify:1 since:21 rev:2 qc:1 zi:2 particles:2 mate:4 tolerant:1 denoted:5 constants:3 suffices:3 correct:4 foundation:1 numerical:1 linear:5 interactions:3 monotone:1 diagonal:1 possibility:2 standard:3 vazirani:1 difficulty:1 reason:1 statistics:1 struggle:4 besides:2 put:1 spencer:1 e1:7 generate:1 log:10 definition:8 pairs:2 interaction:3 a1j:4 could:1 computers:18 times:4 thing:1 length:1 place:3 exponentially:2 circuit:27 specification:1 hence:2 barenco:1 parallel:1 first:11 intuition:1 already:5 probability:25 prevent:1 ρj:2 relate:2 xa:2 powerful:1 number:26 lond:3 restrict:1 randomized:2 done:3 least:3 another:1 robust:1 array:2 unruh:1 open:2 aharonov:2 size:21 given:6 heads:3 fascinating:1 indicate:2 introduction:2 twenty:1 interact:1 system:14 construct:1 grow:3 1a:1 their:6 quadratic:2 rates:14 too:3 realization:3 percentage:1 bits:3 final:5 inner:2 simulates:1 collapse:6 tool:1 next:1 part:1 simulate:4 consult:1 x2:1 than:19 coefficients:2 ben:1 expansions:2 showed:1 jumps:1 vancouver:1 tree:8 depends:5 preparation:1 symposium:4 individual:7 supposed:1 wins:1 outcome:10 distinguished:2 exhibit:2 logarithms:1 generality:2 cohen:1 modern:1 randomly:1 say:2 mates:2 analytically:1 conjugate:1 need:4 seem:3 weinfurter:1 any:20 alive:1 paths:2 strength:1 zero:6 output:10 efficient:9 isolated:3 note:2 ideal:1 costs:1 take:2 forces:2 xi:1 so:10 collapsed:1 qtms:1 decoheres:2 towards:1 2ta:1 allow:2 trace:1 2tb:1 track:2 simulated:5 effective:2 most:4 t2j:1 renormalizing:1 significant:1 organization:1 device:1 coin:1 probabilistic:13 avner:1 branching:8 ka:2 don:1 observation:1 consequences:1 considered:1 average:4 adopt:1 stronger:2 revised:1 looked:1 kq:11 points:1 principle:2 guard:1 physics:2 sum:7 fact:3 incorporate:3 shor:6 show:18 random:18 spaces:1 imitate:1 lloyd:1 participate:2 threshold:1 subtle:1 trivial:2 find:2 fifth:1 giant:1 knowledge:1 writes:3 entangling:1 state:31 topological:1 should:3 lemma:14 only:12 going:1 subsection:1 factor:3 mechanics:1 bernstein:1 local:2 columns:1 stages:1 do:4 mixture:7 goes:2 quantph:1 get:3 emphasizes:1 simplified:2 zurek:2 expectation:4 trees:3 satisfied:1 space1:1 negative:1 words:1 timing:6 applying:5 acm:1 regarding:2 nisan:2 optimistic:1 arxiv:1 fixes:1 yield:1 joined:1 circuits:21 investigate:1 paper:4 34th:1 though:1 wish:1 qj:2 view:5 ignored:2 set:4 computed:2 exists:3 achieved:1 physically:1 undergoes:3 tilde:1 respect:2 operates:6 observed:1 edition:1 computes:8 computer:17 result:10 terms:1 institutes:1 qtm:6 techniques:1 closer:1 a400:2 error:1 nati:1 tensor:7 definite:1 sites:1 eigenstates:2 importance:2 enough:8 various:1 between:9 αk:5 αj:2 c2n:1 αl:6 side:1 preserve:1 gives:6 triplet:2 recently:1 ability:1 extend:2 qubits:73 processes:1 were:1 weak:6 however:2 concentrate:1 key:1 jk:1 distinguish:1 sleator:1 configuration:8 come:1 problem:1 thank:2 suggested:1 both:1 protect:1 realizable:2 last:2 fault:26 taking:4 decay:1 alon:1 according:5 against:4 minus:1 sensitive:1 connection:2 interesting:1 qubit:43 mean:1 whole:1 experimental:1 σt:2 ehud:1 cj:2 ci:9 unclear:1 extent:1 point:2 reasons:1 seems:2 corresponds:6 poly:2 dimensional:4 alone:1 written:3 applicability:1 church:3 cs:2 constant:11 li:8 pr:1 kalai:1 occured:2 second:2 basis:5 trajectory:3 due:1 ai:4 yao:2 describes:1 oλ:1 change:3 basic:8 expected:16 pk:5 ph:2 pi:2 universal:2 pl:5 choose:2 addison:1 life:1 aj:3 corresponding:2 observable:6 coherence:1 wires:1 gap:1 observe:2 lives:2 clusters:22 c2:1 extant:1 careful:1 present:3 applied:13 multi:3 p1:2 look:1 exponential:23 means:1 tolerate:1 value:1 will:27 technical:1 while:1 suppose:1 many:9 situation:1 2k:4 35th:1 unitary:8 laflamme:1 vol:3 vi:2 t1:3 thus:3 them:3 conditioned:5 cluster:20 ik:1 ij:2 il:2 conf:12 hebrew:2 binary:1 different:16 develop:1 demands:2 indistinguishable:1 same:9 complex:5 quant:2 emphasize:1 mixtures:5 proved:2 gets:4 higher:3 development:5 independent:1 clear:2 used:4 infinity:1 oij:1 see:2 i1:1 i2:1 effect:3 noam:1 moment:1 uses:2 delicate:1 entanglement:2 frequently:1 identity:1 eigenvectors:3 scale:1 lower:7 off:1 proceed:1 mention:1 changes:1 lemmas:2 analysis:4 obviously:1 observations:1 without:2 solve:1 tq1:1 tq2:1 sets:2 claims:1 model:25 dimension:1 left:2 gates:30 clog:1 calderbank:1 amnon:1 being:1 multiplied:1 networks:1 chose:2 transforms:5 immediately:1 λk:1 λi:8 yet:1 reduced:3 letting:1 adding:1 death:1 integer:1 density:51 had:2 except:1 simple:2 add:4 other:9 combine:1 maintaining:1 theorem:3 input:16 consideration:1 suominen:1 match:1 real:1 aspects:2 yuval:1 represents:1 rules:2 showing:1 possible:12 early:2 vα:5 vβ:2 entangled:5 birth:1 using:5 bit:1 unique:3 correcting:1 calculate:1 helpful:1 loss:2 like:1 semi:1 sizes:18 workshop:1 identifying:1 serves:1 linial:1 specific:1 arthur:1 ours:1 steps:7 chuang:1 evolutions:1 become:1 works:2 essential:2 potentially:1 mathematical:1 sketch:1 because:5 often:1 deal:2 sequence:3 some:14 back:2 competition:1 polynomial:30 growth:2 choosing:2 specified:2 intend:2 proofs:1 matching:4 generates:2 happens:3 separately:1 total:3 describing:3 richer:1 measurements:9 per:2 does:2 provides:1 assuming:1 proc:3 refer:3 measuring:1 destroys:2 noise:1 obey:1 power:7 performed:1 equivalent:6 entry:2 expansion:2 wesley:1 step:44 binomial:2 bp:14 although:1 putting:1 described:10 stay:1 hilbert:4 stage:1 about:1 oj:1 extension:3 generated:1 o:21 simulation:35 range:4 a2:2 neighbor:3 soc:3 mixed:23 connected:1 discusses:1 denote:3 processor:1 ηf:1 david:1 own:2 decohered:8 presence:1 communication:1 into:2 within:3 bound:16 ηi:3 son:1 down:1 phase:8 appropriate:1 right:2 references:1 raises:1 imitates:2 computational:10 refined:1 jerusalem:2 rows:1 classical:8 strictly:1 there:13 question:4 transform:2 long:2 pages:8 start:2 much:2 low:10 way:2 analyze:3 was:5 naturally:1 function:11 head:5 medium:30 writing:2 simplifications:1 huji:2 regard:1 gz:3 but:10 sophisticated:1 pj:4 gain:1 yoram:1 line:1 trying:1 collapses:12 happening:1 directed:1 made:1 compute:4 surprising:1 places:1 invaluable:1 whether:4 cij:2 inside:2 negating:1 bounds:2 us:3 until:1 below:1 tosses:1 limit:1 distribution:16 define:12 similar:1 called:6 strongly:1 ac:2 definitions:3 associated:4 sight:1 computing:1 defined:8 certain:3 abstract:1 describe:7 generating:6 general:12 peres:1 ap:1 single:15 exist:3 simulations:2 a1l:1 a1i:2 physical:8 chance:2 again:2 functions:2 codes:1 ideally:2 know:1 no:11 realizations:1 ekert:2 when:11 proceedings:1 members:1 acknowledgments:1 interested:1 role:1 formalize:1 4j:2 shrink:1 ρvi:1 node:1 picture:1 briefly:1 kinds:2 superposition:2 completes:1 models:1 αn:1 prepared:3 a1:5 develops:1 important:2 palma:1 allowing:1 variable:2 a8:1 friedgut:2 independently:2 implies:6 longer:1 algorithm:8 acyclic:1 assume:8 pseudo:3 together:3 original:3 4n:1 considering:1 compete:1 parallelism:14 time:47 cleve:1 formulas:1 decoherence:85 requires:1 strings:1 once:2
|
quant-ph9611030.txt |@word consider:1 results:16 roy:1 computation:2 edu:2 expressions:4 contributions:2 whose:1 comtet:1 th:1 under:3 b181:1 very:1 kψ:2 choice:3 exact:21 condition:14 presented:1 list:2 large:4 indices:4 eigenvalues:12 csch2:1 y0:2 sukhatme:6 cosh:1 approximation:1 street:1 index:2 errors:2 appear:1 chicago:2 expressed:1 above:2 lifshitz:1 new:1 subtracting:1 method:10 full:1 led:1 respectively:1 answers:1 sinh:1 address:1 concluding:1 consideration:2 along:2 quite:1 change:6 2by:1 study:1 losses:4 superpotential:4 barclay:2 makes:1 via:2 texts:1 names:1 translational:2 apply:1 total:1 semiclassical:15 use:2 additive:1 handled:1 contains:1 tabulated:2 going:1 a54:1 usp:1 taken:1 e2:6 historically:1 more:2 robbins:1 known:2 iii:2 permits:1 work:3 oscillator:8 reviews:1 values:3 following:1 example:1 performed:1 give:3 states:3 minimum:5 numbers:1 degenerate:1 xmin:4 tan:8 hoc:1 rather:1 eigenenergies:2 how:1 varies:1 sec2:2 answer:1 sin:1 b188:1 ft:6 singularities:1 adhikari:1 plane:1 deviates:1 coming:1 wave:4 types:1 no:1 computations:1 sech:1 explicit:1 so:1 order:3 indeed:1 years:1 paper:3 including:1 captions:1 y2:3 trigonometric:4 energies:5 matrices:1 ll:1 solving:2 better:2 permanent:1 maxwell:1 b161:1 mail:3 main:1 supersymmetry:4 good:1 yl:13 landau:1 units:2 they:5 oxford:1 nov:1 yr:12 yu:1 ba2:3 easily:1 padgett:1 name:2 2r:1 always:4 university:1 level:1 2x:2 l2:3 2b:10 2l:4 2m:1 2n:7 side:1 en:3 significantly:2 belgrade:1 energy:28 ea:3 related:2 carry:1 combining:1 quantum:6 our:2 eq:8 special:2 out:1 shown:7 haymaker:1 rep:1 since:4 rev:7 denotes:1 re:1 ref:1 numerical:4 turning:8 theory:1 possibility:1 standard:5 small:2 approaches:6 khare:5 x0r:1 marina:1 e4:5 e0:3 creagh:1 care:1 r1:1 r2:3 determining:1 could:1 dutt:2 corrections:1 lahiri:1 scarf:4 first:2 xj:1 xl:9 variables:1 number:2 simplified:1 another:1 xr:8 xp:1 given:15 law:1 b150:1 trost:7 hyperbolic:4 introduction:1 sech2:2 their:3 listed:1 final:1 unbroken:2 gives:6 shifted:2 2ab:3 mostly:1 exactly:2 immediate:1 part:1 x2:1 translation:1 than:4 classes:2 a41:1 sec:3 a48:1 w2:1 lowest:2 sees:2 sw:5 rau:1 need:1 cumbersome:1 clearly:1 jour:3 min:6 ideas:3 note:2 potential:11 generalized:2 coincide:1 accuracy:6 a38:1 most:1 involving:1 plan:1 remarks:1 analytically:5 kb:11 morse:6 points:7 reflections:1 mechanical:1 usual:1 physics:1 lying:1 cot2:1 b42:1 nπ:2 bagchi:1 supported:1 d2:1 ground:11 ae2:2 based:2 parameters:8 written:1 analytic:5 only:5 explicitly:1 get:1 dependent:2 familiar:1 superpotentials:2 aα:1 dx:5 dy:6 during:1 coth:9 conditions:5 arxiv:1 yield:1 analytical:1 nα:4 raghunathan:1 set:1 computed:2 see:3 yugoslavia:1 result:3 w0:1 recently:2 contour:1 eigenfunctions:1 mur:1 αx:2 review:1 state:11 various:4 jwkb:1 between:1 invariant:15 approach:9 available:1 terms:3 corresponding:4 attention:1 however:2 here:1 jetp:1 suggested:3 both:1 improved:1 cot:5 limits:1 many:4 taking:1 quantization:20 chosen:1 csch:1 point:1 period:1 dimensional:5 taylor:1 table:11 considering:1 amer:1 transformations:1 ai4:1 due:1 been:4 pb:2 a210:1 bp2:1 expected:2 proposal:1 abstract:1 lett:10 families:1 determination:1 general:1 case:1 tanh:10 harder:1 value:3 choices:2 will:2 error:2 property:2 studied:2 a26:1 wkb:27 ii:7 partner:3 φr:7 make:1 same:1 any:1 complex:1 quant:2 widely:1 modification:1 littlejohn:1 several:3 φl:7 ac:1 higher:1 used:2 infinity:1 i1:1 i3:2 i2:1 i5:2 i4:4 hand:1 a2b:3 levels:10 potentials:31 invariance:2 recent:4 lower:1 depending:2 log:1 position:1 left:1 stringent:1 maslov:6 proposed:1 percent:4 accurate:2 yee:1 shape:17 using:4 campbell:1 alternative:1 scattering:1 nonintegral:4 previous:1 tables:2 cut:1 preprint:1 upton:1 except:1 eckart:2 friedrich:7 valid:1 treatment:1 e0f:1 solvable:2 gave:1 real:1 aspects:1 evaluate:1 possible:1 harmonic:4 department:2 2dl:2 integer:1 mod:1 loss:2 modifications:1 appearing:3 popov:1 specific:1 yields:1 integrals:8 right:2 methods:5 classical:3 some:1 b2:7 cooper:1 yl0:7 bandrauk:1 integration:2 does:2 steps:1 bg:1 ba:2 power:1 step:1 substitution:2 super:2 tanh2:1 takes:1 comparison:2 about:2 discussed:1 dependence:1 o:1 langer:2 practical:1 pergamon:1 into:2 integral:5 bound:2 three:3 assess:1 phase:6 krive:1 ceva:1 references:1 ai3:1 determine:2 sov:1 amsterdam:1 additional:1 wai:1 there:1 specifically:1 low:1 was:3 function:3 complete:2 form:1 keung:1 but:2 ph:2 illustrative:1 compute:1 vmin:3 yr0:8 similar:1 mechanics:4 uic:3 ab:2 constant:1 ad:1 computing:3 int:1 ak:1 denote:1 substantially:3 exist:1 ay:1 supersymmetric:7 functions:1 variety:1 whereas:3 rosen:1 illinois:2 application:1 other:4 test:1 coth2:1 confine:1 deviate:1 conclusion:1 leacock:1 a1:4 a0:12 a2:48 a5:1 a4:1 coulomb:2 assume:1 typically:2 4l:1 northholland:1 4e:2 once:1
|
quant-ph9611031.txt |@word logarithms:2 epeau:8 partial:4 consider:8 chain:1 skip:1 forbidden:1 biblio:1 results:3 leads:1 executing:1 generalize:3 comments:1 computation:59 mimic:1 go:2 sci:1 remarkably:1 bank:1 reasoning:1 issues:1 whose:2 maximally:3 terms:1 violate:2 alamos:5 concerned:2 seriously:1 factoring:2 supported:1 violation:2 finally:2 critical:1 protocols:25 under:2 kwong:1 circumstances:1 program:1 applied:1 charles:3 string:2 advantage:1 returning:1 far:1 implicitly:1 wave:1 probability:6 wishes:1 hewlett:1 fall:1 telling:1 trouble:2 difference:1 matrices:7 securely:7 disturb:3 obvious:2 subsets:1 tra:1 notes:2 trb:2 tre:2 attempts:1 national:1 try:1 discrete:2 insights:1 phase:1 science:7 small:7 provided:2 nine:3 shows:2 barbara:2 noted:1 dieks:1 prevent:3 work:6 grateful:1 ten:3 29th:1 dealing:1 maximization:1 direct:2 grant:1 second:5 equal:2 incidentally:1 further:3 dynamics:1 machines:2 linear:1 even:7 index:1 what:13 xor:5 appear:1 incompatible:1 section:11 contributed:1 expressed:1 goes:1 boundary:1 new:4 ever:2 public:4 heuristically:1 revealing:1 justification:1 led:1 submitted:1 respectively:1 learn:22 here:11 understanding:1 protection:3 focused:1 hkl:1 relaxation:1 alone:1 ignore:1 constructive:3 appears:2 change:7 knowledge:1 box:1 remark:5 generalizing:1 unproven:2 rigorously:2 institute:2 until:1 larger:2 allows:2 los:5 amount:5 simultaneous:4 defeat:4 action:1 opinion:1 implement:5 postponed:1 changes:2 helps:2 useful:9 secure:46 classification:1 apr:1 ardehali:2 namely:1 vii:1 private:17 highly:1 why:2 logically:5 fake:3 apply:2 total:2 remaining:1 standing:1 use:5 cheating:17 takes:1 would:11 prove:10 remains:8 insecurity:6 chooses:2 next:3 vol:2 doubt:1 m1:4 therefore:20 taken:2 survive:1 goldenberg:1 type:3 tell:3 today:1 more:18 yes:1 bennett:5 knows:4 relax:1 composite:2 operators:2 p1:1 validity:1 appendix:1 ignorant:2 normalized:1 particular:6 known:4 foundations:4 cases:5 cardinality:3 iii:1 easiest:1 behalf:1 must:12 me:9 ii:1 springer:4 fatal:2 concretely:1 defeats:2 ρi:20 recall:2 when:9 mj:1 eavesdropper:2 remain:1 paragraph:1 values:13 concepts:1 following:9 my:10 example:14 unconditional:2 proof:16 control:1 spy:1 computers:5 spiller:1 processing:1 give:1 process:1 allowed:1 share:1 purposes:1 states:3 contradicts:1 assumptions:3 caused:1 numbers:1 sense:3 honest:4 simple:2 guarantee:1 normalize:1 information:20 available:1 requirements:10 viewpoint:2 provide:2 discussion:6 get:3 algorithms:2 entangled:2 hoi:1 machine:10 very:6 pair:1 biography:1 pure:2 answer:5 instead:8 ordinary:1 verlag:4 brassard:9 belongs:1 inputs:6 description:3 may:13 max:1 insecure:4 after:5 variant:1 santa:2 applications:7 tries:1 tackle:1 end:19 choice:1 parallel:1 times:1 short:1 imply:1 computations:21 slightly:4 register:3 acknowledged:1 corollary:6 redundant:1 purification:2 sk:6 perhaps:2 so:17 automatically:1 allow:8 things:1 βk:6 order:2 typical:4 executed:1 help:1 piece:1 september:1 indeed:1 over:4 insight:5 closeness:1 satisfied:1 setback:1 course:3 paper:4 through:2 mentioned:1 existence:1 satisfies:2 still:12 ieee:5 its:3 itp:1 before:5 perfect:1 thank:7 personal:3 lo:3 solving:1 cryptology:6 actually:1 html:1 choose:3 annual:4 main:1 might:7 umontreal:1 measurement:17 them:2 someone:1 somebody:1 widely:1 ekert:2 practice:1 prefect:1 encouraging:1 onesided:1 they:3 gate:1 own:3 determines:8 rotation:1 now:11 transparent:3 teller:3 possess:1 represents:1 february:1 profound:1 always:4 university:1 crypto:3 possibilities:1 sufficiently:1 good:1 victory:1 2b:1 each:8 found:1 repeating:1 uninteresting:1 side:1 mean:1 successful:1 schemes:4 successively:2 another:3 weight:1 challenged:1 barnett:1 idea:8 gifford:1 constitute:1 used:11 expect:3 combining:3 quantum:146 eq:21 special:1 really:2 maximizes:1 deals:1 shown:7 matrix:17 space:1 vj2:2 furthermore:1 since:12 crucial:1 qc:1 research:1 acting:1 safety:1 performs:2 internet:1 lecture:2 reexamination:1 ref:2 correct:1 common:2 disclose:1 foundation:3 earlier:3 theory:3 interchange:1 confidence:2 given:4 possibility:2 standard:5 labs:1 reason:3 california:1 execute:2 besides:3 imagine:4 put:1 jozsa:5 publication:1 definition:12 pairs:1 language:1 determining:6 could:2 omit:2 messages:2 tolerant:1 exponentially:2 transfer:23 hence:1 fallen:1 think:1 first:11 indebted:1 major:2 initial:4 manuscript:2 powerful:1 number:4 huttner:1 restrict:1 intuitively:1 set:4 done:3 approximately:1 directly:4 impossible:22 message:4 precisely:4 open:2 summaries:1 story:1 necessarily:3 interesting:1 similarly:2 introduction:3 unknown:2 eqs:8 system:7 construct:1 their:7 attack:9 assumption:2 just:1 normalization:2 typing:2 siam:1 scheme:5 unambiguously:4 gives:2 preserved:1 imperfect:2 collapse:1 minute:1 accurately:1 wootters:2 simplicity:1 part:1 somewhat:1 herself:4 than:12 distance:1 perfectly:3 subroutine:1 showed:1 wiesner:8 isolation:1 require:1 measured:1 richer:1 optimism:3 matter:2 determined:1 contrary:2 supposed:5 were:3 cards:1 collins:1 feeling:1 distinguished:1 cloning:2 sees:2 remained:1 footnote:1 well:6 correction:1 reduction:7 knill:1 argument:4 generalization:2 correspond:1 randomly:1 already:1 say:9 substantial:4 violating:1 manner:2 close:6 need:2 seen:1 sky:1 demonstration:1 any:10 inefficient:2 built:1 zero:2 person:1 convenient:1 storage:1 able:1 violates:2 note:2 instance:2 ideal:38 take:2 honestly:4 relaxed:1 gains:1 accuracy:1 fundamental:1 trace:2 shall:2 arguing:1 who:6 systems:2 most:3 nothing:11 accepting:1 future:1 probabilistic:2 class:5 sigact:2 observation:1 surprising:2 salvail:1 clear:2 later:2 paragraphs:1 typeset:1 proceedings:11 points:3 rev:4 error:1 physics:3 sum:1 fact:1 gain:3 precise:2 saying:1 efficiency:1 super:1 belief:1 show:6 cheat:7 random:2 ending:1 rotating:2 disturbing:1 assembling:1 purifications:2 large:1 trivial:2 find:3 unbreakable:1 completion:1 opponent:1 inspiring:1 dice:3 ment:1 representing:1 specified:1 assertion:2 should:7 only:14 bases:1 black:1 subsection:4 factor:2 various:2 equally:1 oct:2 achieve:5 do:4 his:16 above:5 cryptography:28 means:3 dependent:1 zurek:1 between:4 overall:2 assumed:2 cannot:8 preparing:1 words:4 3b:2 during:5 him:5 nearly:1 prime:1 reveal:1 runs:1 unaddressed:1 held:1 arxiv:1 modern:1 factorization:1 whether:2 investigate:1 cr:8 she:4 contain:1 implication:1 fixed:2 nδ:8 valid:1 view:1 satisfy:6 requirement:18 multiplying:1 computed:8 exists:7 achieved:1 tossing:4 unpublished:2 j1:113 j2:98 j3:3 see:12 computer:12 result:8 discussions:7 simultaneously:2 acts:1 subject:1 learns:7 singularity:1 enlightening:3 subsequent:1 definite:1 partition:2 state:19 unable:1 identification:13 routine:2 crepeau:1 neither:1 reading:1 numerous:1 ensembles:1 discovery:1 knowing:1 notice:12 never:1 recently:1 august:1 right:1 nature:1 initially:1 ask:1 attention:1 however:11 ignorance:1 jm:5 disturbance:1 ji:3 key:11 distinguish:3 news:2 come:1 distribution:9 34th:1 both:14 protect:1 outcome:1 last:2 avoid:1 many:3 gratefully:1 readers:1 according:3 against:4 chosen:4 present:3 bristol:1 receiver:2 argue:5 com:1 finds:7 comes:1 otherwise:4 detailed:1 positive:1 afterwards:1 conclude:1 reasons:3 seems:1 ca:2 simply:6 learning:5 cancel:1 oblivious:33 trust:1 beats:1 conference:1 ensures:2 described:2 transformations:2 fault:1 simplification:1 invert:1 fuchs:2 informed:1 due:2 been:8 strategy:12 secret:2 much:6 combined:1 interest:1 basic:3 applying:5 ph:8 ak:3 lett:6 obtained:1 describe:1 corresponding:1 retrospect:1 relaxing:3 linearity:1 concerning:1 coherence:2 essentially:4 readings:1 optics:1 coherent:1 determination:1 external:1 hughston:1 demand:1 receive:1 despite:1 denote:2 hardness:1 sender:2 case:17 explicitly:1 schmidt:1 unlike:1 pacs:1 solid:1 cash:1 value:43 eigenstate:11 will:17 technical:1 while:5 suppose:8 inaccurately:1 applies:3 situation:4 35th:1 procedure:1 unsatisfactory:1 unitary:22 whenever:3 laflamme:1 almost:2 vi:1 vj:20 thus:6 non:21 iv:1 disappointing:1 itself:2 attributed:1 claimed:3 nonideal:1 iro:1 trusted:1 greater:1 different:4 considerable:1 etc:2 perform:1 suggest:1 make:3 same:6 clearly:2 read:2 parts:1 quant:8 emphasize:1 copying:1 party:70 independent:3 literature:3 http:1 time:1 assignment:1 effect:2 hand:3 persons:1 running:1 uses:6 user:2 hospitality:1 phy94:1 changing:6 langlois:1 totally:1 bob:110 understand:1 recent:1 eigenvectors:1 prescribed:5 task:1 least:3 torino:1 largely:1 nevertheless:2 unconditionally:5 nonetheless:3 epr:6 collaborations:1 thought:1 concrete:1 without:4 oneway:1 claims:2 model:3 possesses:1 prevention:1 left:1 cryptanalysis:2 stringent:1 protocol:53 proposed:5 less:4 being:2 money:5 accurate:2 obtain:2 actions:1 assigned:1 front:1 identify:1 immediately:2 alternative:3 rotates:3 yet:6 succeeding:1 execution:1 preprint:5 providing:1 density:24 regarded:1 point:6 had:2 mathematically:1 vij:5 interested:4 corollaries:3 maintaining:1 easy:2 theorem:4 input:30 formal:2 transformation:17 smart:1 useless:1 real:1 customers:1 aspects:1 bitwise:1 rules:1 advances:4 showing:2 papers:2 unlimited:1 possible:5 early:2 caves:1 know:3 press:1 using:8 bit:38 password:8 like:2 necessary:1 helpful:1 follows:9 signal:3 performing:3 dishonest:6 alice:55 separately:1 communications:3 either:4 arbitrary:1 popular:1 security:40 works:5 continuation:1 reduced:4 shor:1 mathematical:1 www:1 because:14 qed:1 classical:14 absolutely:2 successfully:4 some:5 sight:1 asserted:1 classes:1 wrongly:1 nov:3 holds:1 undisturbed:1 fourth:1 decision:3 measurements:4 subclass:1 everything:1 kilian:5 does:6 decomposition:1 provides:1 assuming:1 closely:1 δk:1 measuring:2 scientific:1 power:3 performed:1 june:1 equivalent:1 wavefunctions:1 unsafe:1 mayers:6 revtex:1 although:1 adversary:1 hilbert:1 bz:1 gained:2 about:30 working:1 anything:2 constraint:1 conceal:1 certainty:1 theorems:2 discussed:2 o:4 practical:3 provably:1 rule:1 illegal:1 pioneering:1 consequently:7 road:1 primitive:3 computational:2 keeps:2 acm:2 into:4 fidelity:8 commitment:35 usa:1 three:1 stop:1 lies:1 weighted:2 references:2 entangles:2 determine:9 parties:6 operator:5 fruitful:1 conceptually:1 rounds:1 imoto:1 criticisms:1 coin:5 her:9 amazingly:1 strictly:1 there:17 question:7 yao:3 long:6 intermediaries:1 sends:1 workshop:2 way:9 αk:6 researchers:1 conceivable:1 analyze:1 was:4 m0:4 function:20 building:2 himself:1 complete:1 enough:1 something:2 hp:1 delayed:1 but:8 sophisticated:1 26th:1 exact:1 related:2 hb:5 adopting:1 ha:4 true:1 bures:1 he:19 condition:1 made:6 compute:3 packard:1 full:2 arrays:1 attached:1 up:2 devices:1 theoretical:2 international:1 below:1 owing:3 those:6 uh:2 sides:1 demonstrate:1 problem:5 unequally:1 similar:3 called:10 mechanics:4 atypical:4 constant:1 ad:5 pin:3 computing:4 defined:4 rather:2 abstract:2 measure:3 am:6 passwords:1 general:4 single:1 exist:1 customer:1 violated:1 chau:5 journal:1 archive:5 metric:1 physical:2 shaky:1 high:5 functions:13 paradox:1 outof:1 no:11 objection:1 extract:1 whereas:1 wavefunction:2 generally:5 detail:1 reality:1 preventing:1 application:1 other:12 details:2 hpl:1 out:22 92a:1 conclusion:4 deviation:1 symposium:5 intend:1 users:1 completes:1 separate:1 keep:1 sided:60 welcome:1 convincing:1 important:5 individual:1 prepares:4 stoke:1 needed:1 fraction:1 acknowledgment:1 cryptographic:6 implies:8 factors:1 i11:1 together:3 original:1 equivalently:1 impossibility:18 cheater:3 weights:1 apart:1 4i:1 cleve:2 serious:4 remarkable:1 requires:3 having:2 once:1
|
quant-ph9611032.txt |@word limited:1 partial:1 consider:1 chain:2 priori:1 rev:6 results:2 existing:1 entropy:31 computation:1 reasoning:1 devoted:1 whose:2 disposal:1 tr:6 environment:5 finally:1 th:1 under:1 conjecture:1 straightforward:1 orthogonal:1 very:1 emphasizes:2 focus:1 print:4 every:1 entries:1 bringing:1 presented:1 transmission:1 issue:1 discrete:1 barbara:2 caltech:1 upper:6 second:1 enclosed:1 rigorous:1 dynamics:1 index:1 subadditivity:3 plays:1 stands:1 giving:1 sum:1 sequential:2 above:2 expresses:1 acknowledgments:1 contrast:1 ibid:1 respectively:1 gathered:1 never:3 here:2 making:3 represented:3 november:1 strong:3 observing:1 appears:1 obtained:3 institute:2 larger:1 allows:2 unitarily:1 leaving:1 prior:1 amount:3 schumacher:3 ραi:3 involves:1 pxy:1 via:5 useful:1 outcomes:2 decrease:1 use:5 prove:1 remains:1 positive:1 negative:3 properties:1 explicitly:1 therefore:2 theoretical:1 diagrams:2 betray:1 operators:2 ρxy:4 particular:2 known:1 producing:1 negativity:1 states:5 valued:1 ρi:23 equation:1 work:1 ρq:1 values:1 westmoreland:1 concepts:1 following:1 ρx:7 arrive:1 could:1 proof:5 calculation:1 define:1 involve:1 indicates:1 performed:2 sense:3 distinguishable:1 information:19 respective:1 holds:1 nondiagonal:1 write:1 necessary:1 pure:1 gate:1 ensemble:1 map:1 product:1 description:1 our:2 ancilla:11 earlier:1 diagram:5 4th:1 lines:1 inform:1 so:2 fundamental:1 representation:2 subsequently:2 bipartite:1 saturated:2 numbers:1 essence:1 over:4 move:1 course:1 including:1 thesis:1 still:3 pointer:1 its:3 itp:1 before:4 aj:3 acknowledge:1 matrices:1 better:1 previously:1 systems:2 constitutes:1 might:1 them:1 combination:1 thea:1 framework:1 effects:1 nov:1 now:4 discuss:1 nos:1 represents:2 term:1 fully:1 university:1 orthonormal:1 inequality:5 side:2 constraints:1 successively:1 reduce:1 idea:1 measurement:35 quantum:39 laboratory:1 operation:2 eq:7 shannon:13 out:1 shown:1 matrix:12 space:4 since:1 induces:1 research:1 content:1 may:2 denoted:1 induced:1 ref:3 shows:1 after:11 theory:8 interactions:1 diagonal:6 standard:1 difficulty:1 california:4 york:1 put:1 estimate:1 ash:1 additional:1 definition:1 interaction:2 derivation:4 trx:1 interacted:1 phy:2 derivations:2 wehrl:1 consequence:2 interact:2 first:2 separable:1 informations:2 xi:11 probability:5 xm:8 variables:2 coding:1 xy:1 simplified:1 another:2 xq:4 given:4 necessarily:1 observer:1 unitarity:3 1x:2 eqs:1 behaves:1 system:14 relations:1 needed:1 summarized:1 perfectly:1 gives:1 collapse:1 tashkent:2 moscow:1 environmental:1 part:2 completes:1 wootters:2 fuchs:3 double:1 preparation:2 succinctly:1 accessed:2 outcome:3 remained:1 explicit:1 unchanged:2 generalization:1 manner:1 need:3 any:2 generalizes:1 latter:1 note:1 extracted:5 internal:5 clarifies:1 transparent:1 added:1 trace:2 trρ:1 measures:1 effecting:1 extending:1 letter:1 definitions:2 reduces:1 considered:2 calculated:1 later:3 stronger:1 points:1 tech:1 physics:1 fact:2 quantity:3 probl:1 show:5 text:1 supported:1 relation:3 analogue:2 find:2 based:3 just:5 distributed:1 only:3 bases:1 summarizing:1 indeed:4 robb:1 his:2 neumark:1 notation:1 means:1 syst:1 zurek:1 truly:1 joint:7 ones:1 words:1 new:1 evolution:3 αm:1 arxiv:1 qa:4 contain:1 through:1 qm:4 set:3 reference:1 achieved:1 acquired:1 correlations:1 maximum:1 observed:1 see:5 result:1 discussions:1 terms:1 subject:1 subsequent:1 uα:3 state:23 between:15 consecutive:2 caves:2 conditions:1 recently:1 flow:1 vanishing:3 key:1 last:1 many:1 according:4 exceeds:1 mean:1 expression:1 extractable:1 bell:1 simple:4 cf:1 simply:3 associated:1 venn:6 described:5 basis:2 union:1 three:1 been:2 phy94:1 defined:2 describes:1 interest:1 basic:1 ph:7 pi:26 fig:10 cerf:4 describe:1 controlled:1 josza:1 wish:1 general:3 present:3 case:3 pacs:1 solid:1 single:1 remaining:1 will:4 invoking:1 while:4 applies:1 property:1 unitary:8 von:3 thus:2 non:8 equal:1 anticipating:1 conf:1 ignoring:2 technology:1 different:1 grant:1 make:2 radiation:1 lett:3 same:1 linked:1 quant:6 split:1 constructed:2 difficult:1 used:2 effect:1 hand:3 moment:1 osawa:1 entanglement:8 identity:1 relies:1 lower:2 maximizing:1 neural:1 locality:1 without:1 components:1 model:5 unified:1 proposed:2 less:1 being:1 when:2 obtain:3 diagrammatic:2 macroscopic:1 previous:1 preprint:1 kluwer:1 density:9 adami:4 improvement:1 pasadena:1 treatment:2 easy:1 theorem:10 guarantees:1 transformation:1 rules:1 possible:1 corresponds:1 kellogg:1 using:7 mod:1 imposed:1 like:2 lost:1 collective:1 specific:1 yields:2 channel:3 arbitrary:2 evolutions:1 revisiting:1 reduced:1 grouping:1 accessible:3 right:2 neumann:3 classical:6 conditional:14 some:2 convex:1 proofs:1 diagonalizing:1 happens:1 describing:1 measurements:5 conditionally:1 arguing:1 ancillae:3 does:2 proc:1 minimal:2 measuring:1 selecting:1 notable:1 pα1:4 santa:2 yuen:1 refers:2 hilbert:2 bz:1 about:5 pα:22 extension:3 probabilities:1 krl:1 act:1 mixed:1 introduced:1 projectors:2 block:1 levitin:2 within:1 obtaining:1 bound:9 nsf:1 because:1 operator:1 methods:1 log:1 area:1 initial:1 start:1 was:3 uncontrollable:1 considerably:1 form:2 but:1 cloned:1 copied:1 intuitive:1 prevents:1 bounds:4 us:6 dordrecht:1 distribution:2 more:3 called:1 entropies:12 proved:1 povm:2 certain:1 combining:1 am:8 proven:1 denote:2 peres:2 conserved:2 arises:1 formulation:2 corresponding:4 commuting:2 physical:9 mutual:35 no:3 generally:1 other:2 role:1 special:1 arithmetic:2 picture:2 elements:3 prepared:2 a1:10 bounded:3 variable:4 fundamentally:1 correlated:2 implies:5 coupling:1 assume:5 impossibility:1 incomplete:1 time:1 decoherence:4 dover:1 original:1
|
quant-ph9611033.txt |@word limited:1 comparatively:1 desirable:2 four:5 localized:1 olshanii:1 calculate:2 γn:7 under:15 γa:1 worth:1 summarizes:1 rise:2 summarized:1 vastly:1 ref:11 unrelated:1 enhance:1 force:5 concise:1 approximation:7 second:18 rigorous:1 spontaneously:3 haake:1 even:10 established:2 interatomic:2 interactions:2 above:43 new:5 increasing:1 consisting:1 simultaneously:1 notions:1 κd:1 never:1 here:16 atoms:70 represented:1 interpret:1 obtained:3 study:1 changed:2 approaches:1 ignoring:1 stressed:1 complicated:1 suitable:1 changes:1 appropriately:1 explained:3 2δk:1 highly:5 neutrons:1 visible:2 achievable:1 total:4 linearly:1 would:49 negative:3 call:1 therefore:5 until:1 inguscio:1 odinger:1 berlin:6 reversible:2 hold:1 must:19 me:3 springer:5 reabsorb:1 temperatures:2 concepts:2 exceptions:1 my:4 example:7 give:2 relativistic:1 organized:1 naturally:1 involve:1 indicates:2 degenerate:6 uaa:2 linearized:1 absolute:8 end:2 verify:1 travel:3 feature:2 how:4 hot:1 enquire:2 significance:1 answer:1 description:5 replacing:2 oscillators:1 after:3 confirmed:1 davis:1 wrong:1 law:6 meaningful:3 constants:2 undesired:1 third:3 neglect:1 maintain:1 correlation:4 operate:2 sackett:1 order:38 interpretation:1 feedback:1 over:10 vary:2 satisfied:16 frequency:19 satisfies:3 linewidth:15 before:5 directional:3 highlights:1 exhibits:1 writing:1 better:1 bunching:1 eventually:1 them:1 combination:2 confuse:1 pegg:1 elementary:7 band:1 effects:1 they:14 represents:4 classified:1 each:4 side:1 mean:44 schemes:1 fairly:1 comprises:1 laboratory:1 damped:2 driving:3 crucial:1 particles:8 re:1 mandl:1 linear:26 written:1 gardiner:3 free:3 standard:2 enormous:1 created:2 filter:1 pfau:1 speeds:1 already:7 features:7 primary:1 deplete:2 adopted:1 another:17 electronic:4 illustrate:1 similarly:2 xii:1 eqs:1 approximately:5 needed:2 master:17 listed:3 hypothetical:1 ordered:2 zeroth:1 superoperator:11 finitely:6 distance:2 zero:6 matter:22 classes:2 enables:2 solely:1 enhancement:3 rewrite:1 modern:1 mind:1 spectrum:8 quency:1 seem:2 convenient:2 latter:4 causing:1 broglie:2 simplify:1 letter:1 phase:52 don:1 calculated:1 points:1 principle:17 sum:1 ritsch:1 saying:2 probe:1 implying:1 gauge:4 substituting:2 analogue:2 proposed:8 explain:1 do:7 mixture:2 dk:3 de:4 stop:1 despite:1 dt:3 du:1 textbooks:1 fields:7 townes:1 acknowledgments:1 twice:1 reference:2 τcoh:6 outgoing:1 detection:2 depends:2 radius:1 result:8 fail:2 best:2 said:1 away:1 motional:1 artificial:1 simplest:1 µd:3 caves:1 approach:4 terms:16 nature:3 weak:1 however:23 unnormalized:1 bose:21 suggested:2 essentially:1 uncertainty:4 against:2 exceeds:1 distinction:1 contribution:3 argue:2 height:1 conference:1 broadening:1 puts:1 three:3 been:17 quickly:1 much:16 basic:2 expected:1 quantities:2 θd:1 coherent:16 reciprocal:2 transformation:4 aim:1 applies:3 property:2 elaborate:1 procedure:1 a20:1 vogel:1 played:2 linked:1 conditioned:1 ii:6 im:1 n2s:1 containing:2 duce:1 suggest:1 make:6 clearly:7 complex:3 quant:1 split:1 filtered:1 dimensionless:2 independent:5 uijk:1 normalization:1 failing:1 quantitative:1 possesses:1 left:1 just:2 scattering:3 yet:2 previous:1 adding:2 infinitely:1 similarities:2 regarded:1 iϕ:1 iω:1 spread:5 transformed:2 easy:3 opt:5 possible:13 replace:2 apart:1 specific:2 arbitrary:5 cooled:1 wavepackets:1 people:1 escape:1 separately:1 fourth:4 electromagnetic:18 quarks:1 intracavity:8 contributing:1 denied:1 slin:1 super:1 properties:10 limitation:1 o:1 collett:2 plus:4 slightly:1 automatically:1 considerations:4 soc:1 markovian:2 presence:3 spreeuw:1 maxwell:1 obtaining:2 bound:1 down:2 amsterdam:1 methods:1 unambiguous:1 initial:2 approximate:4 why:2 width:11 anderson:2 conservation:8 way:7 was:7 lowest:1 medium:1 gaseous:1 irreversibility:4 form:14 attempted:1 differences:5 analyse:2 idealized:6 understandable:1 true:16 inside:1 maximum:1 devices:1 damps:1 moore:1 proves:1 exist:1 promised:2 regime:5 no:19 whereas:2 wavefunction:2 generally:2 setting:1 role:5 np:1 ns:16 picture:4 models:2 preceding:2 variable:1 reabsorption:1 factorized:1 assume:4 dτ:6 interval:1 together:1 time:34 serious:1 n2:4 quantity:1 global:2 reformulating:1 exceeding:1 leads:3 certainly:2 amplification:2 depend:2 passage:1 finally:2 marks:1 analogous:4 brown:1 advantage:1 frequencies:5 exact:2 presented:8 irreducible:1 proposals:3 leave:1 discrete:2 prevent:1 dealing:1 measurable:1 sign:2 substitute:1 spectral:6 adds:3 appear:1 evaporative:9 current:1 goes:2 satisfy:12 supporting:4 burnett:1 understanding:1 groups:1 alone:2 along:1 appears:3 change:7 box:2 commonly:1 poisson:3 usually:2 conveniently:2 useful:3 prefer:1 logical:1 contradictions:1 rarely:2 planck:3 sympathetic:1 prove:2 positive:4 criteria:3 theoretical:1 neglected:1 apparent:3 appendix:2 cases:1 parameterize:2 oscillator:1 believes:1 values:1 hope:1 following:5 making:2 stimulating:1 claim:1 sense:11 allowed:1 occur:2 verlag:1 requirements:1 discussion:2 write:2 criterion:1 pure:1 parameter:2 inputs:2 may:13 sasso:1 applications:4 produce:6 stress:1 natural:2 outline:1 whenever:2 st:1 so:44 definitions:6 typical:5 imagining:1 indeed:3 pointed:1 course:7 statistical:1 argued:1 cold:1 still:11 derive:2 acknowledge:1 interesting:2 decreases:1 constitutes:3 decreased:1 decades:2 non:6 mølmer:1 processes:3 introduce:2 half:2 nov:1 now:11 discuss:3 nor:2 term:12 realistic:3 individually:1 square:1 significantly:2 populated:1 ee:1 gaussian:3 bradley:1 interferometer:1 wavelength:8 approximated:6 avoided:1 eq:25 ultimately:1 space:6 furthermore:2 interference:4 increase:3 collisions:5 investigation:1 suggesting:1 dominate:2 shows:2 theory:8 pumping:2 possibility:4 quite:3 unwanted:1 remainder:1 milburn:2 advance:1 derivation:3 language:1 transition:4 motion:1 βe:1 place:1 massive:1 think:2 first:24 symmetry:1 striking:1 variables:2 coming:1 simplified:1 specifically:1 directly:1 carry:2 impossible:4 size:2 given:12 necessarily:4 cooling:19 realization:1 handbook:1 gives:7 inefficient:2 transverse:7 eliminated:1 representing:1 than:28 population:2 unfortunately:3 require:16 transferred:1 future:1 were:3 guzm:1 pro:1 say:13 saw:1 any:13 symmetrized:1 conversion:1 decorrelated:1 ideal:6 begin:1 normal:1 falls:1 precludes:1 commutation:8 nonlinearity:1 considered:5 average:3 later:2 steady:4 typically:5 laws:2 precise:4 shot:8 show:5 threshold:32 fifth:1 ground:4 fibre:1 ratio:2 ith:1 behind:1 considerable:1 only:28 explicitly:2 black:2 viewpoint:1 get:1 unsurprisingly:1 cannot:16 progress:1 secondary:1 adiabatically:2 wiener:1 summary:2 mewes:2 predicted:2 discussing:1 ignored:2 lasers:37 physically:4 relative:8 namely:2 eliminating:1 violates:1 fails:2 satisfying:7 eigenfunctions:1 ways:1 subsequent:1 pump:3 between:21 αj:1 across:1 arrival:5 spectroscopy:1 concentrate:1 comm:1 multiplier:1 come:2 tractable:1 many:12 σa:1 according:1 propagation:2 iv:7 expression:2 comes:2 filtering:2 characterization:1 period:2 anti:1 moreover:2 considering:1 sensible:3 analogies:2 absence:1 damping:6 direction:4 enable:1 photon:55 external:1 careful:1 diffuse:1 those:5 case:12 xxxvi:1 overcome:1 eig:2 promising:2 irrespective:1 region:2 coupled:4 coupler:2 binary:1 different:10 verified:2 same:19 shifts:1 arguments:1 physical:5 cδk:1 closest:1 trivially:1 sudarshan:3 harris:1 invariance:2 modes:23 roughly:2 without:4 summy:1 model:32 undepleted:1 justify:1 being:9 when:9 guided:1 rest:2 relevant:2 disperse:1 aspect:2 minimized:1 speed:7 heuristic:1 zoller:4 photons:37 seems:6 except:2 interested:1 lett:10 wiseman:5 suominen:1 momentum:3 real:3 moy:1 around:1 decomposed:1 vacuum:3 amp:1 mod:1 adams:1 particle:7 serves:1 either:4 fully:1 served:1 inter:1 stationary:8 sharp:1 duration:1 provided:2 excitation:2 cavity:12 depletion:2 decomposition:1 provides:1 propagating:1 welsch:1 refer:1 eiϕ:1 scientific:1 power:5 seconds:1 equivalent:4 notable:2 eiφ:2 exciting:1 comparison:1 central:1 discussed:3 practical:2 wolf:1 obeys:1 ηd:1 ηa:3 spreading:3 ηj:2 determine:1 operator:25 lastly:1 log:1 assumed:8 strictly:2 there:26 dispersion:15 strict:2 low:3 delocalized:2 combined:1 deepened:1 enough:2 fundamentals:1 elimination:1 irreversible:3 rolston:1 longer:3 ωt:1 liouville:1 ωa:2 ωc:1 ωb:2 regimes:2 aa:9 ab:1 neutralized:1 ak:2 describe:1 am:5 general:3 examine:1 ar:1 governed:1 lifetime:1 again:4 ideally:2 deserve:1 field:117 narrowing:1 spatial:12 unobservable:4 deviation:1 briefly:2 vocabulary:1 superconductivity:1 includes:1 deriving:1 a0:2 a3:3 important:12 a5:1 a4:1 a7:1 observables:1 queensland:1 a8:1 building:1 condensation:3 difficulties:1 mimic:1 mass:2 starting:2 original:2 disp:2 represent:2 consider:6 caused:1 splitting:1 restated:2 follow:3 causes:3 referring:2 former:3 present:11 th:2 stochastic:1 norm:2 amplitudes:1 returning:1 very:17 fall:2 difference:7 condition:61 hamiltonian:19 list:2 t0:1 t1:1 large:12 small:19 rate:19 invention:1 directionality:1 further:1 canonical:1 bilinear:5 what:21 nonlinear:4 sub:1 section:15 brief:1 method:3 contrast:5 edited:2 condensed:3 full:1 eif:1 inverse:1 operating:1 situation:1 directions:2 strong:1 observing:1 conviction:1 losses:1 allows:3 qualify:1 prior:1 published:2 action:3 narrow:2 negligibility:1 via:2 followed:1 requiring:2 establish:1 takes:4 contains:4 ψu:4 ψk:1 ψi:4 ψl:1 imate:1 taken:2 more:22 lowering:2 operators:9 emission:18 basically:1 particular:9 known:4 producing:1 none:2 quantized:2 science:1 equation:25 remain:3 spontaneous:7 stated:9 suggestions:1 accept:1 states:4 νd:1 minimum:1 arise:2 exclude:3 species:2 goal:1 rather:5 breaking:1 explains:1 simplicity:2 wiley:2 derived:4 waves:3 fi:1 shortcomings:1 short:4 parameterized:1 perhaps:3 secs:1 negligible:7 fundamental:17 reservoir:2 cross:4 held:2 thermal:7 paper:6 through:6 filters:1 existence:2 kinetic:4 excitations:1 its:28 termed:1 energies:3 glogower:2 boson:25 actually:3 detected:6 systems:2 superoperators:1 travelling:1 might:7 finer:1 rwa:3 good:2 propose:3 hariharan:2 walls:5 permissible:1 milestone:1 oxford:2 easily:3 always:3 level:7 found:5 formulate:1 energy:17 hard:1 expect:2 measurement:8 quantum:33 operation:5 beyond:1 really:5 solved:1 unnatural:1 since:9 denotes:1 acting:1 induced:1 benjamin:1 belief:1 difficulty:6 reason:6 imagine:1 put:1 definition:24 recast:1 exponentially:1 consequence:3 probability:4 upper:3 number:52 smaller:2 done:3 least:9 miss:1 differ:1 introduction:2 construct:2 sargent:1 regulation:1 assumption:7 statement:3 scheme:1 loudon:2 too:2 optical:26 authors:3 schr:1 believe:1 undefined:1 diffusion:5 double:1 annihilation:6 determined:1 supposed:1 treated:6 deciding:2 motivation:1 electrodynamics:1 pedestrian:1 depleted:1 elsevier:2 concentration:1 built:3 speculative:1 internal:2 build:5 analogy:3 inequalities:1 play:1 added:1 electric:2 mlynek:1 quote:1 measures:1 most:16 significant:3 nothing:2 measured:1 achievement:1 removal:2 kd:3 clear:5 braunstein:1 part:4 electrons:2 exp:11 velocity:1 physics:6 particularly:2 evaporation:1 relation:2 fine:1 find:2 distributed:2 factor:5 begins:1 dominant:2 notation:1 beams:4 combinations:1 continuum:3 arxiv:1 remove:1 common:2 set:6 correspondences:2 achieved:4 unpublished:2 see:7 individual:1 sec:17 arm:1 plasticity:1 dipole:5 various:2 probably:1 conditions:19 available:1 seeded:1 recently:4 creating:1 2m:3 initially:2 premise:2 both:7 contrasted:2 quantization:3 sensitive:2 whole:2 experimental:2 eikz:2 arbitrarily:2 point:7 simple:4 community:3 dimensional:1 simply:9 described:5 create:6 due:9 z1:16 yasuda:1 reduction:1 describes:2 supplying:1 ph:2 sanders:2 transferring:3 gas:7 fokker:3 p2:1 look:1 exponential:1 expanded:1 evaluated:1 while:9 replaced:2 guide:1 unitary:1 vol:2 itself:10 seen:6 fermion:1 shaw:1 allegrini:1 shorter:1 stimulated:14 wilkens:1 higher:2 calculation:2 used:6 moving:1 kǫ2:2 recent:1 lower:2 task:1 analysis:2 parametric:1 stating:1 distances:1 atomic:19 λd:1 alternative:1 workers:1 guaranteed:1 source:51 deliberately:1 input:1 excited:8 generalized:1 australia:1 secondorder:1 entangled:1 imposed:1 follows:5 adiabatic:1 translates:1 ignore:1 flux:5 yields:4 experimentalists:1 essential:7 mathematical:1 often:1 absolutely:5 creation:3 some:16 back:1 understood:4 sight:1 mirror:1 ijk:1 myatt:1 savage:4 gradually:2 scale:5 describing:1 measurements:2 integration:1 per:7 behave:1 eliminate:1 proc:1 remembered:1 aj:6 step:1 lasts:1 output:73 intense:1 analysing:1 cautious:1 range:2 block:1 seeing:1 conserving:1 into:16 within:1 integral:1 appropriate:1 because:33 proportional:6 reabsorbed:1 statistics:9 extremely:4 question:1 long:6 bosons:30 elsewhere:1 repeatedly:1 atom:95 relaxes:2 directed:1 intuitive:2 characteristic:7 up:6 us:4 uk:3 fluctuations:27 similar:2 called:5 constant:9 defined:19 likewise:1 influence:1 single:14 formalism:2 paradox:1 amounts:1 definitely:1 department:1 explaining:2 elements:1 users:1 calculating:2 lucia:1 meaning:4 allowing:2 linearization:1 structure:1 ago:1 gedankenexperiment:1 implies:6 complicating:1 thermalization:2 required:6 diffraction:3 implied:1 presenting:2 far:8 meystre:2 requires:2 having:3 normalized:2 amplifier:8 results:2 gd:1 go:3 contributions:1 excludes:1 gases:2 include:4 wave:15 electron:6 putting:3 resonant:4 try:3 coh:3 optics:11 noted:1 dilute:6 imply:3 dynamics:13 index:2 plays:2 apparatus:1 giving:2 expressed:2 experiment:2 concisely:1 waveguide:4 ihτ:1 body:1 respectively:2 desired:4 sink:7 separation:3 consideration:1 implicit:2 great:1 technical:3 involved:1 larger:3 leaving:1 suggests:1 resulting:1 california:1 implement:1 makes:3 composed:2 examining:1 scales:2 castin:1 names:1 condensates:2 apply:4 analyses:1 standing:2 use:8 haken:1 commun:1 remains:2 next:4 few:1 themselves:2 hulet:1 sort:4 formally:1 becomes:5 labelled:1 discreteness:1 iii:6 ρa:1 challenge:1 reproduce:1 obvious:2 weaker:2 decorrelation:1 process:6 trap:11 high:4 effectively:1 lorentz:2 tan:1 varied:1 holds:1 delay:1 varies:1 instead:2 singular:1 demonstrating:1 martins:2 light:14 lines:1 correspond:1 element:1 monochromaticity:6 divided:1 pulsed:3 produces:3 interpreted:2 produced:3 julienne:1 mentioned:3 gion:1 envisage:1 le:2 longitudinal:14 lc:1 decay:4 chosen:1 temporal:4 li:1 choose:3 rabi:1 defining:4 greater:11 practice:1 gijkl:2 realize:1 february:1 university:2 traced:1 sufficiently:3 l4:4 l5:4 l2:4 mode:77 l1:7 accompanied:1 lorentzian:2 lectures:1 doing:1 related:1 eiωτ:3 books:3 measure:9 transitions:1 dωp:1 special:3 out:7 matrix:2 rep:1 rev:20 favours:3 cause:2 math:1 proviso:1 unwieldy:1 completely:4 york:1 likelihood:2 interaction:8 could:21 times:4 length:16 hence:5 powerful:1 quality:3 ordering:1 condensate:2 system:5 relations:6 realistically:1 their:13 quadratic:1 fermions:3 final:5 futile:1 exactly:5 dynamical:2 observed:3 colleagues:1 holland:4 isolation:1 submitted:2 inversely:3 amplitude:8 bare:1 providing:7 exhibit:1 symmetries:1 fluctuation:2 unchanged:1 discussions:1 need:5 glauber:5 acceleration:8 able:1 gravity:2 mechanism:9 polarization:2 instance:1 accuracy:1 heisenberg:2 nonrelativistically:1 unless:2 courtesy:1 downconverted:1 propagate:2 preliminary:1 device:15 class:2 cka:1 consequences:3 prefactor:1 normally:2 fact:11 superfluidity:1 emerging:1 underpins:1 text:2 rotating:1 purely:1 trivial:3 based:10 knowledge:3 should:10 dalibard:1 molecules:2 constituents:2 local:1 achieve:3 equilibrium:1 regularly:1 means:5 beat:1 familiar:1 quantified:2 beam:31 ones:2 words:1 timing:1 collisional:2 evolution:3 substrate:3 europhys:1 fixed:10 view:2 monochromatic:3 requirement:7 multiplying:1 constructing:2 exists:2 frame:3 intensity:29 closer:1 phases:2 attempting:3 pattern:1 ralph:1 state:40 projecting:1 identification:2 invariant:3 neither:1 comparable:6 reproduced:1 importance:1 emitted:5 hypothesis:2 distribution:4 exclusion:1 observable:4 semiclass:1 limits:1 equal:5 hω:1 marte:1 otherwise:2 ck:1 unclear:2 cm:1 conclude:2 poissonian:6 ca:2 narrower:1 deflected:1 ct:2 addition:5 ai:2 treat:1 proposal:1 define:8 senses:1 corresponding:2 route:2 sufficient:2 coherence:17 c2:1 arisen:1 laser:240 unlike:5 value:9 will:55 almost:3 vi:2 refs:3 thus:30 surprisingly:2 examined:1 generic:6 radiation:3 indistinguishable:1 unity:5 parts:1 wavepacket:6 pauli:1 units:1 finite:3 difficult:4 material:2 slave:1 upon:1 effect:2 variance:2 expand:1 keep:1 lcoh:1 off:1 nevertheless:5 well:26 thought:5 position:3 usual:6 enormously:1 less:3 obtain:3 replenish:2 sources:1 underlying:1 macroscopic:1 rapid:1 density:9 passively:1 reasons:1 add:1 tollett:1 identical:2 saturation:2 increased:3 myth:1 inversion:2 increases:1 five:3 know:2 press:1 immediately:1 loss:4 necessary:14 like:4 δx:2 alternatively:1 δk:14 become:2 δb:3 representation:1 qed:3 classical:12 phenomena:1 self:4 happens:1 chichester:1 lead:2 broad:2 separate:1 graininess:1 does:12 assuming:4 l3:3 noise:14 obey:1 acronym:3 analysed:3 expansion:2 prohibited:1 although:10 approximating:1 cδ:2 gained:1 a1:4 about:5 actual:3 fre:1 world:1 universe:1 dependence:1 recognized:2 carrier:1 unidirectional:1 insufficient:1 introduced:3 equally:3 own:1 a6:1 additional:1 transfer:13 dropping:1 quanta:5 mandel:1 a2:2 interferometry:2 function:21 but:23 hk:1 gain:19 lindblad:3 made:5 instructive:1 whether:7 wish:4 below:10 converted:2 limit:7 pumped:3 demonstrate:1 problem:6 exceeded:1 denote:1 shooting:1 effected:1 compared:9 susskind:2 other:13 conclusion:2 shown:7 variation:1 evaporatively:1 upwards:1 coupling:19 using:20 resolution:1 factors:1 4n:2 portion:1
|
quant-ph9611034.txt |@word customary:3 consider:2 results:4 leads:2 quadrature:1 grateful:1 expressions:1 feeding:1 paris:7 technique:1 tr:5 ts:1 quasi:1 device:3 yˆ1:2 th:2 supported:1 amplitudes:1 straightforward:1 shifters:2 experimentally:1 matrices:1 splitter:1 transmission:1 knight:1 large:1 discrete:1 michler:1 optics:3 der:1 dis:1 inserting:1 employing:1 zh:1 sinh2:1 measurable:1 outcomes:1 second:1 tana:1 implemented:2 port:11 eλa:1 linear:4 apparatus:1 s111:1 access:1 homodyning:4 equivalent:1 respectively:1 realizations:1 commercial:1 jointly:1 reported:1 strong:1 obtained:2 study:1 changed:1 allows:1 commonly:1 atom:1 periodic:1 resulting:1 hospitality:1 fourier:4 convolution:2 namely:2 highly:1 planck:3 use:2 probabilities:1 negative:1 intense:1 a51:2 a50:1 a53:1 a52:1 more:3 yˆ2:2 becomes:1 operators:3 berlin:1 particular:1 known:1 cases:1 alexei:1 account:1 bernstein:1 originally:1 oscillator:6 ρp:1 values:2 following:2 numbers:1 leonhardt:2 figure:3 give:1 calculation:1 carrol:1 states:3 performed:3 occur:1 information:2 end:1 buzek:1 get:1 very:1 opt:4 instead:1 parameter:1 product:2 ft:4 description:4 singular:1 max:3 after:2 diagram:1 plane:1 lay:1 iθn:2 dynamical:1 beam:5 light:1 yielding:1 su:1 element:1 so:1 subsequently:1 order:1 wigner:5 over:1 displayed:1 paper:2 statistical:1 husimi:6 y1:10 y2:6 its:1 group:1 acknowledge:1 chosen:2 interesting:1 boson:2 fruitful:1 detected:1 fig:6 couplers:4 main:2 easier:1 correspondence:1 noh:1 greater:1 tjk:1 they:1 nov:1 now:1 represents:3 university:1 mode:12 each:4 macchiavello:1 2i:1 characterized:1 mean:1 kano:1 ee:1 displacement:1 related:2 operator:3 measurement:7 quantum:10 our:3 eq:9 es:3 mat:1 shown:2 matrix:3 space:15 since:4 rev:18 denotes:1 dλ2:1 dλ1:1 mattle:1 math:1 shows:1 reck:2 fiber:2 theory:1 sudarshan:1 contain:1 iλ2:2 iλ1:2 arccos:1 already:1 features:1 probability:3 variables:4 number:4 least:1 directly:1 illustrate:1 given:2 rewritten:1 glauber:3 ordering:3 eqs:1 relations:1 their:1 realization:1 scheme:2 final:1 gives:4 postgraduate:1 serve:1 eλα:1 optical:5 somewhat:1 authors:1 representing:2 outline:1 wide:1 double:1 wodkiewicz:1 matteo:1 transferred:1 a42:1 amplitude:3 providing:1 result:2 bertani:1 generalization:2 hexagonal:1 any:3 note:1 generalized:2 analogy:1 schematically:1 detector:2 modulus:1 normal:1 mimics:1 eight:2 phase:21 measured:2 class:3 χs:2 considered:1 average:1 milano:1 points:2 principle:2 exp:9 mechanical:1 precise:1 probe:12 d2:3 find:3 symmetric:6 photodetector:1 ksp:5 implementation:1 enough:2 only:2 surveyed:1 various:1 reminiscent:1 partially:1 local:3 his:1 notation:1 means:1 expectation:1 joint:2 cannot:1 a129:1 lossless:3 processes:1 densities:1 arxiv:1 prevents:1 reference:1 detection:3 see:2 descriptions:1 w0:4 terms:5 commutation:1 αa:1 state:7 identification:1 between:2 progress:1 approach:1 αl:1 available:1 recently:1 a40:1 ws:2 here:1 distribution:9 both:1 outcome:2 desired:1 uncertainty:1 fiz:1 a49:1 experimental:3 miranowicz:1 splitters:3 relevant:2 cc:1 homodyne:8 dimensional:3 keitel:1 ordered:2 schleich:1 photocurrents:6 described:1 three:8 been:8 ai:1 combined:2 kronecker:1 transformed:1 ph:1 abstract:1 ariano:3 box:1 corresponding:2 photon:1 precision:1 zeilinger:3 coherent:3 present:1 case:1 laser:1 value:1 excited:1 will:1 squeezed:2 procedure:1 real:3 unitary:3 vogel:2 jpn:1 thus:3 chast:1 ii:1 coupler:15 reads:1 triple:14 technology:1 different:2 grant:1 radiation:2 complex:3 quant:1 schematic:1 used:2 i1:1 i3:1 i2:1 upon:1 effect:1 haus:1 identity:1 lower:1 modes:5 nevertheless:1 elem:1 zukowski:1 components:1 ae:1 left:1 teich:1 proposed:1 less:1 obtain:2 λa:1 paul:3 electronically:1 sampled:1 conjugates:1 density:3 iϕ:1 passive:1 conjugated:2 lett:9 input:5 transformation:1 identical:1 insensitive:1 easily:1 rules:1 couple:1 possible:1 harmonic:2 campos:1 vacuum:6 press:1 using:2 part:1 unique:1 mod:1 displaced:1 signal:8 serves:1 yadra:1 arbitrary:1 output:5 reduced:1 accessible:2 ole:1 classical:2 sequence:1 some:6 examples:3 b2:3 b3:3 γa3:2 iˆn:3 provided:1 entropic:1 lead:1 measurements:1 overlap:1 strahlung:2 provides:1 prof:1 proc:1 refer:1 measuring:1 eiϕ:1 iˆ1:3 iˆ2:5 iˆ3:5 bn:1 chaussee:1 fed:1 bj:2 although:1 bs:5 imaginary:1 properties:1 noisy:1 generated:1 o:3 important:1 mixed:1 germany:1 introduced:3 ρˆp:2 ρˆs:2 soc:1 into:3 photodetection:1 integral:2 pair:2 hermitian:1 references:1 balanced:1 proportional:1 symbolizes:1 k13:1 a115:1 support:1 iˆs:1 transform:3 appl:2 mandel:1 function:10 form:2 iy2:4 weihs:1 delta:1 true:1 longer:1 electr:1 society:2 uu:2 characteristic:4 devices:1 chizhov:5 problem:1 cahill:1 called:1 b1:3 mechanics:1 gesellschaft:1 b60:1 associated:1 defined:1 detectors:1 ak:1 describe:1 general:3 single:3 saleh:1 θn:1 distributions:6 physical:1 functions:4 us:3 no:2 whereas:2 when:1 field:10 other:1 tij:1 elements:1 a1:10 a3:11 a2:7 variable:2 risken:1 factorized:1 assume:1 together:2 factorizes:1 time:1 walker:2
|
quant-ph9611035.txt |@word represent:2 customary:1 consider:8 limited:1 rev:10 results:5 leads:1 roy:1 p01:27 inverse:1 seno:1 paris:6 subjected:1 finally:1 does:1 device:2 worth:2 paying:1 orthogonal:2 very:5 focus:1 kϕ:2 interferometry:8 differentiated:1 did:2 solution:1 large:2 solved:3 convenience:1 small:6 eigenvalues:1 anal:1 optics:1 der:1 inserting:1 smaller:1 occurrence:1 sin2:1 direct:1 approximation:1 rate:3 traveling:1 further:1 will:3 plays:1 section:3 expressed:1 nϕ:3 version:1 a231:1 goes:1 obvious:2 respectively:2 here:3 reported:1 possibility:1 address:1 concluding:1 path:5 along:4 appears:1 obtained:5 involved:3 feasibility:1 example:2 suggests:1 amount:1 usually:4 adopting:1 changes:1 followed:1 substitution:2 outcomes:3 addressed:1 total:1 planck:1 unit:1 conventional:1 proceed:1 would:2 positive:2 readable:1 negative:1 next:1 therefore:2 criteria:1 squeezing:8 tell:1 more:4 optimizing:1 advance:1 outputs:1 occurred:2 validity:1 berlin:2 carrying:1 loss:1 known:3 high:2 valued:1 setup:3 work:1 values:2 burnett:1 following:4 strategies:2 trans:2 route:1 numbers:1 a49:1 figure:1 process:1 expanding:2 states:27 indicates:1 minimum:10 posing:1 performed:2 sense:1 conversely:3 information:2 needs:1 soc:2 goal:1 rather:2 travel:1 acts:1 criterion:3 pure:4 optimal:3 constraints:1 parameter:5 sin:1 ζa:2 may:1 max:1 after:4 derived:3 applications:1 wrong:1 lax:1 value:13 waves:1 improving:1 data:1 parallel:1 2x2:2 physical:1 outline:2 light:2 correspond:1 thorne:1 so:3 ultimate:3 playing:1 indeed:1 over:2 equally:1 paper:3 london:5 statistical:1 still:1 ieee:1 its:1 derive:2 monitor:2 termed:1 interesting:1 fix:1 solving:1 glogower:1 scully:1 actually:4 better:1 complex:2 fig:1 susskind:1 eventually:1 nonorthogonal:1 scaling:2 p11:8 they:3 accumulate:1 nov:1 now:4 transparent:1 nor:1 possess:1 eigenvalue:1 2r:4 always:1 labeling:1 applied:3 mccall:1 mode:2 each:2 2n:1 referred:1 square:1 displacement:1 interferometer:18 variety:1 measurement:11 quantum:10 our:3 approximated:1 eq:16 maximizes:3 travels:1 shown:2 matrix:1 helstrom:2 holevo:3 denotes:2 fta:1 reader:1 denoted:2 formula:2 shows:1 sinh2:2 theory:5 free:1 quite:2 proportionality:1 york:1 ask:1 definition:1 could:2 routes:1 βn:1 first:1 informations:1 probability:24 shapiro:1 number:14 xe:1 intuitively:1 precisely:1 michelson:1 given:8 perturbation:5 introduction:1 leading:2 system:2 construct:1 perturbations:1 scheme:11 final:1 shifted:1 fraction:2 environmental:1 optical:6 x2:5 yurke:1 eliminated:1 than:2 coefficients:1 relative:3 unfortunately:1 double:1 matteo:1 depends:4 discriminating:1 matter:3 classes:2 contrary:1 a43:1 amplitude:1 outcome:3 inferring:2 false:11 generality:1 measure:2 say:1 null:1 any:5 elsewhere:1 zero:5 depending:1 convenient:1 latter:4 able:2 extracted:1 performance:1 detector:1 modulus:1 unperturbed:2 inference:2 opposite:1 price:1 most:1 optimized:7 germany:1 remarks:2 analytically:1 measured:1 mach:2 considered:5 alarm:11 phil:2 detectors:1 order:6 braunstein:1 regards:1 principle:1 exp:10 camb:1 χk:1 fact:3 quantity:3 shot:2 intensity:1 show:1 random:1 relation:3 substituting:1 trivial:1 find:1 based:2 sˆ:2 only:9 x4:2 circle:1 do:1 de:1 satisfied:1 ϕm:8 beam:2 cannot:1 progress:1 neither:1 holland:2 normalizable:1 reveal:1 processes:1 pearson:10 yuen:1 arxiv:1 photodetectors:1 fixed:4 view:1 guessing:1 requirement:1 set:6 testing:2 bounds:3 detection:26 namely:9 result:1 enhanced:4 optimum:1 best:1 concern:1 closes:1 phases:1 probable:1 a47:1 accomplished:1 review:1 αa:1 state:27 between:6 c2k:3 αk:1 caves:2 approach:3 available:2 terms:4 initially:1 attention:1 however:3 efficiency:1 hypothesis:7 multiplier:2 distribution:1 observable:1 cos:8 improved:1 a201:1 uncertainty:1 equal:1 called:1 sensitive:1 estimation:1 expression:1 ck:4 among:1 poissonian:1 homodyne:1 lagrange:2 considering:2 described:1 second:2 been:13 strategy:8 expected:1 ph:1 prototype:1 differently:1 ariano:2 corresponding:2 both:1 photon:12 precision:10 new:1 coherent:14 optimality:1 denote:2 present:1 case:3 variances:1 evaluated:3 aim:1 optimization:2 shift:18 squeezed:4 2k:1 shepard:1 thus:10 surprisingly:1 according:3 reads:3 binary:13 different:7 assure:1 generic:2 make:2 radiation:11 indistinguishable:1 parts:1 quant:1 finite:1 infer:6 difficult:1 independent:2 zehnder:2 upon:1 noticing:2 appreciable:1 infinite:1 frequently:1 implement:1 normalization:1 eigenvectors:1 lower:8 largely:1 no:3 well:2 academic:1 without:2 easily:1 possesses:2 left:1 just:2 being:3 generally:2 obtain:3 press:1 aspect:1 klauder:1 useful:1 eigenstates:3 heuristic:1 density:1 photons:2 iϕ:1 discuss:1 signals:1 lett:4 easy:1 input:6 mod:3 tolerable:2 iφ:1 real:1 around:1 represents:4 devised:1 possible:4 increases:1 confined:1 using:1 part:1 accepted:1 apart:1 naturally:1 kennedy:1 follows:1 signal:6 specific:6 benefit:2 arbitrary:1 become:1 reduced:1 methods:1 classical:1 some:8 choosing:2 specified:1 provided:2 lead:1 realistic:2 decision:12 measurements:2 overlap:9 strahlung:1 proc:1 refer:2 measuring:2 noise:2 chaussee:1 use:2 output:1 occured:1 engaged:1 interferometric:13 stage:1 actual:1 dˆ:8 o:1 mutually:1 chou:1 mean:4 perturbed:5 communication:2 h0:4 h1:6 obtaining:2 bound:12 phase:41 references:1 determine:1 operator:3 amsterdam:1 log:1 probabilistic:1 initial:10 detectable:11 low:3 way:4 was:1 neyman:10 iˆ:3 function:1 north:1 complete:1 form:1 attempted:1 but:1 gaussian:1 encoded:1 line:1 true:5 illustrative:2 whether:1 gravitational:1 variations:1 maximum:1 us:2 record:2 limit:6 ikφ:1 fluctuations:5 problem:18 similar:1 agree:1 gesellschaft:1 constant:1 up:2 defined:1 curve:1 abstract:4 contribute:1 general:10 fed:1 formulation:1 inf:1 defines:1 discriminate:5 nonetheless:1 fixing:1 whereas:2 when:3 field:3 setting:1 role:2 becomes:2 briefly:1 excitation:1 variation:1 prepared:2 allowing:1 lane:1 physics:1 pseudo:1 time:1 starting:1 once:2
|
quant-ph9611036.txt |@word represent:2 concept:2 foug:2 sq:1 rev:15 varying:1 results:10 integration:1 leads:3 zˆi:2 commute:1 generalize:1 expressions:1 forget:1 devoted:3 depend:1 eˆ:8 tr:2 supported:1 finally:1 device:18 those:4 th:1 under:1 worth:1 norm:1 divergent:1 applied:2 probe:9 amplitudes:4 consequently:1 advantage:1 very:2 zˆ2:2 zˆ1:2 tends:3 keeping:1 choice:1 every:1 lynch:1 mixing:1 difference:1 exact:1 condition:3 splitter:10 presented:2 knight:1 tanh:5 quadrature:7 large:1 solved:1 vector:2 phase:39 avoiding:1 small:5 warszawa:1 optics:1 originally:1 trv:4 application:1 strongly:3 smaller:1 sin2:2 za:1 literature:1 cosh:6 past:1 fold:1 second:3 lines:1 further:3 port:14 theory:8 spectral:6 plays:3 apparatus:11 section:7 selected:2 near:2 expressed:2 lengthy:1 ˆb:40 experiment:5 above:3 new:4 acknowledgments:1 coefficient:3 simultaneously:2 submitted:1 degree:1 respectively:2 concepts:1 component:1 equals:2 here:3 xθ:3 cos2:3 sinh:7 address:1 represented:3 based:1 strong:1 change:2 obtained:7 transmittivity:2 incoming:2 inspired:1 larger:1 allows:1 amount:1 simultaneous:1 pick:1 action:1 fourier:3 makes:1 der:1 involves:1 plotted:1 uniquely:1 ix:2 hermite:1 eiφ:2 plenum:1 outcomes:1 scaled:1 phasors:6 limi:2 naimark:1 pythagorean:1 should:1 unit:2 derivatives:1 use:1 asymptotic:1 usa:1 prove:1 remains:1 positive:3 contains:2 uniformly:1 negative:1 hilbert:9 comparing:1 call:1 squeezing:17 theoretical:3 more:4 introducing:1 formally:1 becomes:3 operators:42 berlin:2 normalized:2 particular:3 known:3 projective:1 cases:4 given:1 iii:2 high:1 account:1 valued:3 quantized:1 recall:2 setup:8 work:3 oscillator:7 modified:1 reproduce:1 labeled:1 fock:1 values:5 freedom:4 following:7 example:9 numbers:1 beautiful:1 leonhardt:2 give:2 process:1 introduces:1 dependence:2 states:2 effectively:1 assumptions:1 performed:3 want:1 iφ:5 mixes:2 verlag:2 information:2 respective:1 e2s:2 provide:1 verify:1 discussion:7 antoine:1 write:3 how:2 pair:1 low:1 influences:1 opt:4 acta:1 eight:8 sin:7 simplicity:1 description:5 algebra:3 may:8 earlier:2 derived:10 different:7 permanent:1 quantenmechanik:1 representations:3 fk:2 meaningful:1 short:1 natural:1 dynamical:2 effective:2 joint:2 light:3 parameter:7 explicit:1 sv:2 λ2e:1 so:4 fundamental:1 representation:5 integrand:1 order:8 wigner:19 help:4 indeed:2 over:2 years:1 combinations:1 paper:7 through:6 statistical:4 integrands:1 its:1 before:1 perfect:2 trigonometric:5 tending:1 derive:6 shifts:2 interesting:5 r30:1 boson:4 complex:3 degrees:3 whole:1 derivative:1 main:1 might:2 phasor:10 non:5 noh:2 combination:2 fig:16 obeyed:1 framework:5 walls:1 effects:1 they:4 krzysztof:1 front:1 nov:1 now:1 discuss:2 bigger:1 easily:3 term:1 several:1 englert:4 fizyki:1 2s:9 fully:1 nfm:28 level:1 realistic:3 2f:3 mode:6 each:2 found:1 entirely:1 uniwersytet:1 ports:3 characterized:1 weighted:1 retrieve:1 significantly:1 weight:1 series:2 reduce:2 displacement:1 used:7 investigated:3 disappears:1 interplay:1 entering:1 measure:11 quantum:45 our:6 ep:2 special:1 out:1 shown:2 matrix:1 space:20 restricted:1 rep:1 crucial:1 denotes:4 thickened:1 contained:1 investigation:1 dλ2:1 dλ1:1 denoted:2 formula:8 ref:6 occurs:1 shows:1 counterpart:1 sinh2:8 aˆn:1 after:1 linear:1 associate:1 aˆf:5 albuquerque:1 standard:2 york:2 put:2 rewritten:1 definition:6 interaction:1 could:1 similarly:3 filter:20 ordering:14 assumed:1 first:5 origin:1 informations:1 intuition:1 already:2 probability:3 upper:1 number:4 restrict:1 clear:4 done:2 relations:1 another:2 carry:1 differ:1 necessarily:1 exists:1 glauber:3 introduction:1 leading:1 system:15 construct:3 their:3 manifolds:1 identity:1 calculations:2 1f:3 scheme:7 loudon:1 gives:2 shifted:1 way:7 radiation:1 quasidistribution:1 exactly:1 leaking:6 wiley:1 measurable:1 optical:5 x2:3 sˆ:9 modes:1 relative:1 accordance:1 sections:1 intensity:4 banaszek:1 annihilation:5 contrary:1 fˆ:10 were:3 enables:1 powers:4 minus:2 result:10 exhibit:1 takes:1 rewrite:1 sw:6 unchanged:1 correspond:2 randomly:1 seen:6 any:1 warsaw:1 angle:1 built:1 zero:7 lim:2 self:1 note:2 instance:1 ideal:6 generalized:1 detector:4 canonical:1 analogs:2 even:2 play:1 unless:1 shall:9 probed:1 hv:2 unused:9 algebraic:1 involving:1 connected:2 significant:1 definitions:1 remarks:1 measured:8 es:1 reduces:3 consequences:1 dordrecht:1 calculated:2 detectors:7 typeset:1 graphs:1 part:4 exp:14 mechanical:2 physics:2 sum:1 fact:4 quantity:2 precise:1 selection:1 show:1 random:3 hb:1 relation:2 kbn:1 especially:1 longer:1 d2:4 find:4 ground:1 impact:1 slov:1 photodetector:2 teoretycznej:1 parameters:5 true:1 distributed:2 burak:1 operational:71 moments:6 only:11 explicitly:3 ambiguity:1 factor:5 equivalents:1 employed:2 partially:1 local:7 dn:1 do:1 dk:1 di:1 dependent:3 da:5 beam:14 closely:1 ˆi:1 dv:1 reconstruct:1 lahti:1 evolution:1 podolsky:2 fields:3 arxiv:1 twice:1 investigate:3 experiments:6 common:1 though:1 photodetectors:3 fixed:1 view:2 set:5 constructing:1 reference:3 physically:2 bergou:1 correlations:1 notice:1 richer:1 detection:7 see:12 descriptions:2 enhanced:1 terms:3 eres:2 ways:1 review:2 tend:1 symmetric:1 state:25 αb:1 various:1 between:6 limit:11 justified:1 approach:13 warszawski:1 recently:1 amplitude:8 extend:1 nature:2 however:3 efficiency:5 reproduces:1 analyzed:2 configuration:1 problem:2 observable:9 cos:11 0v:2 reverse:1 many:2 uncertainty:2 equal:5 trigonometry:9 fulfilled:1 connection:1 purely:3 context:2 expand:1 expression:5 experimental:10 otherwise:1 splitters:4 relevant:1 separation:1 periodic:2 simple:7 homodyne:21 concluding:1 polynomial:1 ordered:1 cq:1 cw:9 schleich:2 lies:1 pr:6 quadratures:18 sine:6 described:9 aˆ:7 due:4 been:19 defined:9 cosine:8 combined:1 recognize:2 expected:1 intensities:2 ph:2 ann:1 define:4 generating:4 describe:3 corresponding:14 both:4 quantities:3 theorem:1 else:1 coherent:4 dramatic:1 determination:1 spirit:1 present:5 case:13 k2:1 replaces:1 laser:1 exponential:1 pacs:1 straight:3 nski:2 value:1 will:14 while:1 replaced:2 behavior:1 squeezed:23 situation:1 property:2 procedure:1 reflectance:1 detailed:1 unitary:1 vogel:1 mexico:2 almost:1 vi:1 von:1 iv:2 ii:2 reads:1 ia:2 busch:1 quantization:1 ie:1 piotr:1 containing:1 grant:1 perform:4 make:1 unnormalised:1 intrinsic:10 same:2 propensity:10 unity:4 parts:1 quant:2 louisell:1 figures:1 physical:2 start:2 independent:1 extended:8 infinity:2 stressed:1 effect:2 purpose:1 unimodular:2 changing:2 uˆ:4 normalization:3 shortly:1 center:2 studies:1 poland:2 well:1 analysis:3 obviously:2 mathematische:1 simulated:1 position:6 posses:2 transmittance:5 cosh2:6 just:2 freyberger:2 being:7 photo:1 observed:1 rotated:1 obtain:5 polish:1 paul:2 mittelstaedt:1 previous:3 peres:1 kluwer:1 density:3 point:2 mathematically:1 signals:1 appeared:1 setting:1 lett:6 easy:1 marginal:1 momentum:6 take:1 real:3 iθ:1 depends:1 iα:3 evaluate:1 enable:1 possible:7 corresponds:2 dark:1 vacuum:25 using:10 unique:2 vˆ2:1 advanced:1 mod:3 grundlagen:1 imposed:1 particle:1 calibrating:1 follows:4 signal:7 modulus:1 either:2 integrals:1 arbitrary:12 become:2 works:1 university:1 mathematical:1 because:12 methods:1 classical:16 creation:5 some:2 springer:2 understood:2 proper:1 pψ:1 conclusions:1 provided:2 lead:1 eiθ:1 measurements:7 extensively:1 contributing:1 when:1 does:1 decomposition:4 select:2 provides:1 assuming:1 measuring:4 noise:23 plot:3 selecting:1 equivalent:2 uniform:2 agreement:2 expansion:2 nmf:2 revtex:1 qˆ:2 plots:1 properties:6 simpler:1 about:4 actual:1 carried:2 extension:2 most:1 tracing:1 am:1 basis:7 discussed:2 meaning:1 reduced:5 range:2 plus:1 obeys:1 ow:1 instytut:1 introduced:5 slightly:1 other:1 considerations:1 soc:1 into:3 obtaining:1 nothing:1 hermitian:2 right:3 references:1 yuen:1 einstein:2 operator:25 theoretically:1 neumann:1 additional:8 vˆ:33 riegler:2 treated:1 there:3 dispersion:1 spread:3 much:1 mandel:2 lot:1 ed:1 was:3 naturally:1 function:21 lotnik:1 form:6 removes:1 but:5 hk:1 construction:1 hn:3 ho:1 filed:3 odkiewicz:9 hf:2 auxiliary:1 up:2 devices:1 below:3 operationally:2 fluctuations:1 distribution:4 cahill:2 similar:2 called:6 mechanics:3 associated:4 povm:18 certain:5 abstract:1 measurement:24 influence:1 general:6 dξ:1 single:1 ar:1 pˆ:4 dλ:3 formulation:2 formalism:3 commuting:3 check:1 constructed:3 functions:16 us:3 no:4 whereas:3 rosen:2 cˆ:13 reality:1 field:37 interested:1 role:4 details:1 normal:3 department:1 mathematics:1 ny:1 polar:1 problems:1 walker:1 generated:2 important:2 astronomy:1 2i:3 structure:2 implies:1 coupling:1 assume:6 normally:1 rule:1 electromagnetic:1 far:1 observables:12 dϕ:1 requires:2 original:2 once:1
|
quant-ph9611037.txt |@word aided:1 secondly:1 magnetic:1 four:8 forget:1 relationships:1 whose:3 replacements:1 violate:3 aug:1 paris:1 presents:1 superficially:1 whatsoever:1 under:5 worth:1 pascazio:1 rise:1 replication:1 every:3 selleri:5 experimentally:1 nostrand:1 admissible:1 vector:2 favoured:1 estimates:5 direct:2 surrounding:2 likely:2 estimated:6 even:5 lesser:1 errors:1 above:3 conduct:2 new:12 net:1 officially:2 specialist:2 agreement:2 simultaneously:1 never:8 here:5 reported:3 asymmetry:5 represented:2 interpret:1 balance:1 study:2 ignoring:1 symmetrical:3 criticism:3 elaborated:1 explained:1 plenum:2 highly:2 visible:2 stern:7 glance:1 total:7 would:34 negative:1 therefore:3 type:4 tell:1 separated:1 holt:2 curvature:1 excellent:2 hold:1 must:2 abundance:1 room:1 setup:1 work:9 theories:4 my:11 example:10 sinusoidal:4 ingenuity:1 involve:1 want:1 times:1 end:3 feature:1 how:11 significance:3 answer:1 abstraction:1 description:2 arcs:4 earlier:2 diagram:6 wrong:5 parallel:2 attempt:1 third:1 correlation:27 jack:2 interpretation:1 over:1 vary:5 thesis:6 affect:1 before:2 personal:1 fix:1 writing:2 better:2 fig:29 wales:1 hidden:21 easier:2 versus:3 them:5 affected:1 band:2 effects:2 they:41 represents:2 alternately:1 reasonable:1 each:11 side:1 mean:2 fairly:1 list:1 principles:2 comprises:1 strips:1 magnets:4 clauser:9 laboratory:1 rs:3 recognising:1 particles:8 re:1 multiply:1 reader:4 rn:3 linear:3 given:7 standard:12 subtended:1 checked:1 estimate:15 starts:1 onto:1 features:1 restrict:1 another:5 discriminator:1 illustrate:1 approximately:7 needed:2 rates:1 observations:6 hypothetical:2 gilbert:4 john:3 fuzziness:1 serve:1 took:1 rejected:1 wasted:1 requisite:1 distance:4 showed:1 zero:1 matter:1 solely:1 rae:2 sees:3 mind:1 spectrum:1 raw:4 manner:1 seen:2 seem:1 unaffected:1 genuine:3 analyzers:1 latter:1 elation:1 recommended:1 causing:1 circles:5 though:5 denominator:5 sue:1 involving:2 locality:3 letter:3 phase:3 constancy:2 observation:2 detectors:10 accounted:1 sum:3 came:1 labels:1 padded:1 attempts:3 radio:1 gerlach:7 fuzzy:2 tempted:1 situations:5 explain:4 do:16 de:5 db:7 dc:2 da:7 watson:1 despite:3 report:2 covering:1 ever:1 discs:1 explanations:6 erroneous:1 fair:1 achieves:1 detection:18 result:3 limiting:2 best:2 subject:1 said:1 shimony:4 symmetric:2 score:1 disprove:1 hopefully:1 drawn:5 approach:1 terms:1 nature:3 visualise:1 gedanken:2 weak:3 however:4 extent:1 clues:1 suggested:1 ranges:1 essentially:1 contribution:4 com:1 exemplary:1 wider:1 three:2 been:13 much:1 basic:3 expected:7 refuted:1 quantities:1 spin:8 applied:3 exception:1 aim:1 risco:2 near:2 suppose:3 applies:1 aid:1 property:1 procedure:1 iv:1 ii:1 suggest:1 make:7 quant:1 several:4 perimeter:1 independent:1 emphasise:1 hand:1 thoughts:1 epr:19 greatest:3 centres:1 left:1 just:7 invalidate:1 yes:1 yet:2 previous:1 similarities:1 had:2 spread:1 easy:7 realisations:1 trimming:1 bands:29 possible:5 caps:1 judge:1 unique:1 detector:7 apart:1 mesure:1 remind:1 detections:1 www:1 right:4 somehow:2 counts:2 everything:1 core:1 nonuniform:1 statistician:1 predicting:1 illustration:1 corr:1 properties:1 numerator:2 ensure:1 efforts:1 slightly:4 statements:1 presence:2 marshall:5 obtaining:2 down:1 remarks:1 acad:1 reducing:1 orsay:2 often:1 approximate:2 why:1 width:3 way:5 was:11 form:2 attempted:1 differences:4 satisfactorily:2 true:6 until:1 stages:1 proved:1 abstract:3 evidence:10 exist:7 distributions:1 interferences:2 physical:2 discriminate:2 dotted:1 polarisation:10 generally:3 reality:7 setting:2 role:1 papers:5 test:16 ns:2 intend:1 superposition:1 models:7 variable:20 longer:1 assume:6 together:2 time:5 remarkable:1 varying:3 alternatives:1 skin:1 remarkably:1 depend:1 summarises:1 finally:1 me:1 lrm:8 tacitly:1 geometrical:2 orientations:1 exact:4 presented:4 did:2 magnet:1 coincidences:6 quick:1 upper:1 says:2 dealing:1 prediction:9 sign:1 colin:1 substitute:1 appear:1 favour:1 uniform:2 current:1 shared:2 falling:1 amounting:1 filled:1 understanding:1 appears:3 exemplified:2 vectors:3 commonly:1 bob:14 studies:1 pearle:3 useful:2 marked:2 prove:2 confounded:1 give:10 predictions:17 theoretical:4 diagrams:6 anticorrelation:2 alastair:1 apparent:1 validity:1 appendix:3 cases:4 rotational:2 quoting:1 constraint:1 modified:2 cat:1 values:24 hope:2 following:1 making:2 stream:1 predict:3 arise:1 topic:1 performed:1 allowed:1 occur:2 discussion:2 fourth:1 parameter:1 information:4 may:13 applications:1 produce:9 data:6 stress:1 natural:4 sectors:3 joint:2 ss:14 sq:1 cascade:2 switch:1 so:23 sn:15 representation:1 serge:1 indeed:1 thresholds:2 course:5 experiments:35 cuts:2 differs:1 aber:1 still:1 group:1 interesting:3 jim:1 forms:2 offers:1 constitutes:2 main:4 happened:1 non:4 introduce:1 records:7 half:2 now:9 hall:1 nor:1 possess:1 term:4 equality:2 name:1 realist:1 podolsky:4 arrows:2 possibilities:1 realistic:8 realise:1 entirely:2 cliffs:1 realism:5 significantly:1 ed:1 happen:1 es:1 shown:11 space:2 interference:1 increase:1 rational:1 formula:4 correct:7 shows:4 after:1 theory:19 possibility:2 quite:2 rows:1 remainder:1 inevitable:1 derivation:1 selections:1 collapsing:1 modest:1 motion:2 place:1 routes:1 think:1 first:8 blind:1 intuition:1 symmetry:3 variables:6 simplified:1 directly:3 carry:1 impossible:2 size:1 interchange:1 little:1 sheet:2 1x:1 indicate:7 realization:1 white:3 gives:2 inefficient:1 mostly:1 asymmetric:2 proving:1 tapster:2 ridiculous:1 pnn:2 specialists:2 representing:4 than:15 unfortunately:1 rival:1 require:2 were:16 pre:1 ann:1 say:6 any:12 conversion:1 ideas:4 note:2 ideal:1 objective:3 coincide:1 channel:1 opposite:8 enter:1 algebraic:1 exploited:1 sheets:1 pair:4 considered:2 average:1 later:4 implications:1 show:4 discovered:1 spaces:1 threshold:1 imagined:1 ratio:2 written:1 collapses:1 only:11 explicitly:1 thompson:2 caroline:1 get:6 assistant:2 expectation:1 truly:1 cannot:8 prentice:1 settings:6 roger:6 predicted:2 discussing:1 ignored:2 violated:5 relative:5 fails:1 inequalities:11 managing:1 review:1 label:1 behind:2 between:27 justified:1 across:1 notice:1 vertical:2 screen:1 clayton:1 concentrate:2 article:1 come:1 concentrated:1 quantised:2 many:3 region:2 according:3 expression:2 allowance:2 minima:1 effective:1 associated:3 bizarre:1 considering:1 barry:1 hardly:1 direction:9 enable:2 photon:9 observe:2 irrelevant:1 those:8 case:5 embodying:1 situation:2 margin:1 graphed:2 orientation:1 discrepancy:1 bias:3 different:4 april:1 scientifically:1 same:8 events:2 extended:1 edged:1 edges:1 investigates:1 changing:1 undefined:1 largely:1 no:19 roughly:1 without:2 components:1 very:5 model:26 laboratories:1 figs:2 tobs:17 being:12 when:25 valuable:1 aspect:18 touch:1 widest:1 photons:4 seems:2 instrument:1 priori:1 lett:11 versa:1 momentum:1 real:9 around:2 rules:1 using:10 accepted:1 vertically:1 englewood:1 particle:9 discarded:2 either:4 always:2 output:1 reduced:1 supplementary:2 deduce:2 specified:1 images:1 dimensions:1 forgoing:1 critical:1 provides:1 moderate:1 knife:1 refer:1 measuring:3 process:1 equivalent:2 notably:1 ratios:1 universit:1 comparison:2 conducting:1 discussed:5 generated:1 practical:1 stand:5 act:1 road:1 cambridge:2 communication:1 numerically:1 einstein:6 her:1 area:8 assumed:5 there:30 start:1 low:5 labelling:1 complete:2 enough:2 proportionately:1 alain:2 applying:1 beliefs:1 strongly:1 ac:1 egalit:1 certain:11 am:1 general:5 controlled:1 fill:1 again:2 ideally:1 deserve:1 rosen:5 field:1 valid:5 mathematics:1 you:1 poor:3 requested:1 briefly:1 separate:2 includes:1 a1:1 a3:1 important:7 a5:1 a4:1 recognise:3 curve:14 dramatic:1 once:3 original:4 sci:1 consider:3 caused:2 disc:1 follow:1 decisions:1 reasoning:2 glimpse:1 opportunities:1 stochastic:2 amplitudes:2 straightforward:3 far:6 difference:3 splitter:2 laying:1 large:7 adjust:1 small:2 abbreviated:1 rate:5 pass:3 further:7 situated:1 what:14 sud:1 sub:4 section:6 ticks:3 brief:1 version:7 method:1 contrast:4 full:1 behaviour:2 directions:5 november:1 observing:2 experience:2 amount:2 published:5 action:3 mentions:1 narrow:1 pathological:2 vic:1 followed:1 vii:1 eye:2 probabilities:9 chaotic:12 mysterious:1 more:13 knows:1 emission:4 particular:2 known:5 foundations:2 producing:3 none:1 science:1 equation:1 des:1 history:1 compare:1 challenging:1 accept:2 states:1 sphere:10 minimum:2 numbers:6 sense:2 firmly:1 influenced:1 rather:6 dismissed:1 ensemble:2 intended:3 algebra:2 derived:1 par:1 horizontal:1 derives:1 trois:1 negligible:1 playing:1 help:2 held:1 paper:20 through:4 signs:2 existence:6 its:7 termed:1 reluctance:1 actually:3 symptoms:2 detected:1 might:9 good:3 framework:1 oxford:2 bigger:1 channels:1 2s:1 occasions:1 altering:1 inequality:23 found:8 repeating:1 hard:1 idea:2 wires:1 expect:2 quantum:27 http:1 really:3 since:1 projected:1 research:1 hill:1 difficulty:1 reason:2 members:1 put:2 definition:1 pairs:7 bring:1 conducted:2 consequence:2 undergo:1 probability:10 number:11 linking:3 done:3 least:2 3db:1 story:1 introduction:2 construct:1 redistributing:1 assumption:4 statement:3 too:5 imperfect:2 relationship:6 optical:2 authors:2 believe:1 kind:1 polarized:1 kindly:1 double:2 determined:2 contrary:1 supposed:1 deciding:1 footnote:2 null:1 lie:1 depending:1 analogy:7 towards:1 singles:2 most:5 experiences:1 significant:1 position:1 nothing:1 measured:4 deviations:1 unequal:1 clear:1 sometimes:4 cover:2 part:1 exp:1 physics:5 subpopulations:1 phenomenon:1 relation:1 find:8 dividing:4 factor:2 circle:1 columns:2 his:9 hit:1 dependent:3 feels:1 arxiv:1 investigate:1 common:1 set:5 plausible:1 see:21 individual:3 close:3 currently:1 halves:1 various:1 probably:3 conditions:1 knowing:2 statistically:1 missing:49 attention:4 vanishing:1 invisible:1 both:7 context:2 whole:5 finds:1 experimental:8 elaborating:1 headed:2 simple:4 corresponds:2 coincidence:7 fashion:2 simply:1 described:1 quantisation:1 create:1 due:2 ph:2 pn:4 referee:1 partly:3 precision:1 modelling:2 understand:2 intriguing:1 classifications:1 look:15 talking:1 solid:1 straight:4 replaced:2 error:1 larger:1 itself:2 santos:5 widely:1 conflict:1 used:7 moving:6 necessity:1 infamous:1 recent:1 lower:1 analysis:3 obviously:1 person:1 parametric:1 parametrically:1 distances:1 shape:4 atomic:2 world:3 alternative:2 aiming:1 conclusions:2 workers:1 signals:3 source:6 theorem:1 violations:2 discriminators:4 australia:1 evaluate:1 logical:1 counterintuitive:1 success:2 systematically:1 follows:1 signal:2 translated:1 mcgraw:1 essential:1 spins:4 mathematical:3 sketch:1 methods:1 some:20 back:2 examples:1 sight:1 mirror:1 photomultipliers:1 facing:1 gradually:3 scale:1 shall:3 per:1 efficiencies:2 prog:1 anne:16 patient:1 perpendicular:2 holmes:1 obscured:1 subtract:1 bz:1 anything:1 blackburn:1 simulation:4 deserves:1 credible:1 seeing:2 into:4 within:4 appropriate:6 primarily:1 proportional:4 statistics:1 question:6 long:2 custom:1 sections:1 analysers:1 adjusting:1 line:6 considerable:1 rejection:1 intuitive:1 polariser:1 up:2 us:8 paired:3 uk:1 planes:1 similar:1 bell:39 constant:9 defined:1 influence:1 single:4 numerators:1 steeper:2 ulation:1 paradox:3 objection:1 application:3 points:3 department:1 confine:1 explaining:1 draw:2 elements:1 accidental:1 prepared:1 meaning:1 sides:1 independently:1 correlated:4 implies:1 vice:1 required:2 attaining:1 presenting:1 broad:1 chsh:3 having:2 evenly:1 illustrates:1 results:11 existing:1 bohm:7 go:1 contributions:1 theorist:1 concerned:1 helps:1 random:5 wave:6 valued:1 putting:1 continued:1 positions:4 smaller:4 biased:5 incidentally:2 greenberger:2 analogue:1 apparatus:11 giving:1 experiment:25 poles:1 exercise:1 body:1 degree:2 others:2 consideration:1 sine:8 extreme:2 great:1 parameters:1 involved:2 adjusts:1 leaving:1 suggests:3 opinion:2 shaded:3 makes:1 involves:2 composed:1 apple:2 anomalies:4 apply:1 standing:3 use:10 illegal:2 next:3 few:5 doubt:2 themselves:1 reflects:1 started:1 becomes:1 iii:1 account:1 crosses:1 reproduce:3 obvious:6 thin:1 proof:1 calculation:1 proportions:1 pieces:2 high:3 effectively:2 assumptions:5 holds:1 arrangement:1 regions:7 varies:5 instead:3 sim:1 fran:1 grangier:6 light:7 lines:2 correspond:3 element:1 looking:4 divided:1 horne:6 justifiable:1 move:2 interpreted:1 produced:6 whilst:5 looks:1 mentioned:3 envisage:1 perfect:6 superior:2 imperfection:1 covered:7 eur:3 greater:4 practice:9 mention:2 p19:1 day:1 university:3 identified:1 sufficiently:1 accompanied:1 constraints:1 related:2 constitute:1 books:1 exceeded:1 our:30 special:3 out:9 category:2 respects:1 rep:1 rev:9 asymmetries:2 cause:3 clarify:1 completely:2 york:4 philip:1 geometry:4 could:10 keep:2 hence:1 facilitate:1 diagrammatically:1 reached:1 fascinating:1 system:2 their:14 intermediate:3 perfectly:1 denominators:1 explanation:5 exactly:5 yurke:2 observed:3 things:1 ballard:1 submitted:1 rarity:2 whenever:2 amplitude:2 providing:1 curves:6 need:9 clearly:4 viewed:1 angle:19 able:5 incentive:1 instance:1 mis:1 threeparticle:1 accuracy:2 unless:6 centre:4 who:1 preliminary:1 class:1 subtracted:1 gather:1 graphs:2 mechanical:3 fact:7 violation:13 text:2 agreed:1 purely:2 trivial:3 based:5 should:15 dalibard:2 unable:1 equivalents:1 local:8 interested:2 achieve:1 means:5 convert:2 simplest:2 beam:3 ones:8 perfection:1 words:3 assistants:17 timing:1 delgado:2 areas:11 symbols:1 qt:1 numerous:1 she:1 contain:1 fixed:11 qm:24 view:3 cancelling:1 frame:1 correlations:5 computer:5 acquires:1 wire:2 pattern:2 tend:1 state:4 difficulties:1 correctly:2 nn:2 neither:2 email:1 importance:1 emitted:1 efficiency:2 key:1 probing:1 david:1 restrictions:1 interpretations:1 figured:1 instant:1 limits:1 taking:1 equal:4 agree:1 etc:5 subtending:1 grounds:1 comment:1 adjusted:1 ca:1 dial:1 distinguish:2 deflected:3 respect:2 ct:1 second:4 anomaly:1 define:2 corresponding:2 sufficient:1 coherence:1 cos:1 assert:1 angles:9 present:13 value:11 will:30 almost:3 vi:1 thus:3 site:1 sherlock:1 perhaps:10 radiation:1 parts:1 finite:1 difficult:4 ball:23 infinity:1 reporting:1 upon:1 effect:12 scarcely:1 off:1 fully:2 nevertheless:2 well:5 thought:4 patterns:2 sets:1 firstly:1 comparisons:2 arising:1 usual:1 spherical:1 less:1 accurate:2 obtain:1 cˆ:2 sources:2 underlying:1 voltage:1 web:1 point:3 mathematically:1 reasons:1 book:3 identical:1 tests:8 increased:1 devised:1 know:3 press:2 immediately:2 tick:1 loss:1 necessary:2 like:2 lost:1 sizes:1 alternatively:1 qualitative:2 works:1 page:1 exceed:1 because:6 classical:1 authority:1 gave:1 happens:3 lead:1 demonstrates:1 overlap:2 does:5 assuming:4 demonstrated:3 noise:1 obey:1 slight:2 about:3 actual:12 carried:1 column:1 introduces:1 dependency:1 a2:1 introduced:1 equally:3 own:2 letters:1 promise:1 van:1 recognised:1 function:5 but:22 he:9 made:3 places:1 whether:4 variations:5 imbalances:1 record:3 below:1 limit:2 demonstrate:1 problem:4 mechanics:11 devise:1 linearity:1 relates:1 functions:2 detail:1 other:16 illusion:1 conclusion:2 variation:6 factors:1 rule:1 experimenters:3
|
quant-ph9611038.txt |@word limited:3 similarity:3 squared:2 magnetic:13 four:5 consists:1 whose:2 replacements:1 calculate:4 presents:1 antiferromagnetically:1 mwn:3 alternating:1 digit:1 connects:1 every:10 summarized:1 logarithmically:1 vast:1 believed:1 induction:14 solution:9 vector:6 indices:4 enhance:1 markov:4 degeneracy:2 deutsch:1 plaquette:24 approximation:1 second:3 chem:1 even:12 errors:2 liberty:1 above:15 new:19 construction:14 increasing:1 simultaneously:2 never:1 equals:2 here:13 atoms:1 boghosian:2 active:1 interpret:1 obtained:8 balance:3 study:3 changes:2 der:1 highly:2 turchette:1 counts:1 total:4 unit:1 would:12 jozsa:1 chooses:3 occupying:1 definiteness:1 therefore:10 type:7 until:2 decomposable:1 separated:1 successful:1 odinger:2 aware:1 glass:22 ward:1 hold:1 must:9 work:5 tng:1 temperatures:1 example:7 tnj:13 renormalization:1 indicated:2 give:2 bennett:2 organized:1 involve:4 indicates:4 degenerate:1 feasible:2 absolute:1 ferromagnetically:1 end:3 provide:6 feature:4 very:7 symposium:1 ordinary:2 rightwards:1 brassard:1 bares:1 replacing:1 thermodynamic:32 after:14 hence:2 wrong:2 excited:2 attempt:1 effective:2 parisi:2 complexity:9 maintain:1 algorithms:11 correlation:3 order:33 operations:6 xj:17 interpretation:1 over:15 satisfied:1 london:2 toulouse:1 satisfies:3 before:6 fiz:2 writing:4 destroyed:1 fig:12 xj1:1 schmidt:1 easier:1 overcome:1 eventually:1 them:2 combination:1 break:1 steane:1 effects:1 they:8 goldwasser:1 represents:2 reasonable:1 each:18 bond:49 xgn:1 schemes:1 covered:1 xgi:4 haber:1 isfies:1 hooked:1 f1:5 gˆi:7 reader:1 surprise:1 ri:4 rj:2 rk:8 i2:1 turning:1 linear:6 barrier:1 free:1 standard:1 vazirani:2 assures:1 corrects:1 r1:11 tolerant:1 creates:2 incorporated:1 already:5 another:6 zalka:1 hood:1 illustrate:1 similarly:4 tor:1 xij:1 stack:1 needed:6 too:1 wootters:1 collapse:1 binney:1 somewhat:2 distance:1 showed:1 approximations:2 tree:8 likely:3 preparation:1 matter:2 tion:1 enables:1 minus:1 entail:1 minn:1 mind:1 spectrum:1 manner:3 seen:7 seem:2 seek:3 strength:3 realm:1 ideas:1 convenient:2 latter:2 isolated:8 maxn:1 shall:1 denominator:1 boltzmann:2 involving:2 phase:9 acknowledgements:1 calculated:2 partition:15 vertices:3 points:2 principle:1 section:11 random:17 speedup:1 attempts:4 defects:1 tempted:1 resemblance:1 proposed:2 implementation:1 t0j:1 ekert:4 x4:9 constant:5 hamiltonians:3 do:2 yielded:2 altogether:2 runs:2 fields:3 analytical:3 implication:1 edited:1 depends:2 w2:20 w1:20 discussions:1 best:1 techniques:2 exponent:2 tantamount:1 simplest:2 drawn:1 approach:5 terms:15 extend:1 nature:1 wn:5 however:15 wi:4 wu:1 huang:1 wx:12 received:1 hypercubic:1 fault:1 raimond:1 qubit:27 argue:1 collecting:2 polynomial:6 presumable:1 basis:6 three:6 been:10 much:3 interest:2 basic:2 expected:1 dots:1 θk:4 θi:26 θn:23 deeper:1 quantities:4 undefined:1 spin:82 applied:5 transformation:10 employ:7 contemp:1 near:2 suppose:6 applies:5 property:1 35th:1 leaves:1 procedure:8 2βj:1 iv:7 ii:15 ik:1 cond:1 il:2 hebrew:2 ia:1 nonunitary:1 perform:3 recursion:1 make:1 complex:2 quant:6 split:2 avoids:1 several:2 grows:3 independent:2 i1:1 numerical:6 differing:1 hand:3 nir:1 normalization:4 simulates:9 immaterial:1 xjn:1 xji:2 academic:3 simulated:3 left:1 entanglements:1 just:1 aside:1 shorthand:1 rotates:2 succeeding:2 previous:5 eli:1 regarded:1 had:1 transformed:4 easy:1 insensitive:1 possible:8 spanned:1 replace:2 apart:1 appearing:1 performing:1 specific:6 remind:1 steps:6 arbitrary:7 www:1 right:1 deal:5 escape:1 ignore:1 comments:1 exposition:1 landscape:1 substitutes:1 pose:1 binder:2 properties:2 proceed:4 numerator:1 o:24 plus:2 raised:1 formerly:1 presence:4 obtaining:5 bound:3 negative:3 down:9 formidable:1 suffice:2 initial:2 stuck:2 accordingly:3 conservation:1 way:3 infinitedimensional:1 was:12 gij:10 lowest:2 form:8 heat:1 true:1 emin:4 maximum:1 considered:6 complications:1 anew:1 stages:1 zeroes:1 later:2 proved:5 computing:3 improper:1 peres:1 proves:4 simulations:6 commuting:3 check:2 interferences:1 constructed:4 no:13 whereas:5 wavefunction:1 generally:2 interested:2 role:1 digital:1 np:4 superposition:35 models:31 faster:1 assume:7 together:4 remarked:1 moreover:2 neighbors:1 chain:24 global:2 branches:1 leads:2 roy:1 computation:7 row:1 inverse:1 depend:1 graph:1 gerber:1 environment:2 finally:3 analogous:1 orthogonal:3 choice:2 maali:1 entries:4 exact:4 solves:1 presented:2 turns:5 leave:1 solved:3 guy:1 accumulation:1 upper:6 undoes:1 dealing:1 cosh:7 cost:1 t2j:1 appear:6 current:1 sequential:1 suspect:1 satisfy:4 realizations:5 lange:1 groups:2 address:2 alone:5 along:3 appears:3 change:2 ref:2 institute:1 vectors:3 commonly:2 accomplished:4 ineffective:1 dorit:1 studies:2 useful:7 griffiths:1 extra:3 problematic:1 wang:1 alamitos:1 working:1 prove:10 positive:3 going:1 memory:1 scope:1 meyer:1 today:1 introducing:2 everywhere:2 cases:10 insights:1 originally:1 modified:1 ferro:16 achieve:1 following:12 making:1 nearest:4 arise:5 sample:1 performed:7 allowed:4 occur:2 redundancy:1 s3:3 s2:22 s1:53 s0:1 s4:3 write:3 fourth:1 familiar:1 guarantee:2 parameter:1 r2n:1 product:3 mat:1 may:16 max:2 produce:3 designed:2 representations:1 grow:2 natural:2 dynamical:1 succeeded:1 whenever:1 nussenzveig:1 explicit:2 yielding:1 sk:74 sj:134 switch:1 so:31 sn:104 sm:8 representation:3 superscript:2 exclusive:1 breaking:1 noteworthy:1 indeed:10 mainly:1 flips:1 years:2 course:3 statistical:6 omitting:1 argued:2 still:1 ieee:1 group:1 thank:1 how:6 interesting:4 jij:14 vicinity:2 coordinates:1 offers:1 decreased:1 main:3 decades:1 correspondence:1 non:4 introduce:8 scaling:1 half:3 now:31 discuss:3 nor:1 susceptibility:2 term:8 equality:1 drop:1 arrows:3 possibilities:1 entirely:1 square:4 ei:3 scheme:1 gaussian:1 ex:1 approximated:2 eq:48 shown:8 resonators:1 space:8 furthermore:4 interference:19 increase:4 formula:1 squares:2 correct:13 earlier:1 theory:6 possibility:1 california:1 advance:1 transition:3 ck:1 turn:1 antiferro:1 place:2 βh:3 βj:6 first:22 origin:1 xi:5 xn:5 variables:1 flipping:5 directly:1 open:11 xw:2 size:9 given:19 checked:5 1w:2 unitarity:3 anderson:4 indicate:1 1d:32 realization:5 bits:2 gives:1 exploring:1 kirkpatrick:2 continuous:2 proving:2 eliminates:2 pnm:3 x2:1 x1:1 representing:2 than:12 specify:1 wiesner:1 gik:10 require:6 were:2 outcome:1 spectra:2 generality:3 correction:6 argument:2 generalization:2 say:2 exchanging:1 weinfurter:1 occupied:2 any:20 sat:1 computationally:2 efficient:4 isolate:1 overcoming:1 converges:1 note:4 potential:7 take:3 performance:1 strengths:2 begin:1 opposite:2 price:1 satisfying:2 successive:5 pair:3 analytically:2 especially:2 discarding:2 average:5 adopt:1 implications:1 feynman:2 typically:2 mabuchi:1 quantity:1 shor:5 show:9 unfrustrated:20 recipe:2 ground:18 slow:1 ratio:3 written:8 only:32 explicitly:4 correctly:4 quantph:3 get:1 freezing:1 cannot:9 invariant:1 neither:1 yield:2 summary:1 umesh:1 racah:1 ence:1 physically:1 ity:1 j1:13 j2:10 j3:11 relative:2 namely:4 stanley:1 uncorrelated:3 wonder:2 fails:2 suffer:2 commutation:8 review:1 sites:2 enough:2 plaquettes:30 between:18 αi:2 geometric:1 multiplied:1 sompolinsky:1 vertical:5 qubits:10 jp:2 jr:1 jm:2 jn:63 concentrate:1 ji:36 suppressed:1 tractable:1 many:7 according:5 flipped:2 expression:2 comes:1 minima:4 sampling:1 exploit:1 cancel:1 ordered:2 v2n:4 considering:3 better:1 tuning:1 capable:1 come:1 combined:4 prototype:1 eβj:2 direction:1 covers:1 those:2 case:46 hughes:1 x2j:7 engineering:1 vecchi:1 promising:1 bazhanov:1 situation:5 rosenbluth:2 coupled:1 cluster:3 regularity:1 bias:1 binary:11 different:9 verified:2 assure:1 media:1 paz:1 same:16 arguments:2 physical:3 extended:1 singapore:1 running:1 entanglement:6 changing:1 totally:2 traps:1 without:7 solve:7 model:28 dimension:1 gates:1 among:3 being:4 when:14 neon:2 valuable:1 oxford:3 2jn:7 zoller:1 except:4 treatment:1 samples:1 real:2 around:1 2j1:1 replaced:1 decomposed:1 sums:1 predetermined:2 using:21 execution:1 correcting:1 mod:2 particle:1 facing:1 either:7 always:5 erase:2 hurst:1 specified:2 intact:2 reasons:1 generates:2 provided:1 dimensions:6 considers:1 critical:11 decomposition:1 provides:6 x3j:1 measuring:3 biased:4 scientific:2 power:5 equivalent:2 broken:1 qnm:3 refers:1 repeating:3 acc:1 comparison:1 central:1 ferromagnetic:14 discussed:1 mixes:1 whence:2 neighbor:3 mixed:4 outlook:1 communication:1 determine:2 elementary:2 jerusalem:2 classicality:1 technically:1 log:13 prepare:1 there:21 start:1 low:7 complete:1 metastable:2 huji:2 suffers:2 technologies:1 irreversible:1 longer:2 applying:3 vice:1 ωi:2 h0j:2 ωn:12 agree:1 connect:6 detailed:4 ac:2 cirac:1 ai:4 certain:1 describe:1 deep:1 general:11 loops:4 kimble:1 av:1 again:5 ideally:1 green:1 field:18 valid:3 briefly:1 divincenzo:4 time:11 includes:3 a1:5 important:6 bounded:1 ising:79 studied:1 included:2 ilar:1 building:1 parallelism:1 decoherence:2 starting:5 original:2 represent:2 monte:8 consider:17 crucial:1 lack:1 commute:6 generalize:1 follow:1 denotes:1 causes:1 content:1 tn:22 fundamentally:1 daniel:1 tk:2 tc:3 norm:1 amplitudes:5 straightforward:1 returning:1 far:3 corollary:7 sons:1 difference:6 condition:2 treating:1 hamiltonian:21 wsj:2 t2:5 large:10 small:4 employing:1 harder:1 zero:4 perspective:1 further:1 what:4 xor:1 brackets:1 sum:5 version:2 subspaces:4 sup:1 method:1 contrast:1 quenched:6 full:8 berkeley:3 equations:2 allows:8 periodic:1 uniquely:3 followed:2 requiring:1 takes:4 probabilities:9 comparing:2 ψn:1 taken:1 achieving:1 more:13 lowering:1 israel:2 operators:17 vi2:1 controlling:1 particular:8 known:7 foundations:2 evolves:1 science:5 equation:5 remain:3 strategies:1 x4j:13 f0:6 ions:1 hamburger:1 scan:1 share:2 states:26 unbiased:1 minimum:7 sense:4 huge:1 needs:5 csi:2 rather:2 acts:1 utilize:1 acta:1 simplicity:3 fu:1 algebra:1 weaknesses:1 mapping:2 connectivity:2 tries:1 plane:1 faculty:1 develop:2 horizontal:6 fk:1 fn:7 shortcomings:2 short:3 register:15 negligible:1 ith:1 developed:1 paper:4 signs:3 existence:1 y2:1 its:7 rapidly:1 energies:1 fruitful:1 absence:1 systems:33 might:7 good:2 return:3 communities:1 easily:7 finite:9 fully:5 level:2 2x:1 2d:26 inequality:1 2b:1 2c:17 found:7 2n:56 polynomially:1 2j:11 2k:2 cθ1:2 cθ2:2 weight:17 energy:15 hard:3 reduce:2 idea:2 slowdown:1 deterministically:1 expect:1 measurement:19 quantum:65 operation:7 beyond:1 biham:16 robert:1 since:35 research:1 si:193 issue:2 interscience:1 difficulty:3 reason:4 members:1 imagine:1 beginning:1 generate:4 definition:2 pairs:7 ion:1 computers:17 exponentially:8 eqs:8 reversing:1 probability:34 number:34 instances:1 done:8 construct:5 differ:4 temperature:12 utilization:1 introduction:6 least:1 calculations:4 molecular:1 exponents:2 store:1 statement:1 trapped:1 recursively:1 optical:1 sign:31 mezard:1 kind:1 john:1 determines:3 double:2 determined:5 dani:2 motivation:1 comput:1 defect:1 randomly:5 vilenkin:1 hexagonal:2 lie:1 depending:1 odd:7 generalized:2 finding:4 jsn:2 measures:1 reach:2 jsi:2 jsk:1 most:5 nothing:1 probabilistic:3 kb:4 cause:1 ke:2 clear:2 ko:2 physica:4 h2o:1 part:4 electrons:1 exp:13 physics:5 relation:5 fine:1 find:14 simulating:7 parameters:2 distributed:1 failed:1 generators:1 factor:3 bernstein:1 morgenstern:1 columns:1 intractable:1 dominant:7 notation:6 dependent:1 zurek:2 express:1 fastest:1 competing:1 combinations:7 lattices:5 resolve:1 arxiv:1 factorization:2 common:2 locating:2 set:13 ser:1 sep:1 unpublished:2 see:6 sec:7 close:9 ergodicity:1 probable:2 diluted:4 various:2 consecutive:1 conditions:7 available:2 notoriously:1 eˆi:2 selectively:1 eˆn:8 both:8 prospects:1 cubes:2 last:25 reverse:1 annual:1 context:2 finds:3 experimental:1 arbitrarily:2 point:13 simple:1 corresponds:9 dimensional:13 simply:3 pr:7 described:4 transformations:8 mises:1 due:8 dropping:1 ph:6 lett:11 generating:2 versa:1 precision:3 fritz:1 understand:1 exponential:2 while:4 superposed:2 pressed:1 behavior:1 error:5 loop:11 unitary:10 laflamme:1 vol:1 von:1 itself:2 ready:2 belong:1 stimulated:1 modification:1 products:1 barnea:1 composition:2 higher:14 development:2 used:8 comprehensive:1 moment:1 moving:2 purpose:1 fabrication:2 lower:4 task:2 analysis:2 obviously:1 edge:1 i2n:1 chemistry:1 plagues:1 calderbank:1 atomic:1 questions:1 world:2 accepted:2 kluwer:1 conclusions:2 guaranteed:1 source:1 location:1 input:5 remaining:1 euler:1 build:1 showing:1 bit:3 like:3 rotate:1 follows:7 separately:1 continue:1 yields:4 disorder:5 spins:31 mathematical:2 methods:4 creation:2 some:15 back:1 emanate:1 understood:1 b1:6 gradually:1 describing:1 nondeterministic:1 measurements:15 integration:1 per:3 connecting:6 tends:1 proc:1 minimal:2 inserting:2 run:5 redoing:1 s12:5 bi:7 step:2 xsk:2 dictated:1 hilbert:1 xsi:4 pδ:1 simulation:7 range:5 regular:3 block:5 computational:1 into:18 within:2 appropriate:2 statistics:1 few:2 measured:2 question:4 long:5 sections:2 elsewhere:1 branching:2 properly:2 repeatedly:1 line:2 collapses:2 cik:4 cij:3 up:10 us:12 planes:1 autocorrelation:1 similar:5 associated:2 defined:2 coincides:1 single:10 formalism:2 defines:2 codes:3 amounts:1 dashed:2 edwards:2 application:7 coded:1 department:1 wrongly:1 calculating:1 problems:8 prepared:1 generated:4 graphically:2 prepares:1 fisher:1 structure:1 correlated:1 implies:2 algorithm:67 negating:1 required:8 calculates:1 weights:13 walker:3 requires:2 having:6 once:5 code:1 partial:2 results:11 existing:2 edu:2 gn:14 gi:19 young:1 include:8 ingredient:1 g2:1 g1:1 wishes:1 putting:1 matrices:2 entire:6 notes:1 michael:1 try:3 dealt:2 noted:3 configurations:23 zn:56 smaller:1 disordered:1 metropolis:4 enclosed:1 dynamics:3 carlo:8 analogue:1 index:2 plays:1 expressed:1 access:1 3j:5 waiting:1 expresses:1 3d:20 body:2 led:1 exchange:1 respectively:8 spacing:1 desired:9 ramsey:1 z4:2 consideration:1 invented:1 z0:1 z2:4 suggest:1 popkov:1 involved:1 larger:1 barahona:2 leaving:5 suggests:1 resulting:5 defeat:1 composed:3 claim:1 private:1 summation:2 apply:3 tools:2 virasoro:1 use:9 superpositions:2 commun:2 remains:4 next:11 calculation:10 depicted:2 kaler:1 means:6 bethe:9 becomes:2 normalized:2 iii:6 bimodal:1 entangle:1 onsager:1 obvious:2 closing:15 averages:3 proof:7 control:11 process:5 haroche:1 high:1 effectively:1 sis:1 z21:1 z20:1 holds:4 located:1 sik:6 sij:30 sin:30 sim:1 blocks:2 θ2n:5 demonstrating:1 efficiently:4 realized:1 computations:3 light:1 lines:2 correspond:3 allow:1 2sn:1 produces:5 move:3 symbols:1 boils:1 including:5 during:2 jnm:14 ld:1 chosen:3 clusters:2 defining:1 originator:1 symmetrization:1 greater:1 outlined:1 newman:1 instead:8 rotation:6 dirac:1 university:4 identified:1 sufficiently:1 soc:1 macchiavello:1 glasses:5 baxter:3 map:1 doing:1 xors:2 related:4 operator:16 measure:1 separating:1 our:7 transitions:3 special:4 out:6 matrix:12 rev:32 produced:2 lecture:1 suffices:2 integrated:2 math:1 approached:2 interactions:5 maintains:1 undo:1 ban:1 york:3 ofer:1 likelihood:1 interaction:7 geometry:3 determining:1 could:4 times:1 length:5 barriers:1 physik:1 manuscript:1 klimyk:1 intuitively:1 reached:1 aharonov:3 los:1 achieved:1 system:31 relations:6 their:6 intermediate:4 siam:1 final:1 s34:1 exactly:9 wiley:1 simulate:2 diminish:1 completes:2 ben:3 submitted:2 amplitude:3 naturally:1 result:15 exhibit:3 benny:1 miquel:1 need:7 constrained:2 demonstration:1 clearly:9 min:2 able:4 annealing:1 smolin:1 accuracy:1 who:1 connected:4 overlapping:1 class:9 url:2 proceedings:1 hi:6 mechanical:2 fact:8 purely:1 lloyd:3 βhn:10 trivial:2 agrees:1 staff:1 based:2 knowledge:1 should:15 employed:2 amplify:1 local:10 hope:3 equilibrium:2 bonds:51 βh0:7 ones:3 words:3 procedures:2 gray:3 optimally:1 unfeasible:1 fixed:2 view:2 exists:2 notational:1 fictitious:1 computer:31 operated:1 packed:1 closes:2 phases:1 interacting:3 pattern:1 state:42 identification:1 closed:23 confusion:1 progress:2 boundary:6 frustrated:32 email:2 brune:1 publishers:2 barenco:3 ability:1 importance:1 interfere:1 implementing:1 hypothesis:3 key:1 demonstrate:2 sleator:1 configuration:20 problem:28 david:1 restrictions:2 taking:1 equal:12 etc:3 figures:1 kets:1 comment:1 cj:6 ci:5 cn:10 conclude:2 ca:2 walk:3 taylor:2 table:2 geometries:1 addition:3 nb:3 slowly:1 treat:2 erases:1 define:2 arises:3 corresponding:22 sufficient:1 subspace:2 cos:18 angles:3 essentially:7 present:11 splits:1 unlike:3 lz:1 nd:2 appearance:1 swendsen:1 value:2 choices:1 will:41 vi:11 vk:2 thus:29 site:3 vn:7 hardware:1 vs:1 gibbs:3 gets:1 φn:24 difficult:1 http:2 cubic:2 upon:3 effect:5 v1:2 v2:1 infinite:1 identity:2 keep:1 schr:2 center:1 nevertheless:1 well:11 s23:1 position:2 usual:1 magnetization:2 less:4 accurate:1 identically:1 numbering:1 obtain:7 stored:1 predicts:1 preprint:9 density:2 lattice:30 add:1 teller:2 gms:1 identical:5 increased:1 lanl:9 increases:3 five:1 know:2 press:3 loss:3 necessary:1 helpful:2 excluding:1 efficiency:2 extremely:1 eβ:8 xsj:1 become:3 works:1 xsn:4 accessible:1 parity:1 dordrecht:1 classical:22 sequence:3 phenomena:3 searching:1 haim:1 choosing:6 proper:2 lead:1 broad:1 avoid:1 kandel:1 2c3:14 does:9 assuming:2 demonstrated:1 selecting:1 journal:1 expansion:1 clarendon:1 although:4 analyses:1 stage:4 about:4 actual:2 extension:2 column:1 introduced:5 converging:1 equally:2 own:1 h2:2 h0:13 h1:17 consecutively:1 additional:3 transfer:4 lidar:13 frustration:3 suzuki:1 interferometry:1 function:15 triangular:3 but:16 hk:2 repeated:2 lowered:2 hn:42 highest:2 partially:2 made:3 coefficients:1 places:1 society:1 whether:8 antiferromagnetic:34 cells:1 flip:1 excitement:1 placed:1 below:1 βgi:1 distribution:7 mechanics:4 θj:1 int:1 universal:1 slowing:4 denote:5 ing:1 happen:1 functions:5 compared:4 variety:3 slovaca:1 detail:2 other:15 details:1 suppress:2 theor:1 stat:2 repeat:1 upwards:1 domany:1 coupling:3 baker:1 factors:1 rule:1 intentionally:1 portion:2 gelatt:1 4j:4 4d:1
|
quant-ph9611039.txt |@word represent:1 measurements:1 customary:3 consider:6 remarkable:2 crucial:1 global:3 results:2 four:3 quadrature:2 comments:1 sci:1 expressions:1 contributions:1 whose:2 referring:1 paris:10 equivalence:6 tr:6 supported:1 does:1 device:11 th:2 under:5 γa:1 worth:1 alexei:1 random:1 straightforward:3 very:5 frequencies:1 zˆ1:1 keeping:1 choice:2 impinged:1 electron:4 mattle:1 mixing:1 affect:1 difference:2 matrices:1 splitter:6 freyberger:2 presented:1 transmission:1 knight:2 large:1 discrete:1 convenience:1 harry:1 michler:1 optics:3 der:1 iˆ4:3 unexpected:1 occurrence:1 arccos:1 measurable:2 second:2 ˆi1:1 evaluated:2 further:1 implemented:2 port:32 canonical:1 even:1 appear:1 apparatus:1 section:8 expressed:2 3k:1 ˆa:2 homodyning:1 version:1 values:1 bn:1 full:3 pm1:1 respectively:1 realizations:1 commercial:1 jointly:3 reported:3 represented:1 strong:1 z1:15 z2:12 obtained:4 trans:1 incoming:1 rigorously:1 involved:3 losses:2 allows:1 reason:2 arthurs:1 exiting:1 renzi:1 amount:2 substituted:1 resulting:2 hospitality:1 fourier:8 studies:1 involves:1 technique:1 convolution:7 instr:1 yuen:3 shifters:3 highly:3 sacchi:1 planck:2 unit:6 fed:1 additive:1 takes:1 would:2 prove:1 remains:1 positive:2 photocurrent:21 negative:3 properties:1 a51:2 process:5 depicted:1 a52:2 examination:5 therefore:3 taken:2 survive:1 means:4 reflects:1 more:8 introducing:2 becomes:2 operators:1 berlin:2 known:4 cases:2 me:1 states:2 account:5 bernstein:1 gabriel:1 setup:3 work:1 oscillator:10 glauber:2 obvious:3 following:6 arrive:1 example:1 leonhardt:2 figure:6 transmissivity:3 calculation:1 carrol:3 organized:1 implementations:1 involve:1 performed:4 allowed:1 rescaling:4 busch:1 information:9 counting:2 provide:3 buzek:2 six:9 feature:1 write:3 how:1 zˆ2:1 opt:13 wolf:1 sin:1 product:1 ζc:1 ft:4 description:2 max:2 after:2 derived:1 containing:1 diagram:4 plane:3 demonstrating:1 coming:2 cambridge:1 realized:1 iθn:2 outline:1 effective:1 beam:17 light:1 ρnn:2 bs:5 element:1 rather:2 so:4 decreasing:1 uˆ1:1 uˆ2:4 uˆ3:2 order:9 haus:1 acts:1 wigner:7 indeed:4 pointed:2 soc:1 lahti:1 paper:5 through:1 experimentally:1 mentioned:1 still:1 ieee:3 perfect:3 derive:1 group:1 thank:2 termed:1 chosen:1 lo:4 lai:1 r30:1 actually:3 detected:4 fig:8 symbolizes:1 couplers:1 a91:1 inefficiency:4 them:2 noh:3 tjk:2 noticing:1 hariharan:1 stenholm:5 effects:2 they:11 nov:1 now:5 represents:2 term:1 double:1 lies:2 fully:2 university:2 a53:1 hermitian:1 realistic:3 theory:1 mode:50 each:4 references:1 macchiavello:1 2i:1 characterized:3 referred:1 domain:3 schemes:9 successively:1 gaussian:1 related:2 balanced:3 milan:1 frequency:5 entering:2 measure:3 quantum:25 operatorial:1 eq:24 aˆ1:1 aˆ2:1 aˆ3:1 principles:1 emerges:1 shown:2 matrix:5 space:8 nuovo:1 interference:1 denotes:4 fta:1 cahill:2 denoted:3 formula:1 occurs:1 shows:2 reck:2 fiber:2 linear:4 contain:1 iˆs:1 little:1 possibility:1 completely:1 orm:2 advantages:1 convolutions:1 members:1 definition:3 interaction:2 ˆb:2 unexcited:1 ordering:1 iz2:3 choices:1 place:1 u4:1 facilitate:1 neglect:1 first:3 origin:1 mkl:1 features:2 probability:11 enhances:1 variables:1 valentina:1 number:2 intuitively:1 u3:2 directly:2 smoothing:1 open:1 appl:3 given:10 necessarily:1 rewritten:1 needed:1 introduction:1 leading:2 eqs:6 their:6 intermediate:1 alfred:1 realization:1 scheme:20 inserting:2 final:6 gives:1 way:1 postgraduate:1 reversed:1 part:7 shifter:2 authors:1 natural:1 representing:1 than:1 relative:2 kind:6 roles:1 was:1 require:1 matteo:1 intensity:2 smoothed:1 a46:1 a47:2 a45:1 contrary:1 amplitude:2 ia4:2 outcome:2 ia3:1 ia2:2 bertani:1 argument:1 generalization:2 already:3 say:1 idler:3 close:1 hexagonal:1 kelley:1 any:6 inefficient:9 conversion:1 ρmm:1 efficient:1 pursued:1 latter:8 offer:1 able:1 mechanism:1 note:2 ideal:4 take:1 analogy:1 schematically:1 detector:9 modulus:1 gη:2 electric:2 normal:1 probed:1 reach:1 optimized:1 regular:1 eight:17 remarks:1 weihs:1 inserted:1 class:4 kb:7 give:1 considered:4 adopt:1 coincides:2 playing:2 optical:6 χb:2 exp:16 mechanical:1 redirected:1 duplication:1 sum:2 fact:8 incorporate:1 simulate:1 show:4 probe:12 purely:1 s111:1 substituting:1 d2:4 make:1 redirect:1 access:2 implementation:2 less:1 written:2 only:7 explicitly:1 black:1 summarizing:1 equipped:2 originally:1 constant:1 partially:1 local:10 his:1 get:1 de:2 joint:8 cannot:3 radiophysics:1 a129:1 dt:1 lossless:3 evolution:1 countries:1 fields:1 arxiv:1 experiments:1 qe:2 common:1 photodetectors:10 pulses:2 fixed:1 wodkiewicz:4 view:1 reveals:1 set:1 computed:1 physically:1 detection:15 differs:1 namely:2 justification:1 us:6 discussions:1 recently:2 arm:1 subject:1 preparation:1 hilbert:1 ways:1 distinctive:1 review:1 b60:2 symmetric:5 state:11 heterodyne:10 limit:2 available:1 notice:1 terms:8 wb:2 wa:2 sampled:1 she:1 filter:2 sole:1 however:7 efficiency:13 comm:3 here:2 analyzed:2 holds:1 observable:3 cos:1 taking:1 conclusions:1 equal:1 foreign:1 admit:1 hω:1 a48:2 interesting:1 a49:1 expression:2 experimental:3 among:1 relevant:5 shapiro:3 point:4 homodyne:26 dimensional:3 probing:3 pom:1 simply:1 keitel:2 ae:1 writing:1 considers:1 photocurrents:18 considering:3 quadratures:1 described:1 transformations:2 leads:3 aˆ:2 three:10 been:15 appears:2 ai:1 describes:2 combined:2 interest:2 kronecker:1 expected:1 transformed:1 ph:1 abstract:2 pm:4 ariano:5 box:2 corresponding:2 both:3 am:1 coherence:1 photon:3 zeilinger:4 coherent:3 determination:1 denote:4 case:10 multi:1 laser:2 single:9 value:1 transformation:3 will:11 shift:1 region:1 procedure:3 identical:3 unitary:3 saleh:1 vogel:1 riv:1 characteristics:1 refs:2 thus:7 surprisingly:1 according:6 coupler:11 propensities:1 converts:1 triple:9 accounting:1 rid:1 technology:1 result:3 different:13 generic:1 realizing:1 belong:2 radiation:7 same:5 complex:9 quant:4 schematic:4 mauro:1 independent:1 used:4 upon:3 effect:1 hand:2 purpose:1 genuine:1 concluding:1 identity:2 suitable:2 modes:24 nevertheless:1 whole:1 non:3 zukowski:1 components:2 lim:1 position:2 scholarship:1 teich:1 splitters:7 being:8 wagner:1 obtain:5 cˆ:2 sources:1 filtering:1 paul:3 zernike:1 electronically:1 previous:1 profitable:1 subsequently:1 conjugates:1 elo:1 density:3 photons:3 phototube:1 goodman:1 sometimes:1 passive:2 conjugated:2 lett:12 theorem:1 input:11 excited:8 momentum:2 iφ:1 real:5 insensitive:1 rev:23 easily:2 couple:1 multiport:3 measurement:10 possible:4 corresponds:1 possibly:1 campos:1 entangled:1 vacuum:6 press:1 using:2 unique:2 moreover:1 mod:3 insert:1 follows:1 signal:26 specific:1 remind:1 always:2 output:24 stationary:1 reduced:2 χu1:1 mathematical:1 heisenberg:1 kb1:2 ole:1 sequence:1 2iη:1 some:7 b4:2 b1:4 b2:4 b3:4 sen:1 iˆn:2 iˆk:1 provided:3 entropic:1 describing:2 lead:1 though:2 microwave:1 schleich:2 kleiner:1 strahlung:2 decomposition:1 manipulate:2 provides:3 unavoidably:3 prof:2 welsch:1 minimal:2 refer:2 measuring:2 noise:10 iˆ1:7 iˆ2:11 iˆ3:11 equivalent:6 chaussee:1 bj:3 bk:3 binomial:1 although:1 eiφ:1 imaginary:5 intense:4 stage:3 comparison:3 about:1 actual:1 o:11 sake:1 plus:1 mixed:2 germany:1 introduced:6 jex:3 ηe:1 contains:1 ηa:2 into:5 photodetection:16 due:3 phase:15 appropriate:1 accounts:1 operator:5 proportional:2 next:1 statistics:8 a115:1 additional:4 periodic:1 measured:6 strictly:1 there:2 u1:10 transform:7 long:2 u2:4 start:2 window:1 mandel:4 fraction:1 analyze:1 sections:1 a54:1 function:12 complete:1 form:5 enough:1 denoting:1 displacement:1 gain:1 delta:1 true:1 factorized:2 society:1 characteristic:4 devices:8 ωi:7 placed:6 ui:1 uj:2 chizhov:2 distribution:15 stages:2 gesellschaft:1 ab:1 proved:4 defined:3 detectors:7 ak:3 describe:4 chan:1 general:6 examine:1 interchanged:1 our:2 θn:1 inf:1 distributions:1 physical:1 again:1 compared:1 cim:1 no:1 whereas:12 when:6 detail:2 arctan:1 field:21 other:4 role:2 tij:1 out:2 ˆi2:1 principle:1 briefly:1 elements:1 χa:2 symbol:1 a1:19 a3:12 a2:11 a4:5 suppression:1 heffner:1 generalized:4 acknowledgment:1 coupling:2 dω:2 assume:1 interval:1 together:1 time:4 walker:4 observables:1 starting:1 original:3
|
quant-ph9611040.txt |@word footing:6 sci:1 consider:2 rev:6 global:1 desirable:1 results:3 correo:1 eds:1 ciudad:1 go:2 contributions:2 albeverio:1 devoted:1 whose:1 certainly:1 const:1 gˆ:3 concerned:1 pˆl:1 tp:1 ıa:2 finally:1 does:5 alvarez:1 tk:29 th:1 under:6 p2:7 hibbs:1 geometrical:3 replaces:1 putting:1 summarized:1 difference:1 exact:3 condition:5 treating:1 entire:3 p4:1 solves:2 hamiltonian:15 turns:1 t4:1 t5:1 differentiating:1 solution:8 t1:2 discrete:1 vector:4 interpolating:5 succession:1 berezin:1 jacobians:1 consistent:1 sign:1 approximation:3 zero:2 value:3 rigorous:1 canonical:18 even:2 t2k:34 appear:1 euclidean:1 giving:1 section:12 version:5 goes:2 ri:1 values:2 method:1 satisfy:2 pˆa:2 wavefunctions:1 degree:1 mω:1 here:1 tangent:4 possibility:1 hkm:1 represented:1 path:33 along:2 change:4 obtained:5 instituto:1 studied:1 allows:1 commonly:1 example:1 suggests:2 dewitt:1 extremes:1 resulting:1 action:16 suitable:1 changes:2 rafael:1 involves:1 formulated:1 usp:1 although:3 consejo:1 discontinuous:1 explained:1 replace:3 roles:1 lanczos:1 ıficas:1 semiclassical:1 propagators:4 tn:3 use:7 takes:1 would:2 remains:1 played:1 zeits:1 generate:3 classically:1 explicitly:1 therefore:3 m3:1 m2:5 reflects:1 more:2 sort:1 flat:1 applicable:1 conclusions:2 apparent:1 odinger:6 curvature:2 particular:1 known:2 iii:4 1tk:1 must:8 account:2 join:1 mc:2 integrating:1 ed:1 equation:21 work:1 det:11 modified:1 infinitesimal:15 del:1 canonically:3 making:1 could:4 dn:5 give:4 relativistic:4 exactas:1 sense:2 pieces:4 something:1 endowing:1 handle:1 tan:2 6m2:1 guarantee:2 information:2 scalar:4 end:1 turn:1 get:2 feature:1 skeletonization:21 how:3 nontrivial:1 buenos:4 instead:1 explains:1 sin:2 fp:12 product:4 proc:2 blocks:1 singular:1 replacing:3 after:2 containing:1 reflect:1 corrections:1 physik:1 coming:3 cambridge:2 requirements:2 wave:5 data:1 parallel:2 constants:1 ambiguous:1 short:10 whenever:1 author:1 bitensor:1 their:3 wishes:1 so:5 realizes:2 allow:1 enter:1 representation:2 order:13 prefactor:1 holds:1 wigner:2 eqs:5 displayed:1 choose:1 symbols:2 course:2 wiener:1 paper:3 through:2 its:7 symmetric:2 derive:1 remark:1 thank:1 qˆ:3 trieste:1 chosen:4 coordinates:24 actually:2 systems:5 jacobi:22 derivative:1 argentina:3 emphasize:1 symmetrization:2 non:3 good:1 combination:1 qp:1 matches:1 fiziev:1 introduce:2 geodesic:4 hamilton:17 they:4 thanks:1 oxford:1 now:2 nor:1 easily:1 term:3 several:1 dirac:2 name:1 university:2 level:1 alternately:1 hermitian:1 composition:2 astronom:1 6m:1 each:9 found:1 2i:2 2j:2 mean:2 hermiticity:1 weyl:2 weight:8 t2:2 ea:4 principles:4 related:3 joined:1 τ2k:2 obtains:1 measure:21 quantum:8 our:4 eq:31 out:1 ultimately:1 matrix:1 space:27 contravariantly:1 since:5 lagrangian:2 transforming:1 hill:1 induced:4 ref:6 integrated:1 interchanging:1 shows:1 ibidem:1 wiley:1 linear:1 assured:1 retrieved:1 splitted:1 ısica:2 departamento:1 standard:3 york:2 besides:1 span:1 sowjetunion:1 finite:4 definition:1 qj:3 applications:1 recipes:2 times:3 ordering:16 length:1 universidad:2 consequence:2 retain:1 assign:1 integrand:1 origin:5 initial:10 probability:1 variables:4 reflected:1 linking:1 iafe:1 illustrate:1 given:1 law:1 guaranteeing:1 needed:2 introduction:2 leading:1 πh:1 system:17 indicate:1 intermediate:1 kleinert:1 statement:1 j5:1 variational:3 behaved:1 final:6 gives:3 free:1 helpful:1 huv:1 part:3 jordan:1 expanding:1 kind:1 scheme:3 showed:1 see:4 gij:1 determined:1 assume:2 amplitude:1 were:4 pǫ:1 treated:1 lowest:1 cohen:2 argument:5 already:1 manuscript:1 grosche:2 manner:1 any:5 symmetrized:1 paths:1 issue:1 newtonian:2 depending:1 convenient:1 responsible:1 able:1 ideas:1 instance:2 k1:2 potential:3 take:2 jacobian:2 finding:1 new:2 techniques:1 ecnicas:1 8m3:1 lectures:1 added:2 unless:1 normal:13 rhs:1 chart:1 qˆl:1 qˆm:8 exploited:1 connected:1 aires:4 formulae:1 phase:19 clear:1 coincides:2 km:1 feynman:5 ferraro:3 points:9 exp:20 typical:1 physics:2 came:1 joining:4 parker:1 show:2 supported:1 recipe:4 anyway:1 merit:1 iǫ:1 relation:2 solutions:9 trivial:1 find:2 principal:17 q1:2 q0:1 q2:1 based:4 proposed:4 spite:1 written:2 should:15 only:4 going:3 stated:1 integrate:4 pj:7 continuity:2 do:2 his:1 legendre:3 means:4 michigan:1 de:7 preferred:1 satisfied:1 remedy:1 ones:1 dx:1 invariant:12 dt:1 boundary:2 dp:14 dq:21 cleanly:1 evolution:2 qt:3 introduced:1 approach:1 arxiv:1 acknowledgments:1 morette:1 qk:33 fixed:2 guessed:1 qn:4 riemannian:2 set:5 exists:1 j4:1 smooth:1 j0:1 j1:1 j2:1 j3:1 namely:1 bare:1 result:6 discussions:1 seems:1 hilbert:2 evaluation:1 eigenfunctions:2 ways:1 boundaries:3 state:2 between:11 consecutive:1 neither:2 reading:1 conditions:1 preserve:1 terms:4 2m:8 attention:1 ignorance:1 interpolate:1 however:6 jl:4 concentrate:1 p2k:15 jk:1 universitaria:1 configuration:6 pˆk:9 topology:1 suggested:1 both:9 cos:3 prescription:5 candidate:1 taking:2 compton:1 equal:9 quantization:1 fulfilled:2 propagation:1 connection:1 contribution:3 expression:1 pabell:1 point:3 had:1 ca:1 corresponds:1 whatever:2 coincidence:1 dimensional:1 anti:1 exhibits:1 associated:8 writing:1 second:1 pp:2 pq:1 transformations:3 pt:1 basis:9 addition:2 trajectory:1 due:1 been:4 cient:1 pa:30 treat:3 interest:1 basic:1 shorttime:1 pk:17 ph:1 define:4 determinant:2 corresponding:1 ωt:3 σ2k:4 composing:1 sufficient:1 math:5 covariance:1 t3:1 confers:1 mail:1 c3:1 c2:1 worked:1 those:2 case:8 kuchaˇr:2 hdt:1 look:1 exponential:1 pacs:1 expanded:2 ij:2 conserved:2 evaluated:3 will:11 cast:1 ar:1 replaced:4 behavior:2 property:2 precede:1 procedure:1 polymer:1 unitary:1 espacio:1 vi:2 metric:3 cerdeira:1 thus:8 centenary:1 surface:1 iv:4 ii:2 ih:2 itself:2 im:1 dual:1 investigaciones:1 mod:2 φp:5 different:7 sensitive:1 make:3 hψ:1 same:2 rules:2 quant:1 arguments:8 gets:6 privileged:1 higher:1 status:1 independent:1 used:4 singapore:2 cubic:1 differing:1 moving:1 changing:1 invariance:2 landau:1 identity:1 prescribed:2 schr:6 modes:6 recurrence:1 well:3 magical:1 thought:1 contact:2 i2m:2 components:5 lim:2 coordinate:6 dimension:1 left:2 manifold:4 just:1 dover:1 being:4 compel:1 newton:2 obtain:1 rest:1 mid:3 orthonormality:1 transforms:1 world:1 momenta:16 eigenstates:2 previous:2 cut:1 generator:1 density:10 regarded:4 character:4 nacional:1 apr:1 conjugated:4 natl:1 dqn:1 guarantees:1 transformation:2 momentum:2 generalized:1 manage:1 read:1 early:1 ciencias:1 press:2 2p:1 ams:1 unique:1 dq1:1 naturally:2 like:5 particle:2 splitting:1 reduces:1 specific:1 integrals:2 arbitrary:3 become:1 stationary:7 essential:1 depend:3 mathematical:2 because:4 methods:1 classical:25 successfully:1 some:3 born:1 acad:1 pτ:1 respect:2 proper:2 gave:1 transport:2 describing:1 dimensions:1 unavoidable:1 integration:16 comments:1 conservative:2 providence:1 behave:1 hep:1 propagating:1 bessel:1 lifshitz:1 scientific:2 power:2 retains:3 equivalent:2 q2k:13 agreement:1 expansion:2 hǫ:3 casilla:1 substitution:3 imaginary:1 includes:1 dictated:2 properties:2 schulman:1 comparison:1 about:3 usa:1 concretely:1 mcgraw:1 o:12 idq:1 mixed:3 2k:11 consequently:1 2iπ:1 therein:1 equally:1 contains:1 garc:1 follows:1 pergamon:1 into:4 integral:6 functional:17 pair:3 appropriate:1 right:1 references:1 sov:1 operator:17 proportional:1 behaving:2 statistics:1 van:3 additional:1 governed:1 there:1 transform:4 anderson:1 quadratic:2 facultad:1 inner:2 way:1 series:2 forward:1 was:6 propagator:34 x2γ:1 etc:1 function:21 complete:12 form:12 hp:1 regard:1 but:4 idea:1 failure:1 convergence:1 naturales:1 begins:1 evident:1 uv:7 variations:1 up:1 us:6 discretized:1 liouville:1 limit:6 lays:1 problem:2 piece:6 similar:1 called:2 mechanics:9 fulfills:1 vleck:3 defined:3 general:2 schutz:1 consulted:1 proves:1 pˆ:3 rule:2 wavelength:1 controlled:1 formalism:1 functions:8 amounts:1 wavefunction:3 when:9 proceedings:1 build:1 valid:2 role:1 theor:1 may:1 congress:1 symbol:1 unitarity:1 meaning:4 uba:1 replacement:1 building:1 bases:1 implies:2 dφ:1 factors:1 dq2:1 together:2 fact:6 time:16 appl:1 2mω:1 having:1 once:3
|
quant-ph9611041.txt |@word limited:1 now:10 todays:1 consider:4 results:4 unchanged:2 four:9 received:4 comments:1 shimony:1 go:1 integrity:1 certainly:2 amplification:7 violate:11 disposal:1 contained:1 send:3 finally:4 protocols:1 excluded:1 under:2 applied:2 conjecture:4 random:7 advantage:2 orthogonal:2 very:4 choice:6 decide:1 summarized:1 experimentally:1 manageable:1 matrices:3 condition:3 presented:3 transmission:4 eve:59 large:4 vector:7 noted:1 upper:1 averaged:1 deutsch:1 discover:1 hillery:4 rate:8 cost:4 displays:1 machines:5 even:3 will:2 what:3 errors:2 plays:1 giving:2 section:10 axes:1 expressed:1 waiting:1 version:2 above:12 utkenhaus:1 shared:1 increasing:1 method:1 full:2 simultaneously:2 chose:1 degree:3 lange:1 answers:1 diagonal:1 ranges:1 intercept:4 strategies:8 represented:4 along:5 standard:5 appears:1 wait:2 obtained:7 provably:3 brilliant:1 studied:2 amount:1 published:2 bob:56 plotted:1 buˇzek:4 useful:1 secure:3 extra:1 problematic:1 unitarity:1 mor:1 turchette:1 alamitos:1 use:23 figure:6 would:7 prove:1 remains:2 positive:1 interception:1 chooses:1 optimize:2 calculation:1 depicted:3 call:2 therefore:4 encode:1 themselves:1 until:3 marginally:1 more:21 introducing:1 bennett:2 knows:1 ecole:1 becomes:3 freedom:4 validity:1 particular:4 known:5 logarithm:1 states:11 contradicts:1 setup:4 work:1 modified:1 values:1 tracing:1 following:7 making:1 example:5 performed:1 compare:1 corrupted:1 indicated:1 give:2 process:1 introduces:3 allowed:1 share:1 purposes:2 high:2 sphere:7 minimum:1 numbers:1 want:2 sense:2 validated:1 gains:6 information:50 end:1 straightforward:2 provide:1 technology:1 discussion:3 η2m:1 delay:1 till:3 criterion:4 pure:1 optimal:11 axis:4 preferable:1 sin:30 brassard:1 inputs:1 product:2 may:19 ancilla:2 clone:2 after:4 lab:1 applications:2 produce:1 adventure:1 noise:2 horizontal:1 data:9 effective:1 parameter:1 explicit:1 correspond:1 purification:1 broadcasting:4 so:6 allow:2 representation:2 order:5 operations:1 horne:1 breaking:4 indeed:5 mainly:1 iae:9 produced:2 course:1 already:2 through:1 eavesdropping:13 fidelity:6 still:10 ieee:1 its:4 before:2 perfect:1 machine:29 group:1 probability:1 how:4 chosen:3 interesting:5 cryptology:1 actually:1 better:4 degrees:3 choose:4 feasible:1 hidden:1 versus:1 them:2 good:7 influences:1 combination:4 impossible:1 introduce:2 break:1 they:10 half:1 nov:1 mimicking:1 possess:1 easily:1 equality:1 always:1 university:2 b3:1 crypto:1 establishing:1 2d:1 realistic:2 2f:2 inequality:29 transmitted:1 reasonable:1 each:5 crossing:1 found:3 entirely:2 mean:2 square:1 financial:1 directly:1 series:1 reduce:1 idea:1 related:2 society:1 frequency:1 gates:1 measurement:17 quantum:50 our:7 beyond:1 eq:11 out:4 shown:8 fundamentally:1 space:6 restricted:3 since:4 rev:9 chaos:1 particles:8 similarly:2 posteriori:1 safety:1 socalled:1 performs:1 interchanging:1 shows:2 foundation:1 log2:5 given:8 free:1 quite:1 labs:1 reason:1 base:1 complicated:1 asi:1 jozsa:1 additional:2 pairs:3 interaction:4 prepare:1 could:2 impose:1 keep:3 turn:1 explored:1 due:1 hence:6 view:1 eqs:2 first:5 initial:9 symmetry:8 powerful:3 huttner:1 restrict:2 done:1 adopted:1 another:3 reached:1 precisely:3 quality:2 hood:1 size:1 passes:1 little:2 perturbation:3 exists:1 likely:1 privacy:7 introduction:2 unknown:4 interact:2 system:4 least:2 iab:4 their:10 rates:2 john:1 bits:2 final:2 adopts:1 imperfect:1 fraction:1 geneva:2 mentionned:1 speakable:1 broadcast:3 copy:7 bobs:4 than:18 intrinsically:2 albeit:1 kind:2 scheme:1 fuchs:4 second:2 distill:1 determined:1 contrary:1 ber:19 gives:1 result:2 mini:2 motivation:1 fashion:1 rewrite:1 sab:2 correction:2 qpa:3 curves:1 talking:1 say:3 need:4 seen:1 cumbersome:1 any:6 symmetrized:5 angle:1 bers:3 efficient:4 latter:2 note:7 instance:1 ideal:1 potential:1 generalized:1 techniques:1 channel:8 added:1 optimizes:1 shall:8 who:4 systems:1 singlet:1 most:2 letter:2 quantitative:1 nothing:1 inequalities:3 laboratories:1 salvail:1 clear:1 adopt:1 proceedings:1 points:3 principle:2 mechanical:1 hear:1 physics:2 sum:1 channels:1 laws:1 shor:2 intensity:15 show:2 violation:7 probe:26 king:1 find:6 ratio:1 popescu:3 parameters:3 representing:2 state:28 should:3 examples:1 only:22 bases:15 tape:1 pretty:5 attained:1 announce:2 circle:4 bernstein:1 interested:1 exchanged:1 do:5 his:4 goes:1 cryptography:5 get:6 dependent:1 de:3 overall:1 truly:1 joint:4 ones:1 words:1 new:1 resend:4 reveal:2 evolution:5 approach:1 arxiv:1 factorization:1 acknowledgments:1 she:13 though:1 switzerland:1 approaching:1 available:1 set:2 reference:3 undergoes:1 frame:2 testing:2 maximum:1 detection:2 see:8 computer:4 cloning:15 close:3 optimum:3 violates:1 analog:2 unsymmetrized:1 interacting:2 mabuchi:1 symmetric:3 initially:1 enough:4 various:6 between:14 conditions:1 sciences:1 recently:5 creating:2 vertical:1 qubits:10 however:12 gratefully:1 here:3 key:10 probing:1 percival:1 thank:1 both:18 cos:36 enables:1 prescription:1 many:1 extracts:1 termed:1 equal:3 players:1 figures:1 distinction:1 qubit:15 arbitrarily:1 ch:1 bell:11 simple:4 annual:1 ca:1 corresponds:2 scientifique:1 dimensional:7 directions:7 simply:5 moreover:4 fruitful:1 complication:1 described:8 raise:1 puts:1 basis:8 addition:1 arbitrary:1 three:2 been:1 strategy:31 cvitanovic:1 secret:7 much:3 itano:1 ph:1 abstract:1 fig:17 dots:1 refered:1 aj:2 corresponding:9 restrictions:1 sufficient:1 recherche:1 uqcm:10 lets:1 sae:2 stems:1 spin:1 former:1 present:1 case:12 multi:1 look:1 publicly:2 auxiliary:1 reliable:1 bb84:3 value:5 choices:3 aim:1 receive:1 while:8 optimization:2 cannot:2 error:12 fun:1 irrespective:1 35th:1 procedure:1 opt:2 unitary:9 dθ:1 von:2 thus:3 violating:1 reads:1 itself:3 fonds:1 interacts:1 monroe:1 different:3 perform:2 make:2 indistinguishable:3 same:17 poincar:7 checking:1 quant:1 copying:6 distilled:1 several:2 infer:1 higher:1 development:2 independent:4 used:10 parametrizes:1 keys:1 schumacher:1 effect:1 hand:2 moment:1 uses:5 uni:2 entanglement:2 highly:1 implement:1 identity:1 recent:1 off:1 acknowledge:1 epr:1 increases:1 non:1 dashed:3 swiss:1 position:1 paradigm:1 ekert:5 know:2 restore:1 protocol:6 just:2 less:5 being:1 distribute:2 rotated:2 obtain:4 relevant:2 questions:3 immediately:3 rotates:1 yet:1 amusingly:2 previous:2 disturbance:2 generator:1 density:16 point:2 seems:1 source:2 add:2 setting:1 nato:1 lett:6 easy:2 input:3 transformation:4 take:1 real:3 entangles:1 around:1 depends:2 represents:1 read:2 devised:1 possible:12 suspiciously:1 game:1 entangled:2 sanpera:1 press:1 using:10 bit:3 intersection:1 calculate:1 necessary:1 like:3 particle:2 alternatively:1 signal:1 alice:43 either:10 follows:2 setups:4 become:1 interestingly:1 terminology:1 copies:4 because:1 often:1 classical:14 people:1 sends:3 undistinguishable:1 some:7 b4:1 b1:1 choosing:2 respect:5 ourselves:1 reasons:1 fopt:1 avoid:3 measurements:9 best:2 everything:1 does:7 provides:3 assuming:3 analyzed:1 measuring:3 measures:2 equivalent:1 processing:5 bj:4 rue:1 step:1 although:2 explicitely:1 refers:1 hilbert:5 simpler:1 gained:2 about:9 simplest:1 eavesdropper:3 universe:1 discussed:1 o:2 practical:1 mutually:2 introduced:1 slightly:1 bloch:9 automatically:1 perturbed:3 cambridge:1 significant:1 wineland:1 communication:1 into:2 numerically:1 transformations:1 fidelities:1 perturbing:1 references:1 national:1 frames:2 reducing:2 neumann:2 forwarded:1 her:20 interacted:1 assumed:1 support:1 there:6 question:1 long:1 los:1 accordingly:1 low:4 way:7 ed:1 analyze:3 was:5 function:3 form:1 something:1 becoming:1 bite:1 but:15 cloned:2 link:1 gain:7 larger:2 line:5 true:1 copied:3 he:1 info:1 applying:1 calls:2 horodecki:3 wish:1 up:3 us:3 below:2 limit:5 qcm:1 problem:2 similar:4 called:2 gisin:1 mechanics:1 fulfills:1 later:1 associated:1 b2:1 probes:1 defined:4 universal:3 measure:7 direction:1 proven:1 general:9 peres:5 imagination:1 kimble:1 proves:1 violated:2 means:2 check:2 mutual:2 compared:1 dotted:3 no:7 amounts:2 extract:4 whereas:1 relax:1 when:12 meekhof:1 application:1 other:7 test:6 shrink:1 dashes:1 conclusion:1 poor:1 symposium:1 holt:1 users:2 vocabulary:1 lend:1 a1:2 a3:2 a2:2 a5:1 a4:2 vectors:2 prepares:1 sides:1 matrix:14 cryptographic:3 independently:4 implies:1 longer:1 algorithm:3 practically:1 assume:1 chsh:5 clauser:1 curve:5 together:1 having:1 equivalently:2 write:1 unspeakable:1 time:2 requires:3 original:10 restored:1 once:1
|
quant-ph9611042.txt |@word limited:1 managed:1 rev:2 results:3 existing:2 four:1 follow:5 ptt:1 careful:1 should:1 send:3 containing:1 environment:1 compensate:2 protocols:1 stable:3 sent:7 applied:1 advantage:1 orthogonal:3 very:9 differently:1 choice:2 electron:2 balancing:1 trough:1 experimentally:1 difference:1 cable:2 transmission:10 issue:1 t2:1 eve:6 large:1 small:1 glued:1 challenge:1 prevent:2 version:1 pms:1 till:1 pulse:14 discriminated:1 second:5 compensates:2 further:1 implemented:1 what:2 letts:2 rate:1 access:1 experiment:1 above:1 new:2 d1:1 waveguide:1 contrast:1 coefficient:1 exchange:3 respectively:2 modify:1 here:1 cancelled:1 kilometers:2 alone:1 path:11 constructive:2 change:2 obtained:4 sending:3 luther:2 incoming:5 sender:1 shift:2 losses:3 completely:1 leaving:1 usually:1 bob:35 makes:2 secure:2 extra:4 explained:1 ls:1 private:1 replace:2 herzog:1 apply:1 total:1 use:8 would:10 chooses:2 few:4 m1:11 therefore:4 m3:6 m2:9 encode:1 scope:1 type:1 more:3 knows:1 ecole:1 attenuates:1 factor:1 visibility:7 initiates:1 carrying:1 informally:1 known:4 aligned:1 states:3 middle:1 setup:9 work:1 morgan:2 following:1 arrive:2 example:1 control:4 modulation:1 figure:2 mirrors:9 bennett:3 implementations:2 high:2 times:1 information:9 needs:3 end:2 travel:1 means:1 american:1 delay:10 occuring:1 instead:1 ordinary:3 multiplexed:1 brassard:2 circular:1 23m:1 fr:3 may:2 after:2 different:7 applications:2 date:1 monitoring:1 horizontal:2 destructive:4 fm:5 short:3 attempt:1 remember:1 ss:1 light:9 ghz:1 patent:1 switch:1 cannot:3 so:4 keeps:1 order:8 pulsed:1 produces:1 telecom:4 indeed:3 over:3 choose:1 installed:1 stability:2 course:2 experiments:2 pulses:31 eavesdropping:4 still:1 its:1 before:3 group:1 monitor:1 shifts:3 chosen:1 interesting:2 ll:1 cryptology:1 detected:1 systems:10 couplers:1 main:2 pending:1 outside:1 eventually:1 them:5 good:3 similar:3 polarizations:2 practice:1 introduce:1 reciprocally:1 effects:5 they:3 arriving:2 nov:1 now:5 easily:3 february:1 lithium:1 modulator:5 pc2:1 preferable:1 university:1 synchronize:1 fringes:2 each:4 disregard:1 did:1 interfering:3 side:10 schemes:1 financial:1 another:2 reduce:1 t3:1 interferometer:8 attenuation:2 measure:2 quantum:11 wavelength:1 special:1 out:3 maximizes:1 shown:1 since:3 interference:13 looking:2 replacing:1 europhys:2 receiving:1 suffices:1 correct:1 shows:2 fiber:7 fluctuates:1 birefringence:8 seventh:1 standard:3 difficulty:1 reason:1 complicated:1 muller:4 r2:1 optics:1 could:6 keep:2 creates:1 length:3 consequence:1 first:10 major:1 already:2 features:1 encoding:3 reflected:6 huttner:3 channels:1 instances:1 done:1 fast:1 directly:2 carry:3 given:1 needed:1 system:14 their:4 wrapped:1 inconvenient:2 perfectly:2 bits:1 townsend:2 discussion:1 shifted:1 implements:2 way:2 geneva:4 sl:1 asymmetric:1 relative:3 exactly:3 tapster:1 part:7 kept:1 than:2 coefficients:1 albeit:1 scheme:2 unfortunately:2 double:1 require:4 see:2 rarity:1 modulators:2 were:1 enables:1 distinguished:1 randomly:2 say:1 need:8 seen:2 demonstration:2 any:8 paths:4 rochester:2 mostly:1 self:1 interferes:1 able:2 polarization:25 martinelli:1 ideal:1 simplified:1 detector:10 channel:1 play:5 towards:5 opposite:1 measures:2 most:4 regular:1 letter:2 preliminary:1 phase:39 acknowledgements:1 why:2 mach:2 average:1 later:1 detectors:1 optical:6 built:1 physics:1 fact:2 show:4 random:1 contemporary:1 discovered:1 fine:1 d0:12 piezoelectric:1 based:5 state:5 operational:1 being:1 only:7 going:6 essence:1 alde:1 do:5 his:1 goes:4 cryptography:3 get:4 dependent:4 beams:1 de:2 stop:1 da:3 ones:2 longest:1 altogether:1 timing:1 during:3 years:1 settings:4 arxiv:1 qc:6 paper:1 she:5 switzerland:2 through:4 arrival:1 reference:1 attenuated:2 detection:3 intensity:7 arm:4 fails:1 detect:2 pattern:1 currently:1 modulate:3 case:3 enough:2 various:3 between:9 tens:4 progress:1 preserve:2 gives:1 creating:2 vertical:2 betwen:1 commercial:1 weak:6 however:5 implementing:1 add:2 key:8 demonstrate:1 distribution:5 thank:1 concentrated:1 both:9 last:1 many:2 propagation:1 receiver:1 experimental:4 strongly:4 ch:1 cm:1 point:1 simple:1 corresponds:4 unprotected:1 simply:6 spans:1 cancel:1 moreover:2 telecommunications:1 conference:1 ensures:1 strong:4 tremendous:1 due:1 been:1 strategy:2 frs:1 secret:1 much:3 ph:1 prototype:1 fig:2 enable:1 tittel:1 suppress:2 coherence:1 photon:10 gap:1 ensuring:1 understand:1 c3:2 c2:5 c1:1 repetition:1 present:2 provably:1 p2:11 hughes:2 p1:11 laser:5 straight:1 bb84:1 value:2 choices:1 will:6 while:5 promising:1 rotator:1 irrespective:1 fms:1 couplings:1 opt:2 delaying:1 thus:5 marrone:1 coupler:10 lengthy:1 fibers:7 lengths:1 lett:3 same:11 φa:2 φb:2 parts:1 quant:1 split:4 schematic:1 gets:1 infer:1 independent:1 used:6 trivially:1 keys:2 zehnder:2 effect:3 kit:2 driven:1 moment:1 levels:1 changing:1 totally:1 implement:2 recent:2 relies:1 interferometers:4 tracking:1 off:1 reflection:2 fully:1 well:3 davis:1 without:3 components:2 swiss:1 possesses:1 usual:1 distances:2 protocol:1 proposed:1 transmitting:3 adjustments:2 obtain:7 front:1 thanks:1 immediately:1 rotates:1 macroscopic:1 yet:1 modulates:2 adding:2 except:1 signals:1 lets:1 other:1 attractive:1 versa:1 identical:2 around:1 rotators:2 possible:6 simmons:1 know:1 using:4 bit:4 divert:1 mod:2 multiplexing:2 insert:1 necessary:1 like:3 visible:1 follows:2 alice:41 transform:1 either:1 always:5 output:2 security:1 because:1 some:2 back:6 bounce:1 added:1 faraday:9 provided:1 scale:1 proceeding:1 lead:1 per:2 does:4 refer:1 measuring:1 noise:1 scientific:1 oscillating:1 rue:1 how:1 ratios:1 become:1 properties:1 stage:1 plug:6 about:3 working:1 eavesdropper:1 certainty:1 fringe:2 discussed:2 dependence:2 practical:4 carrier:1 ensure:1 discard:1 introduced:2 slightly:1 automatically:3 communication:2 into:5 within:3 three:1 down:1 references:1 niobate:1 mere:1 rely:3 her:3 transfer:1 support:1 there:1 reduction:1 long:6 start:1 low:1 fraction:1 call:1 was:4 1khz:1 delayed:4 but:7 alway:1 encoded:5 line:9 proposal:1 he:2 count:4 attenuate:1 up:1 us:3 fluctuations:1 problem:1 pm:8 minutes:1 called:2 gisin:4 mechanics:1 khz:1 stronger:2 abstract:1 mirror:2 general:1 peres:1 single:4 our:7 corresponding:2 cables:2 simplest:1 again:2 nm:2 no:9 air:1 ekert:2 when:1 ny:1 setting:1 spatial:2 users:1 separate:1 distance:1 interferometric:2 palma:1 allowing:1 cryptographic:3 zbinden:3 coupling:1 vice:1 time:11 dyer:1 requires:1 original:1
|
quant-ph9611043.txt |@word limited:1 secondly:1 dynamic:1 four:1 ginzburg:1 localized:3 factorizing:1 whose:7 feeding:2 aug:1 baym:2 under:4 rise:4 every:1 figs:3 affect:1 basics:1 called:8 ref:1 solution:11 solid:1 vector:5 markov:10 consistent:4 approximation:26 second:6 rigorous:1 qualitatively:1 estimated:1 even:1 interatomic:3 trapping:13 qsde:1 consequent:1 above:6 new:2 net:1 ever:1 t1234:6 coefficient:3 simultaneously:2 behavior:4 equals:1 here:8 atoms:17 met:1 represented:1 path:3 interpret:2 obtained:3 balance:1 study:1 changed:1 fourier:1 changes:4 projection:3 replace:1 nk1:3 nk2:2 nk3:3 total:10 would:5 e1:1 statevector:1 call:5 therefore:1 e2:1 type:1 separated:3 odinger:2 berlin:2 correspondingly:2 kgl:1 must:16 springer:3 uehling:17 permits:1 work:5 iheff:1 burnett:6 example:5 griffin:3 give:12 involve:4 indicates:1 want:6 keep:1 provide:2 how:1 methodology:1 adjacent:1 significance:2 description:28 replacing:1 diagram:1 davis:1 third:1 summing:1 maintain:1 green:1 correlation:10 sackett:2 order:16 interpretation:2 kampen:2 over:14 satisfied:5 satisfies:1 before:2 fiz:1 exhibits:1 production:1 fig:5 overcome:1 snoke:4 eventually:2 them:4 amenable:1 band:15 effects:6 they:4 represents:2 each:12 side:2 mean:13 financial:1 used:9 substantially:1 borne:1 restricted:1 particles:17 ri:1 linear:1 gardiner:6 midpoint:1 little:2 free:5 standard:1 formation:4 estimate:3 universally:1 starts:1 corrections:1 onto:3 already:3 restrict:1 ensher:2 another:1 clarity:1 illustrate:2 similarly:2 approximately:3 needed:2 master:37 observations:1 leggett:2 somewhat:1 distance:1 eq1:1 approximations:7 zero:12 project:1 enables:2 boston:2 modern:1 mind:1 spectrum:4 manner:1 increment:1 seen:5 seem:1 relatively:1 chem:1 genuine:3 convenient:1 responsible:1 shall:3 effective:1 victoria:1 boltzmann:24 involving:1 phase:25 zealand:1 chemistry:1 sum:1 dover:1 signatures:1 nπ:2 labels:1 iǫ:1 solutions:5 substituting:1 d3:80 41a:2 41b:2 41c:2 situations:3 do:8 dk:3 preferred:1 dx:1 dw:10 dt:9 carmichael:1 traverses:1 textbooks:1 twice:1 pitaevskii:7 traverse:1 depends:2 result:10 discussions:1 best:3 techniques:1 erez:1 symmetric:1 µn:2 simplest:1 conceptual:1 approach:1 preserve:2 terms:55 nature:4 wn:11 weak:11 however:14 ws:8 extent:5 bose:53 essentially:10 uncertainty:2 variance:1 contribution:2 regarded:1 andrews:3 presumably:1 factorize:1 broadening:3 basis:2 simplification:1 three:7 been:10 much:11 interest:4 basic:4 expected:2 quantities:4 concerning:1 chui:1 coherent:15 spin:1 applied:2 heidelberg:2 near:1 suppose:3 aid:1 property:2 leaves:1 procedure:4 phenomenological:1 iv:4 ii:3 characterize:1 ik:6 smoothest:1 disappear:1 make:6 quant:1 grows:1 independent:2 orderung:1 trajectories:1 hand:3 potentials:1 hartree:1 normalization:3 weakly:7 kept:1 academic:2 contact:1 left:1 unified:1 lc3:3 just:1 bandwidth:3 transforms:2 scattering:21 eigenstates:4 divide:1 adding:1 infinitely:1 cornell:2 ease:1 spread:2 easy:3 opt:2 bands:10 innsbruck:2 possible:6 unique:2 apart:3 appearing:1 ψk2:2 ψk1:1 specific:1 steps:1 arbitrary:1 ıctor:1 wavepackets:3 deal:3 successfully:1 born:8 separately:2 cooper:2 undisturbed:1 contributing:1 shlyapnikov:3 2µk:1 permitted:2 proceed:1 zur:1 42m:1 wavelets:2 o:6 ensure:1 efforts:1 slightly:1 considerations:2 soc:2 markovian:2 presence:2 bath:5 sov:2 amsterdam:1 often:1 support:1 initial:4 approximate:6 dzyaloshinski:1 width:2 anderson:1 conservation:3 physicists:1 way:3 was:6 medium:1 form:18 differences:1 δkk:4 drummond:2 heat:3 true:3 builds:1 versions:2 inside:4 maximum:1 discretized:1 stages:1 computing:1 covers:1 conserved:4 exist:1 simulations:1 distributions:3 physical:5 ni:5 nk:2 no:16 na:6 whereas:1 wavefunction:8 when:11 vanishes:2 ny:1 setting:1 role:5 picture:2 variable:1 longer:2 assume:9 dτ:4 interval:1 packets:1 together:1 time:24 n1:8 n2:12 n3:12 n4:12 lett:18 particular:4 leads:5 roy:1 inverse:2 depend:1 semikoz:1 technique:1 ıa:1 finally:5 analogous:3 division:1 charles:1 orthogonal:2 frequencies:7 none:1 choice:1 refractive:1 exact:9 preuss:1 presented:1 dodd:2 discrete:3 team:1 der:1 upper:3 dealing:1 ρa3:1 appear:3 evaporative:1 current:5 lifshitz:2 appeal:1 appears:2 change:10 box:3 52a:1 52b:1 shift:3 πu2:2 simultaneous:1 commutators:1 spatially:2 inducing:1 projector:3 positive:1 only:29 criteria:1 scope:1 theoretical:4 validity:11 cases:7 insights:1 modified:1 fock:1 values:1 following:1 making:1 arrive:1 grained:3 degenerate:1 sitzungsber:1 occur:5 verlag:1 divided:1 orthogonality:1 write:14 parameter:1 product:1 may:2 applications:2 produce:1 data:2 grow:1 times:4 kurn:3 natural:3 explicit:2 st:1 so:34 definitions:2 typical:7 indeed:1 years:1 course:7 experiments:4 statistical:5 still:2 derive:9 thank:1 jin:1 interesting:1 main:2 non:21 mølmer:1 processes:13 introduce:6 eµ:8 nov:1 now:19 nor:1 matched:1 ωk3:3 ωk2:7 term:38 name:1 drop:2 arrows:1 establishing:1 realistic:6 entirely:1 ei:6 significantly:2 populated:1 gaussian:4 bradley:1 inhomogeneous:1 wavelength:6 approximated:2 eq:10 shown:4 space:35 furthermore:1 collisions:19 correct:2 shows:1 theory:25 possibility:1 quite:2 complicated:1 e4:1 remainder:2 e3:1 care:1 derivation:14 transition:4 motion:11 turn:2 place:2 neglect:7 first:7 intuition:2 simplifies:1 symmetry:10 ignored:1 variables:1 xg:1 transform:2 simplified:7 gases:3 carry:1 impossible:1 open:1 size:17 given:28 necessarily:3 theoretische:1 cooling:1 white:1 williams:1 gives:10 nordheim:2 fraction:2 continuous:3 artifact:1 x2:7 eliminated:3 x1:6 than:16 wide:1 impractical:1 unfortunately:1 require:3 transferred:2 superfluid:1 future:2 were:1 correction:1 argument:1 generalization:3 say:1 any:9 downwards:1 ideas:3 note:3 ideal:2 potential:22 take:2 wanting:1 sect:2 trace:1 opposite:1 considered:4 average:2 later:2 typically:1 quantity:1 precise:2 spaced:1 show:8 delta:6 contemporary:1 threshold:1 proportion:1 state:10 quasiparticles:1 explicitly:4 essence:1 coherences:2 get:13 straightforwardly:2 truly:1 cannot:4 clearest:1 druten:3 yield:1 summary:1 mewes:3 kernel:1 parkins:1 physically:2 namely:1 differentiable:2 ignores:1 diagonally:1 commutation:2 subsequent:2 label:1 outside:3 between:26 justified:2 notice:6 condensing:2 houbiers:1 jk:9 jetp:3 come:1 vk1:1 pertain:1 according:2 contract:1 laplace:3 propagation:1 expression:1 comes:2 hvk:1 overview:1 associated:6 considering:1 145b:1 capable:1 invert:1 mark:1 fk:18 6a:9 6b:1 6c:1 careful:1 those:5 case:11 developing:1 yakhot:1 single:6 many:3 situation:14 eik:5 vk2:1 helium:1 binary:1 different:16 develop:8 same:19 shifts:3 arguments:3 regime:9 events:1 extended:1 trivially:1 relies:1 modes:11 largely:2 wellington:1 without:5 solve:1 components:1 liouvillian:2 coordinate:5 dimension:2 being:5 generally:1 guided:1 valuable:1 aspect:2 speed:1 guides:1 gdn:1 zoller:4 seems:1 except:2 interested:3 treatment:8 momentum:50 ross:1 aspects:5 eigenvalue:2 thermalized:3 sums:2 vacuum:1 confined:1 using:12 accepted:2 particle:15 reduces:2 either:3 integrals:1 always:2 stationary:14 specified:2 matching:3 nonzero:2 provided:1 provides:2 refer:1 process:5 equivalent:2 wavefunctions:3 inherent:2 refers:1 comparison:1 central:1 instantaneously:1 discussed:1 obeys:1 uhlenbeck:17 cambridge:4 spreading:7 garc:1 references:2 inverting:1 einstein:8 elementary:1 log:1 refinements:1 there:24 low:4 assumes:4 tight:1 complete:3 regard:1 dissipative:3 factorized:4 applying:1 quantitatively:1 ωi:1 ωk:4 semiclass:1 ωe:9 obtains:1 detailed:2 diverges:1 certain:1 ak:4 describe:5 am:1 resultant:1 examine:1 governed:1 formulation:8 encompass:1 moves:1 nonhermitian:2 dalfovo:1 again:1 completeness:1 field:14 valid:16 spatial:6 mathematics:1 you:3 separate:1 includes:5 deriving:5 commutator:5 bounded:1 included:4 m18:1 delineate:1 condensation:30 mass:1 decoherence:1 resolution:3 original:3 represent:3 consider:7 caused:1 follow:2 content:1 preserves:1 illustrates:1 tr:4 nonlocal:1 preserved:2 stochastic:15 belonging:1 straightforward:2 very:24 levich:1 difference:3 condition:18 treating:1 induced:1 hamiltonian:6 applicable:1 large:9 small:7 l3:1 go:1 rate:1 invention:1 canonical:4 what:6 nonlinear:2 stoof:3 section:3 localization:1 version:2 ballagh:1 method:6 contrast:1 2kt:1 edited:1 condensed:5 full:8 component:1 ranges:5 ansatz:2 irrespective:1 strong:5 equations:9 ruprecht:3 δqi:3 requiring:1 summations:1 esry:1 readily:2 conventional:1 takes:4 probabilities:1 contains:3 ψk:67 ψn:10 taken:2 minor:1 more:10 operators:15 varying:3 known:4 evolves:1 keeping:1 quantized:2 science:1 equation:113 compare:2 stated:2 states:9 collision:16 numbers:8 arise:5 sharp:2 goal:1 rather:4 acts:2 e2i:1 simplicity:3 algebra:1 derived:6 treatments:2 reflect:1 coming:1 horizontal:1 derives:1 short:2 negligible:8 specifying:1 fundamental:1 2u:2 developed:5 2πkt:1 held:1 thermal:12 paper:17 through:4 y1:9 existence:1 kinetic:34 y2:9 its:4 discretizing:2 rapidly:1 sodium:2 energies:1 actually:1 absence:2 systems:4 might:1 finer:2 wieman:2 oxford:1 yu:4 smoothness:2 bigger:1 easily:2 designation:1 fully:2 level:6 factorizable:1 2g:2 2a:1 2m:20 universit:1 energy:18 idea:3 investigated:1 expect:2 quantum:92 really:3 ketterle:3 since:13 projected:3 denoted:1 δrr:2 issue:1 occurs:2 found:1 difficulty:2 multifield:1 put:2 matthews:2 generate:1 definition:5 retained:1 persists:1 integrand:2 major:4 excitonic:1 probability:5 lovelace:1 ql2:11 number:15 smaller:2 done:2 perturbation:1 temperature:5 forschung:1 introduction:2 leading:3 smoother:1 least:1 assumption:13 rates:3 molecular:3 too:1 trapped:1 akad:1 optical:2 wissenschaftlichen:1 schr:2 peaked:1 kind:8 treated:4 77e:4 77a:5 77b:1 lim:1 lin:1 k3:37 k2:80 k1:67 analogy:1 k4:31 stringari:5 play:3 added:1 goldman:1 measures:1 most:3 significant:6 extremely:1 clear:2 broadened:2 part:7 qbe:1 exp:7 kt:21 velocity:3 kx:1 physics:7 wavenumber:1 ambiguities:1 pethick:1 relation:4 find:10 occupation:8 wolfe:3 assertion:1 factor:3 notation:1 dependent:1 rest:1 λmfp:8 resolve:1 continuum:1 arxiv:1 factorization:3 ik3:2 ik2:1 ik1:1 set:9 ik4:2 unpublished:2 see:16 sec:8 descriptions:1 close:2 forthcoming:2 mechanically:1 uδ:2 various:2 conditions:7 available:1 creating:1 iπδ:1 vanishing:1 preprint:3 phasespace:1 luiten:1 both:5 last:5 tkachev:1 hki:1 whole:2 finds:1 experimental:1 point:6 simple:7 corresponds:6 dimensional:2 simply:2 indefinite:1 described:3 dum:1 due:2 describes:5 initiation:1 coarse:5 combine:1 ph:1 pn:13 pm:2 addison:1 gas:13 fund:1 understand:1 p2:1 indefinitely:1 siggia:1 expanded:1 evaluated:1 while:7 replaced:2 compactness:1 evaluating:1 hωk:2 resolved:3 vol:1 itself:4 kikuchi:1 vanish:5 stimulated:1 widely:1 grand:3 modification:3 composition:1 higher:3 literature:1 levels:9 appreciable:1 recent:3 lower:2 analysis:1 obviously:5 redistribution:1 λt:7 shape:2 intervals:1 atomic:7 useful:1 cut:2 kluwer:1 conclusions:1 source:1 location:1 remaining:1 lacking:1 silvera:1 projects:1 formal:1 modifications:3 δx:3 follows:4 microcanonical:1 manifest:1 ignore:1 yields:5 essential:3 mathematical:1 methods:8 creation:3 some:6 back:1 streaming:10 michinel:1 scale:3 describing:3 though:2 integration:2 per:3 connecting:3 eliminate:1 proc:1 jumps:2 simulation:2 range:12 extensions:1 bloch:1 incoherence:2 into:19 within:10 integral:7 predictions:1 appropriate:6 proportional:4 uncertainties:2 statistics:3 institut:1 question:1 long:3 u2:3 λ3t:1 handbook:1 kagan:4 forward:11 sections:1 considerably:3 elsewhere:1 sde:1 atom:7 line:6 durfee:3 intuitive:1 characteristic:5 up:5 us:4 ur:1 ue:16 fluctuations:1 ug:5 similar:4 ki:1 sometimes:1 constant:1 defined:12 chan:1 chap:1 formalism:2 jaksch:1 amounts:1 edwards:4 thanks:1 invalid:1 application:2 department:1 elements:3 excitation:2 gross:6 develops:1 sides:1 structure:2 multimode:1 independently:1 implies:2 required:3 kinetics:7 graining:2 far:1 requires:4 magnetically:1 gp:2 results:5 eds:1 lewenstein:3 intricate:1 contributions:2 centers:1 issues:1 include:2 random:1 implicitly:1 wave:5 wishes:1 incoherent:8 notes:1 trb:2 deals:2 dealt:2 manifestly:1 eigenvalues:4 optics:5 configurations:3 dilute:4 zh:1 carter:2 jump:3 imply:1 insertion:1 manipulating:1 dynamics:10 eik2:1 eik1:1 dψ0:1 index:1 plays:2 giving:3 cell:20 consistently:1 experiment:2 3c:1 3a:2 justification:3 degree:1 eksp:1 spacing:2 objects:1 focused:1 separation:3 extreme:2 great:3 technical:2 involved:1 larger:4 leaving:1 resulting:1 makes:1 involves:1 composed:2 formulated:4 clark:2 nearest:1 castin:2 austria:1 names:1 summation:1 use:10 next:1 few:2 themselves:1 hulet:2 becomes:6 normalized:1 iii:4 account:3 ρb:4 integrating:1 ρs:1 obvious:2 averages:4 proof:1 decorrelation:1 calculation:1 proportions:1 purposes:1 high:1 effectively:1 assumptions:1 something:2 reynolds:1 instead:1 sin:4 philosophy:2 factored:1 physik:1 computations:1 correspond:1 element:1 discussion:1 nonequilibrium:1 wigner:11 including:3 perfect:1 chemical:2 outer:1 lc:21 decay:2 chosen:3 h2:12 lt:3 choose:5 pergamon:1 covered:1 defining:1 greater:5 practice:3 landau:1 day:1 university:3 sufficiently:3 magnitude:9 l2:8 trap:9 identifies:1 homogeneous:1 related:1 operator:30 frequency:1 measure:1 multiparticle:1 our:14 transitions:6 out:5 matrix:6 rev:37 chaos:3 postpone:1 cause:2 math:1 interactions:3 diagonal:12 completely:1 thrust:1 region:3 likelihood:1 interaction:8 could:3 feasible:1 length:7 derivations:2 assumed:2 hence:1 teor:1 dispersive:1 publication:1 condensate:43 system:18 relations:1 their:3 intermediate:2 townsend:2 exactly:4 reflecting:1 holland:5 bec:4 submitted:1 limiting:5 appealing:1 amplitude:2 sw:1 unchanged:1 factorizations:1 delineated:1 need:2 constrained:1 demonstration:1 clearly:5 viewed:4 angle:1 studying:1 able:4 heff:4 heisenberg:1 lectures:1 unless:4 rearrange:1 walraven:2 connected:1 but:26 gorkov:1 neighboring:1 stronger:1 hi:9 mechanical:14 normally:4 fact:8 supported:1 purely:4 svistunov:2 trivial:1 principal:1 kadanoff:1 based:7 irreversible:1 should:9 dalibard:2 quasimomentum:1 employed:2 marsden:1 local:5 achieve:1 equilibrium:13 cube:1 means:10 familiar:3 joint:1 exchanges:3 osterreichische:1 collisional:4 evolution:8 differential:3 contain:2 view:4 requirement:6 correlations:2 packet:1 usefulness:1 interacting:9 surkov:1 wiss:1 written:10 wavelet:16 closed:3 understood:1 reproduces:1 key:2 lb:9 configuration:6 problem:8 taking:3 la:10 equal:2 hω:2 figures:1 regimes:1 otherwise:1 relevant:2 huang:1 cirac:2 respect:1 addition:2 slowly:2 treat:3 define:8 arises:8 corresponding:10 finishes:1 sufficient:1 coherence:6 subspace:1 present:4 laser:3 discretely:1 value:9 will:59 revisited:1 abrikosov:1 almost:2 vi:1 vk:13 thus:30 vm:16 vn:41 vt:3 fonds:1 conserve:1 cross:1 parts:9 wavepacket:8 largest:2 finite:1 difficult:1 guises:1 infinity:1 conceived:1 effect:3 infinite:3 identity:1 destruction:4 off:1 nevertheless:2 modeled:1 well:11 thought:1 firstly:1 position:7 fk2:9 fk3:9 arising:6 usual:5 less:5 accurate:2 obtain:1 momenta:5 bogoliubov:3 vτ:1 density:31 add:1 extends:1 attractive:1 identical:1 ωk1:6 press:4 loss:5 necessary:7 like:9 success:1 qualitative:1 δr:1 δp:3 alkali:1 δk:3 become:6 replacement:1 because:9 classical:2 smoothly:1 phenomena:1 growth:4 warmer:1 convex:1 huse:1 transport:12 lead:1 broad:2 avoid:1 instantaneous:1 does:7 assuming:10 mode:3 noise:5 slight:1 expansion:3 wesley:1 although:4 stage:1 about:2 extension:2 introduces:1 dependence:3 carries:1 projectors:2 previously:1 h3:3 h0:2 sharpness:1 bosonic:2 mere:1 van:5 transfer:2 quanta:3 naturally:3 function:33 north:1 ht:2 volume:7 hk:1 construction:2 gain:8 hm:1 hb:5 hc:5 ha:10 hf:4 illustrative:1 made:5 temp:1 whether:1 wish:1 cells:20 smooth:5 below:5 projecting:1 limit:4 distribution:17 mechanics:7 contribute:1 ing:1 happen:1 functions:21 compared:4 other:14 conclusion:1 expressible:1 kirkwood:1 acknowledgment:1 factors:1 determination:1
|
quant-ph9611044.txt |@word represent:2 transitions:3 consider:3 ron:7 rev:9 lack:1 results:10 leads:3 controversial:1 go:2 dα:1 factorizing:2 relationships:1 whose:3 preserves:1 depend:2 superpositions:1 subjected:1 tr:1 presents:1 lower:1 finally:5 compensate:1 helps:2 a27:1 stable:9 stochastic:1 anharmonic:16 must:1 presentation:1 worth:1 versus:1 evolves:2 very:9 frequencies:2 keeping:1 semi:1 wave:9 electron:3 variance:4 exact:4 fakult:1 condition:2 portugal:1 level:3 positions:2 notes:1 solution:4 damped:9 large:9 solved:1 variances:1 small:4 markov:1 optics:4 attracting:2 prevent:1 zn:1 smaller:4 force:3 dealing:1 consistent:2 estimates:1 modified:1 approximation:4 second:3 perspective:1 equal:1 further:5 dynamics:9 situated:1 linear:1 even:5 what:2 nonlinear:2 appear:1 rate:4 brackets:1 itˆ:1 section:7 brief:1 experiment:12 localized:7 above:2 capital:1 new:5 method:6 relaxation:3 satisfy:2 justification:2 mechanisms:2 human:1 never:2 κa:3 here:6 understanding:2 behaviour:7 fairly:1 situation:3 represented:3 along:2 coupling:1 equations:3 appears:2 extreme:1 obtained:4 great:1 property:1 involved:1 study:5 larger:8 allows:5 ignoring:1 amount:1 real:2 resonance:1 therein:1 studies:1 holmes:1 schack:2 useful:1 scales:1 suddenly:2 addressed:1 localizes:1 apply:2 environment:2 use:3 takes:1 would:2 commun:4 distinct:2 positive:1 coupled:3 quasi:1 intense:3 classically:4 depicted:2 tm:7 taken:3 stage:1 type:1 theoretical:1 more:5 introducing:4 artner:1 becomes:2 operators:2 under:3 clue:1 introduces:2 berlin:1 transient:3 observing:1 particular:7 known:3 cases:3 iii:2 insights:1 ρa:1 states:8 account:1 crosses:1 decay:5 equation:15 oscillator:22 ρl:2 reproduce:1 remain:1 examined:1 values:11 three:5 evolved:1 cal:1 following:7 making:1 example:5 stimulating:1 initial:4 transition:46 figure:12 give:1 process:2 relativistic:2 organized:1 involve:2 minimum:1 furtado:1 hides:1 sense:2 spanning:1 simulation:3 occur:1 simple:1 tseng:1 motion:8 united:1 monitoring:3 recovery:1 provide:2 discussion:2 feature:1 regions:1 how:3 ramped:1 pure:4 answer:1 parameter:2 ensemble:9 simplicity:1 pleasure:1 description:11 udiger:1 reconciled:1 after:4 derived:2 jump:2 freiburg:2 jumping:1 induce:1 physik:1 choice:1 reconciles:1 varied:1 realized:1 short:1 physical:6 dynamical:4 third:1 light:1 explicit:1 deutsche:1 complexity:1 so:4 automatically:1 fundamental:2 correlation:1 representation:4 praxis:1 order:10 typical:2 restriction:1 interpretation:1 help:1 reservoir:2 produces:2 numbers:1 over:12 move:1 characteristic:3 stability:2 thermal:5 paper:4 london:1 statistical:3 satisfies:1 still:3 its:12 before:3 observational:3 delay:9 a28:2 lc:1 located:1 chosen:4 continued:1 solving:2 lj:12 expectations:3 exhibits:4 destroyed:3 attraction:3 absence:2 nonmarkovian:1 systems:11 hidden:3 carmichael:1 might:2 setting:1 outside:2 maximal:1 them:2 good:1 motivated:1 combination:1 delocalization:1 numerically:1 evolution:12 introduce:2 landau:1 framework:1 walls:9 effects:3 they:7 sweeping:1 nov:1 now:2 bigger:1 represents:6 finite:2 always:3 university:1 presented:3 sufficiently:1 trap:3 reasonable:1 each:2 2m:1 universit:1 mean:35 domain:7 differential:2 financial:2 evolve:1 doing:1 series:2 hypergeometric:2 related:3 used:9 expect:1 measurement:17 quantum:89 our:4 avoided:1 nonlinearities:1 event:1 neighbourhood:1 out:2 shown:5 matrix:3 driving:9 space:8 furthermore:4 since:2 crucial:1 chaos:3 diffusive:2 re:1 dominated:1 lecture:1 induced:2 ref:1 correct:3 math:1 shows:7 occurs:3 numerical:1 theory:8 barrier:2 localization:3 mω:1 given:7 possibility:1 approaches:1 york:2 milburn:2 rigo:2 interaction:1 regarding:1 starts:3 bistability:29 times:7 counterpart:2 turn:1 place:1 nondemolition:1 assumed:1 hence:3 experimenter:2 neglected:2 programme:2 neglect:1 first:5 origin:4 already:1 perturb:1 variables:1 number:18 theoretische:1 clear:1 alternatively:1 fast:1 knight:1 neighborhood:1 precisely:1 open:5 appl:1 size:2 dispersive:2 properties:2 publication:1 needed:1 introduction:1 leading:2 system:33 approximately:1 their:2 intermediate:3 master:6 linearities:1 realization:3 fmf:1 rates:2 egham:1 frame:1 recovered:4 gives:4 fraction:1 a34:1 centered:3 tool:1 continuous:3 todd:1 forschungsgemeinschaft:1 quan:1 opti:1 representing:1 than:16 coefficients:1 cheng:2 diffusion:6 observed:5 sections:1 approximations:2 zero:3 limiting:2 project:1 mobility:1 appealing:1 a42:1 speaking:1 amplitude:5 tackled:1 toward:1 a48:1 descriptions:1 exhibit:4 fig:6 sees:1 fluctuation:2 dynamically:1 spectrum:1 spent:1 eqn:1 width:8 emphasizing:1 close:1 seen:2 confirms:1 border:1 any:11 viewed:1 strength:2 depending:3 anharmonicity:5 self:1 able:1 mechanism:1 oriented:1 instance:1 high:4 potential:1 generalized:1 analogy:2 kaplan:1 haake:1 switching:3 towards:3 trace:1 opposite:2 measures:1 sequence:1 most:1 germany:1 but:11 an2:1 quantitative:1 phase:8 measured:4 why:1 observation:6 considered:5 average:1 later:1 steady:18 physica:1 possesses:1 optical:4 principle:1 mechanical:4 penning:3 positivity:1 fact:1 surrey:1 show:6 text:1 random:3 rotating:3 purely:2 solutions:4 carefully:1 schenzle:1 line:6 aρ:1 q2:2 just:1 parameters:13 situations:1 written:1 should:4 being:1 only:10 explicitly:1 specify:1 acknowledge:2 integrable:1 local:2 equilibrium:34 goes:1 distance:2 dependent:1 luke:1 between:21 dykman:1 expectation:4 cannot:1 photoelectric:1 expresses:1 during:2 dt:7 holloway:1 infrequent:1 processes:5 percival:6 upper:1 conditions:6 arxiv:1 wiener:1 yield:1 summary:1 twice:1 experiments:2 double:1 analytical:3 through:2 fixed:2 valid:4 view:2 set:4 computed:4 clarified:1 δjk:1 correlations:4 uses:2 packet:8 detection:2 depends:3 individual:4 result:21 localize:2 discussions:1 terms:1 reversed:2 springer:1 subject:1 overlapping:1 said:1 mechanically:1 resonantly:2 review:1 ralph:1 consequence:2 artificial:1 tend:1 state:42 various:1 correctly:1 simplest:1 approach:3 email:1 preserve:1 notice:3 realizations:1 recently:4 a40:1 relative:2 nature:1 initially:4 however:2 continuously:1 reproduces:2 tum:1 extent:1 demonstrate:1 distinguish:2 come:1 problem:1 both:3 a104:1 instant:1 reverse:1 limits:1 gratefully:1 mono:1 region:4 density:6 according:7 acknowledged:1 called:3 fulfilled:1 connection:1 context:3 distinction:3 gisin:4 expression:2 experimental:4 minima:1 relevant:2 point:20 reasons:1 address:1 period:3 simply:2 assertions:1 away:4 respect:2 strong:1 described:5 basis:1 addition:1 trajectory:10 ing:1 due:4 been:14 alicki:1 detuning:18 describes:3 damping:3 interest:3 expected:4 ph:1 prototype:1 define:2 wants:1 direction:2 corresponding:2 qsd:31 am:2 photon:6 coherent:6 observe:4 understand:2 xxi:1 former:1 present:1 case:4 exponential:1 pacs:1 crossed:1 value:8 will:12 while:3 harmonic:1 behavior:1 applies:1 exist:1 tunneling:4 mota:1 a25:1 vogel:3 played:2 phenomenological:1 vi:1 thus:10 non:2 iv:3 ii:3 characterize:2 reads:2 fluctuating:1 im:2 vanish:1 different:6 moves:1 verified:1 anymore:1 approximatively:1 acknowledgments:1 make:2 lett:3 same:4 clearly:2 shorter:3 complex:4 quant:1 widely:1 several:2 independent:1 investigated:2 see:6 trajectories:7 upon:3 effect:6 hysteresis:21 driven:15 moving:1 recover:1 changing:1 a52:1 gauss:1 center:1 tecnologica:1 disappears:1 no:5 well:7 roughly:2 analysis:1 academic:1 de:1 without:2 temperature:2 position:8 model:15 latter:1 proposed:1 less:3 moments:1 accurate:1 obtain:4 valuable:1 fluctuates:1 atomic:2 predicts:1 part:3 mahony:1 followed:1 rotation:1 previous:3 nicolas:1 conclusions:1 archetypical:1 royal:1 ideal:5 nacional:1 gabrielse:2 source:4 other:13 combine:1 questioned:1 relevance:1 extensive:1 wiseman:1 momentum:7 divided:1 kingdom:1 iκ:1 aspects:2 around:6 easily:2 quasidistribution:1 big:1 showing:8 possible:3 corresponds:3 know:1 press:1 using:7 emergence:3 accepted:1 occurring:1 bistable:16 like:3 particle:2 follows:1 qualitative:2 adiabatic:2 brun:2 a26:2 continue:1 unstable:4 either:2 arbitrary:1 become:1 stationary:2 quantal:1 accessible:2 right:1 often:1 classical:52 smoothly:1 creation:1 phenomena:1 back:1 calculated:1 equivalent:2 choosing:1 unraveling:1 neglecting:1 practical:1 happens:1 provided:3 vol:1 scale:4 describing:1 a13:1 confirm:3 support:2 electromagnetic:1 measurements:1 langevin:1 integration:2 does:15 exit:1 provides:1 tends:1 lifshitz:1 demonstrated:1 mode:1 noise:1 performed:3 jumps:3 agreement:1 step:3 instability:1 periodically:1 bz:1 projector:1 carried:3 discussed:1 o:2 alber:2 compatible:1 remains:2 range:1 act:1 mixed:1 introduced:2 spiller:1 gamma:1 exactly:1 final:1 pergamon:1 into:4 within:2 obtaining:1 bath:2 appropriate:1 because:3 references:1 determine:1 operator:7 next:1 classicality:1 deal:1 waits:1 fluctuate:1 strictly:1 there:3 question:2 tw20:1 long:4 spread:2 much:13 low:6 way:3 delocalized:1 was:2 garraway:1 function:3 form:1 enough:2 metastable:1 some:3 differences:1 drummond:8 lindblad:4 dissipative:18 basin:3 dξk:2 dξj:5 full:3 whether:3 wish:1 inside:1 take:3 up:1 us:3 ur:1 placed:1 frequency:9 limit:13 uk:1 ωa:1 fluctuations:28 distribution:1 similar:2 display:2 regimes:1 mechanics:3 dots:1 ac:1 b60:1 associated:2 lowering:1 defined:1 decreases:1 describe:14 influence:1 general:2 dξ:2 eu:1 single:6 eigenfrequency:1 simulations:1 hamiltonian:4 check:1 regime:5 physics:2 again:2 functions:3 compared:7 entirely:1 dotted:3 variety:1 whereas:1 when:11 detail:1 junta:1 field:5 points:20 role:2 special:1 investigations:1 papers:1 department:1 mathematics:1 explains:1 optically:1 briefly:1 excitation:21 savage:3 preceding:1 problems:1 includes:2 a2:4 bounded:1 dissipation:2 risken:4 m18:1 sides:1 longer:5 dψ:1 assume:2 typically:1 curve:4 mass:1 time:71 far:2 determination:1 integrates:1 once:3
|
quant-ph9611045.txt |@word limited:1 saturating:1 interference:3 four:4 consists:2 localized:3 forget:1 whose:4 γt:12 γm:1 under:5 lore:2 worth:1 every:2 govern:1 overcomes:1 affect:2 logarithmically:1 solution:2 ups:1 force:8 consistent:1 direct:2 approximation:2 likely:1 qualitatively:2 even:16 established:2 specification:1 8m:2 above:4 suppose:1 increasing:3 consisting:1 κn:5 evanescent:1 behavior:2 here:6 possibility:1 path:7 eliciting:1 logarithmic:2 obtained:3 study:3 changed:2 completely:3 natures:1 fourier:4 york:2 explained:1 plenum:1 highly:1 modulated:1 total:1 propagators:3 linearly:3 derivatives:1 would:6 cirac:3 chooses:1 definiteness:1 noting:1 kinematics:1 therefore:15 survive:1 tell:1 γl:9 odinger:9 aware:1 hold:1 must:4 permits:1 schmiedmayer:1 work:4 temperatures:13 endow:1 example:10 kσ:1 give:1 relativistic:1 involve:2 keep:4 advancing:1 guarantee:1 end:2 provide:1 feature:1 far:7 significance:1 ordinary:1 oscillatory:2 oscillators:3 demanding:1 lay:1 quadratically:4 summarize:1 effective:5 wint:4 correlation:1 order:17 origin:3 interpretation:2 over:12 vary:1 expects:1 before:3 heretofore:1 fix:1 writing:1 production:1 differently:2 easier:1 versus:2 them:6 combination:2 amenable:1 effects:4 they:6 represents:3 overdamped:2 reasonably:1 each:7 d40:1 d47:1 mean:3 successively:1 independent:8 series:2 principles:5 literature:2 laboratory:2 borne:1 quantify:1 particles:6 mγ:1 gov:2 forth:1 numerical:1 linear:27 associate:1 mω:1 free:6 standard:1 ramos:1 r2:1 created:1 days:1 domokos:1 disturbed:1 tempting:1 signature:1 moving:1 already:1 features:3 wash:1 another:1 hood:1 toy:2 top:3 master:3 too:2 eqn:4 leggett:2 iδ:1 insightful:1 a31:1 dissipationless:1 somewhat:2 distance:12 roles:1 approximations:1 second:6 precipitously:1 preparation:2 matter:2 spectrum:2 manner:1 seen:2 seem:2 relatively:1 strength:7 realm:1 convenient:3 responsible:1 isolated:1 absorbed:1 forces:1 though:4 object:1 wells:1 simplify:1 involving:1 phase:6 coil:2 acknowledgements:1 dummy:1 inferred:1 orderly:1 points:6 principle:6 sum:1 labels:1 fleming:4 subtle:1 tempted:2 proposed:4 specify:1 constant:19 hamiltonians:1 dn:12 do:3 dl:15 mixture:2 dk:3 df:1 de:1 stop:1 leisure:1 uncountably:1 dx:5 dy:2 dt:21 fields:1 decides:1 reference:8 sensitivity:1 observed:2 habib:2 depends:2 result:4 fail:1 said:1 exponent:2 µt:1 away:1 symmetric:1 d53:1 approach:2 terms:13 extend:1 nature:1 weak:1 however:14 extent:1 suggested:1 cos:17 pits:1 raimond:1 logic:1 distinction:1 argue:1 suggest:1 timescale:4 height:1 written:2 springs:2 basis:1 observing:1 three:4 been:17 much:11 basic:4 expected:1 quantities:4 concerning:1 coherent:3 spin:2 applied:1 tanh:2 fcen:1 near:3 neat:1 property:2 characterizing:1 provocative:1 phenomenological:3 iv:4 ii:5 ik:7 interacts:2 confirmed:1 things:1 make:5 quant:2 phenomenology:3 dimensionless:1 several:4 grows:3 evolve:5 peaks:1 trajectories:7 hand:2 normalization:3 weakly:1 scenario:3 academic:1 prescribes:1 just:2 identify:2 transforms:1 yet:1 previous:4 infinitely:1 regarded:1 deconstructing:1 easy:7 apart:1 casting:1 possible:2 occurring:1 appearing:1 performing:2 harmonically:1 arbitrary:2 a2ω:1 right:1 theorists:2 rapidity:1 bottom:2 electromagnetic:1 comments:1 unit:1 unstable:2 illustration:2 properties:2 o:3 plus:1 slightly:1 markovian:2 wineland:1 dyson:1 obtaining:1 bound:2 bath:6 down:2 support:2 initial:19 transform:2 physicists:1 way:3 astrophysics:1 overhead:1 was:1 medium:1 form:9 offer:1 differences:2 idealized:2 heat:2 surprising:1 inside:1 simplifying:1 moore:1 computing:1 evidence:2 dξ:1 promised:1 distributions:1 dα:4 nm:1 locality:1 nd:9 vanishes:3 meekhof:1 schwinger:1 setting:1 role:2 papers:4 picture:3 intend:1 superposition:5 models:10 dissipation:7 regime:4 longer:4 dω:17 assume:9 interval:1 dσ:1 dπ:1 time:34 remarkable:2 brownian:22 focus:1 supplement:1 certainly:4 inverse:2 depend:1 environment:29 quasi:2 analogous:1 orthogonal:1 frequencies:4 choice:2 exact:2 perceived:1 presented:1 turns:1 solved:3 upper:1 insignificant:1 measurable:1 cosh:4 spectral:2 appear:4 axes:2 current:2 suspect:1 commensurate:1 filled:1 supporting:1 realizations:1 lange:1 dissipates:1 understanding:2 q2:2 smearing:1 alone:1 along:10 appears:4 change:2 noticeable:2 studied:6 suggestion:1 conveniently:1 studies:4 plotted:4 adjustable:1 spatially:2 ekstrom:1 merely:4 working:1 positive:1 predictions:1 explicitly:3 memory:2 scope:1 theoretical:9 today:2 conductor:3 validity:1 appendix:1 cases:15 easiest:1 graphic:1 deformed:1 originally:1 oscillator:15 cat:9 following:2 attain:1 figure:5 predict:1 expanding:1 arise:1 performed:3 dxi:3 allowed:1 dxf:1 rescaling:1 occur:2 monitoring:1 discussion:1 write:6 pure:1 fpr:1 absolute:1 displacements:1 product:1 may:18 applications:1 produce:1 designed:1 data:1 grow:2 man:3 branches:3 dynamical:1 explicit:2 τdec:2 so:14 representation:3 prefactor:4 indeed:4 course:2 experiments:11 statistical:1 argued:2 still:4 derive:5 thumb:1 how:2 interesting:3 window:4 mail:1 correspondence:1 non:24 thereby:1 processes:1 hamilton:1 nov:1 now:6 discuss:1 possess:1 term:4 establishing:1 possibilities:2 realistic:3 entirely:2 square:3 ei:5 significantly:3 ed:2 gaussian:8 inhomogeneous:1 entering:1 ez:1 counteract:1 monitors:1 shown:3 space:9 furthermore:1 lagrangian:1 increase:2 investigation:3 gaussians:3 formula:4 dominate:1 correct:1 shows:3 theory:3 qf:8 divergence:1 fisica:1 departamento:1 quite:4 complicated:7 emblematic:1 remainder:1 derivation:2 language:1 motion:4 turn:3 gordon:1 routes:1 view:1 neglect:2 first:15 exotic:1 xi:9 variables:6 xf:12 simplified:1 fast:1 directly:3 impossible:1 message:1 open:2 angular:1 given:7 necessarily:2 unitarity:1 unruh:1 indicate:2 white:2 exerted:1 exploring:2 ryzhik:1 alan:1 x0:3 representing:1 than:11 semantics:1 wide:4 require:1 future:2 were:4 lmat:1 resistivity:1 dynamically:1 locations:3 any:13 efficient:1 note:6 ideal:1 potential:1 take:7 new:6 formulas:2 trace:1 opposite:1 incidence:1 successive:3 pair:2 analytically:2 especially:1 nonlinearity:1 considered:4 later:2 implications:2 drive:1 arguably:1 typically:2 precise:2 drastically:1 show:4 timedependent:1 delta:3 bright:1 ground:4 slow:1 aω:2 histories:1 only:15 going:1 parabolic:1 truly:1 aα:1 cannot:1 differentiating:1 adiabatically:1 discussing:1 learn:1 burst:2 relative:1 uncorrelated:3 nonlocality:1 caldeira:3 mabuchi:1 sites:2 label:1 enough:4 between:15 sited:1 diagonalized:1 across:2 multiplied:1 vertical:2 multiplies:1 universitaria:1 suppressed:2 reaction:1 tractable:2 many:6 region:1 according:3 σp:2 expression:2 characterization:1 period:1 moreover:1 considering:3 capable:1 locally:3 damping:2 fig:3 direction:1 enable:1 dramatic:1 external:2 careful:1 irrelevant:1 those:2 case:19 regimes:3 engineering:1 investigating:1 eik:2 ivd:1 coupled:5 ivn:1 dubious:1 couples:1 zhang:2 different:9 paz:5 supra:2 constructed:1 trivially:1 drives:2 entanglement:1 invariance:1 totally:3 cartoon:1 modes:3 no:11 roughly:1 without:2 solve:1 components:1 model:28 laboratories:1 dimension:1 charged:1 being:4 generally:1 rest:1 ch:1 speed:1 zoller:3 hint:3 seems:2 except:2 interested:1 lett:4 grating:1 real:4 aspects:1 around:1 rules:1 early:4 confined:1 world:3 mod:1 counterterm:1 particle:38 michael:1 integrals:5 fully:1 reduced:6 deduce:2 table:1 provided:1 dimensions:6 confirm:1 cavity:1 langevin:1 extensively:1 provides:1 propagating:1 bessel:1 refer:2 power:2 equivalent:1 2m:3 comparison:1 conducting:3 origins:1 discussed:1 image:2 rising:1 operator:1 valuable:1 classicality:5 legget:1 assumed:2 there:15 los:2 low:5 relic:1 complete:4 regard:1 philosophers:1 dissipative:2 applying:1 ωt:14 liouville:1 ωm:1 obtains:1 strongly:1 diverges:1 ag:1 certain:4 describe:1 general:10 aq:1 ap:2 examine:1 ar:1 ay:1 again:5 extending:1 igr:1 storage:1 field:15 valid:3 spatial:7 massless:2 deriving:1 a2:5 calls:1 perturbatively:2 mass:2 resembles:1 decoherence:81 original:1 represent:2 consider:7 ciudad:1 expressions:2 causes:1 tr:2 nonlocal:1 tf:5 stochastic:2 presentation:1 subtleties:1 paying:1 straightforward:1 very:11 coloured:1 condition:2 hamiltonian:6 lengthscale:1 t2:31 t1:28 large:15 mile:1 small:5 employing:1 renormalized:2 intricate:1 rate:10 timescales:2 salman:1 pass:1 further:5 canonical:3 what:4 nonlinear:1 section:15 brief:1 thickness:1 judicious:1 method:1 full:1 backreaction:2 behaviour:11 dimensionality:1 strong:5 equations:3 search:1 ahead:1 introductory:1 allows:2 amount:1 action:1 narrow:1 via:1 shorthand:1 poyatos:2 rises:2 proceed:3 distinct:1 contains:2 charge:2 comparing:1 ψi:1 taken:2 more:16 operators:2 tested:1 particular:2 known:1 evolves:1 science:1 equation:36 evolved:1 γkb:1 f1:8 compare:2 computers:1 prompt:1 accept:1 states:14 numbers:1 sense:1 firmly:1 information:1 goal:1 rather:5 acts:2 buenos:1 ensemble:1 simplicity:1 ubiquitous:1 derived:2 ff:1 coming:1 fk:4 fascinating:2 short:5 negligibly:2 negligible:4 turnover:2 reservoir:1 soon:1 held:1 thermal:4 paper:5 through:3 same:7 y1:9 existence:2 y2:11 its:13 environmentally:2 rapidly:5 solving:5 scully:1 actually:8 late:1 detected:1 systems:4 argentina:1 might:8 good:1 motivated:1 anticipates:1 easily:5 always:2 level:2 2d:1 2g:1 2a:2 2b:2 2c:1 found:3 2n:3 2i:2 characterized:1 2k:2 heavy:1 weight:1 generation:1 mesoscopic:1 energy:3 idea:1 expect:8 measurement:1 quantum:31 beyond:1 really:3 dominates:1 since:15 denotes:2 acting:2 darling:1 induced:2 issue:1 occurs:6 put:2 earliest:1 beginning:3 fiat:2 definition:1 needing:1 noted:1 exponentially:1 consequence:1 exhibited:1 number:5 done:1 construct:1 miss:1 differ:2 temperature:14 introduction:1 leading:2 5th:1 least:3 checkpoint:2 assumption:2 calculations:2 dt2:4 dt1:5 scheme:2 observations:1 trapped:1 part:3 schr:9 translation:1 oscillate:1 albeit:1 anticipate:1 determined:5 electrodynamics:1 zero:6 self:1 onset:2 universalities:1 analogy:1 jacobian:1 play:2 warnings:2 quote:1 most:6 aires:1 significant:7 nothing:1 kb:11 clear:2 saturate:3 kl:3 barred:2 exp:20 kt:2 physics:6 dragged:1 sector:1 particularly:2 phenomenon:5 relation:3 impressively:1 find:6 causality:1 parameters:2 distributed:1 subsection:1 factor:4 gains:1 notation:2 king:1 spurious:1 zurek:7 express:1 fastest:1 closely:2 during:3 coth:5 continuum:2 progressive:1 ohmic:15 investigate:2 common:1 set:9 ary:1 collectively:1 see:10 bare:3 close:1 contour:2 currently:3 dipole:1 various:3 conditions:4 recently:2 initially:2 attention:1 vanishing:1 disturbance:1 premise:1 distinguish:2 both:6 prescription:1 reverse:2 barely:1 sensitive:2 whole:1 finds:2 experimental:8 sinh:7 point:10 simple:20 dimensional:2 instants:2 regulated:1 expensive:1 kernels:3 ensures:1 described:1 create:1 due:1 geoffrey:1 describes:1 pf:8 ph:3 pi:11 generating:1 gas:2 understand:1 representative:1 realms:1 p2:4 p0:6 look:1 exponential:6 pacs:1 indefinitely:1 empirical:1 evaluated:1 forgetting:1 while:5 replaced:1 evaluating:2 turchette:1 laflamme:1 encountered:1 itself:6 monroe:2 shorter:1 products:2 higher:5 calculation:3 used:1 uses:1 robust:1 recent:1 lower:2 task:1 analysis:1 distances:4 λt:1 shape:1 intervals:1 using:6 k3:1 cut:9 conclusions:2 scales:5 source:2 internal:7 deliberately:1 plateau:1 solvable:1 euler:1 evaluate:4 entangled:1 emergence:3 imposed:1 semi:1 follows:1 adiabatic:3 continue:1 indication:1 sketch:1 often:7 spring:1 some:22 back:3 examples:3 mirror:1 pω:7 ourselves:1 gradually:1 scale:17 integration:5 tends:2 inserting:1 ba:1 continuing:1 agreement:1 step:1 br:1 become:3 plots:1 hilbert:1 bz:1 sharper:1 constraint:1 tortuous:1 range:10 consequently:3 into:9 within:3 integral:10 unbarred:1 proportional:2 span:1 classically:1 question:1 long:6 forward:1 sections:4 propagator:1 atom:3 line:5 uv:5 up:4 us:2 similar:4 called:2 associated:1 defined:4 likewise:1 influence:13 single:9 dragging:2 amounts:1 dashed:1 draw:1 elements:2 generated:1 suppression:2 depicting:1 land:3 implies:4 lanl:2 naively:1 presenting:2 requires:1 having:3 once:3 gr:6 results:17 eds:1 go:1 contributions:1 issues:1 gh:7 theorist:1 alamos:2 concerned:1 anglin:4 stable:2 include:1 dramatically:1 sent:1 probe:1 g2:7 implicitly:1 wave:6 electron:2 putting:1 incoherent:2 positions:3 tre:1 dealt:1 optics:2 enforce:2 smaller:1 sin2:2 crop:1 dynamics:7 odd:1 ode:1 3z:1 apparatus:1 giving:1 expressed:4 consistently:2 experiment:4 nonlinearly:1 degree:3 respectively:1 explore:1 objects:1 separation:2 consideration:1 implicit:1 great:1 ρz:1 involved:1 resulting:1 shaded:1 involves:1 composed:1 examining:1 danger:1 addressed:1 api:1 apply:1 apf:1 manipulate:1 use:5 metaphor:1 superpositions:2 remains:2 few:1 doubt:1 sort:1 formally:2 becomes:4 occurred:1 haroche:1 iii:4 integrating:1 when:10 reproduce:1 crossed:2 ρv:1 drops:1 plate:4 process:3 purposes:1 high:23 effectively:3 assumptions:2 something:1 varied:1 holds:2 regions:1 dependent:1 frontiers:1 instead:7 sin:12 profile:2 collection:1 ambiguous:1 realized:1 physical:3 light:1 separations:2 correspond:1 gleiser:1 allow:3 nonequilibrium:1 wigner:8 produces:1 despite:1 meter:1 sions:1 saturates:2 looks:1 decay:3 ln:2 temporal:2 previously:1 degrees:4 derivative:1 defining:2 violating:1 greater:1 parabola:2 front:1 realize:1 undertaking:1 traced:1 identified:1 sufficiently:2 magnitude:1 truth:1 crossing:2 lorentzian:2 constraints:1 homogeneous:1 arxiv:1 related:3 frequency:11 interplay:1 measure:1 our:25 special:3 out:10 matrix:7 weert:1 rep:1 rev:22 b288:1 theoretically:2 integrated:1 approached:1 interactions:2 diagonal:2 approaches:5 convolutions:1 van:1 interaction:14 could:1 times:11 marcelo:1 length:4 isotropic:1 hence:1 retain:1 diminishes:1 predominate:1 powerful:1 reaches:2 hitherto:2 reached:1 precisely:2 πg:1 ordering:2 system:20 their:8 travelled:1 final:3 evacuated:1 exactly:6 environmental:8 natural:4 zβ:3 isolation:1 limiting:1 amplitude:1 providing:1 shrinks:1 fluctuation:2 curves:1 discussions:2 unlikely:1 need:1 border:3 clearly:5 studying:1 able:7 mechanism:1 detector:1 gω:1 connected:2 gradshteyn:1 why:1 whz:1 afresh:1 consequences:1 lines:2 landsman:1 fact:6 impression:2 violation:1 purely:2 trivial:5 agrees:2 q0:6 pause:1 should:7 postulated:1 attained:1 local:5 hope:1 equilibrium:1 slows:1 means:1 familiar:4 overall:1 beam:1 ones:2 words:2 procedures:1 pωi:7 evolution:9 substrate:1 differential:1 contain:1 qi:9 fixed:10 dpi:1 qn:2 requirement:3 constructing:1 exists:1 hγ:2 national:1 hα:2 merits:1 coils:1 limit1:1 interacting:2 pattern:1 tend:1 state:28 progress:1 boundary:5 brune:3 variability:1 ability:2 opening:1 implementing:1 swift:1 thank:1 limits:1 equal:4 hω:3 figures:1 hρ:1 hφ:6 boyer:1 detailed:1 relevant:3 co:2 conclude:1 harmonic:5 environments:8 walk:1 ab:1 respect:2 superselection:2 addition:1 slowly:1 proposal:1 define:5 coherence:1 essentially:2 bulk:1 present:9 novel:2 wellknown:1 appearance:1 kimble:1 value:1 will:56 ultra:1 layer:1 vd:5 almost:1 vi:1 refs:1 thus:8 vn:5 examined:3 prose:1 generic:1 parts:1 pauli:1 units:3 finite:3 difficult:1 cubic:1 effect:2 ion:1 v2:4 infinite:1 frequently:1 expense:1 off:10 nevertheless:1 restricted:1 well:5 patterns:1 position:3 fk2:4 less:6 increasingly:1 accurate:1 obtain:14 sources:1 macroscopic:4 rapid:5 density:9 add:1 usage:1 dqi:1 saturation:3 putative:1 increases:1 know:1 press:1 displaced:3 necessary:1 like:6 simply:7 accessible:1 because:8 classical:17 phenomena:2 growth:2 choosing:2 γa2:1 neglecting:2 transport:1 lead:1 broad:1 mines:1 overlap:1 manipulations:1 does:7 assuming:3 noise:5 inaccurate:2 q2f:1 q2i:1 although:2 about:4 actual:2 extension:1 freedom:7 eqns:1 dependence:4 important:5 introduced:2 px:1 own:2 h2:7 h0:8 functional:12 mere:1 ridge:3 artifacts:1 quadratic:1 inner:1 naturally:1 function:26 hr:1 but:38 hu:2 hk:3 construction:1 highest:2 illustrative:1 made:2 compute:2 places:1 whether:1 placed:1 below:1 limit:14 problem:3 universal:1 linearity:4 ing:1 approximated:2 functions:15 variety:1 detail:2 other:9 suppress:1 conclusion:1 kinds:1 fω:9 uba:2 qω:5 pi2:1 ghost:1 coupling:12 4m:2 4i:1 4d:1
|
quant-ph9611046.txt |@word represent:6 measurements:2 transitions:1 consider:5 remarkable:1 caused:1 magnetic:1 global:1 results:2 feynman:1 leads:3 roy:2 scalar:2 code:1 computation:13 faster:1 duplicated:1 devoted:1 whose:1 theorist:1 amplification:1 terms:2 superpositions:1 irrelevant:1 simplify:1 vs:1 extraneous:1 environment:18 finally:2 critical:1 device:1 whatsoever:1 under:3 stabilizing:3 analogous:2 include:1 sent:1 applied:1 labels:1 amplitudes:1 virtue:1 orthogonal:12 very:2 continues:1 keeping:1 induce:1 wave:1 print:4 affect:2 difference:1 prevents:1 uniquely:1 entire:5 hamiltonian:6 altering:1 issue:2 applicable:1 fewer:1 occurs:2 large:10 discrete:2 vector:2 demonstrated:1 small:8 eigenvalues:1 shows:2 barbara:1 equation:1 smaller:3 force:2 specially:1 deutsch:4 repetitive:1 direct:4 zb:1 sign:1 feasibility:1 second:2 design:2 zt:2 further:2 dynamics:1 implemented:4 zr:2 theory:8 subscripts:1 index:4 what:4 errors:34 appear:1 apparatus:7 giving:1 interactions:1 decoding:7 access:1 version:1 goes:1 shared:1 contributes:1 ever:1 consisting:2 coefficient:1 σaz:5 submitted:1 relationships:1 respectively:3 never:2 spacing:1 residual:4 here:4 automatic:1 symmetrizations:2 groups:2 address:1 represented:1 safer:1 strong:1 z0:16 imperfections:1 digits:1 ref:3 antisymmetric:4 institute:3 involved:2 larger:2 ignoring:1 amount:2 simultaneous:1 products:3 permutation:1 domains:1 complicated:5 suitable:1 makes:1 cja:2 involves:1 readability:1 via:1 see:2 projection:1 figure:3 extra:1 merely:1 explained:2 plenum:1 logical:22 highly:4 brought:1 sloane:1 unpredictable:1 total:2 establish:1 readily:1 use:9 refers:1 flaws:1 handled:2 would:10 codewords:26 remains:1 positive:1 laflamme:2 toffoli:1 negative:1 generate:1 distinct:2 few:1 doubt:1 call:1 therefore:13 taken:3 scope:1 themselves:2 techniques:1 type:9 theoretical:2 more:10 introducing:1 israel:2 permutations:1 furthermore:1 clearly:1 becomes:1 factor:3 corrected:7 labelled:1 proceed:1 particular:4 known:3 foundations:1 hold:1 cryptography:1 must:6 recoiled:1 high:4 none:2 stabilized:1 word:1 quantized:1 effectively:1 science:2 originally:2 work:1 theories:1 remain:1 arrangements:1 values:4 resources:1 concepts:1 following:4 spontaneous:1 example:9 proof:1 control:2 ions:5 computers:23 xz1:10 corrupted:8 indicated:1 give:1 process:11 bennett:3 neglected:1 states:15 sphere:1 performed:5 want:1 tolerant:3 occur:2 information:9 redundancy:3 soc:2 recovery:2 defective:2 rather:2 interacts:1 discussion:2 acts:1 37th:1 algorithms:1 orthogonality:1 write:3 how:9 nontrivial:1 occasionally:1 behave:1 pure:2 answer:1 instead:4 ordinary:5 preferable:1 zurek:2 brassard:2 belongs:1 simplicity:2 product:4 designer:2 description:1 may:18 ancilla:24 began:1 xzy:1 containing:1 symmetrisation:1 constraint:1 designed:3 gates:1 representations:2 codes:3 types:3 goal:1 transposed:1 physical:30 dynamical:4 third:1 conscious:1 computations:1 correspond:1 redundant:4 element:1 fortunately:1 ones:6 so:4 sect:6 fundamental:2 enter:2 representation:6 order:10 typical:1 operations:2 executed:3 interpretation:1 help:1 22n:1 numbers:2 developed:1 over:3 equally:1 symbols:2 course:1 thermal:1 relative:1 including:2 same:9 berthiaume:2 signs:1 captions:1 still:10 ieee:2 its:14 receiver:1 david:1 don:2 le:1 group:1 symmetry:10 la:1 chosen:4 complex:4 coordinates:1 actually:6 detected:2 permanent:1 systems:3 omitted:2 might:1 syndromes:3 symmetrization:15 them:7 good:2 return:1 fourth:1 combination:4 prevented:2 runs:1 introduce:1 anticipated:1 mention:1 steane:3 aborted:1 hands:1 accumulate:1 nov:1 mimicking:1 discuss:1 represents:2 term:7 several:11 dirac:1 name:1 goldstein:1 always:3 university:2 asher:1 into:8 fig:5 trap:2 truth:1 each:12 did:1 repeating:1 higher:1 macchiavello:1 side:2 constraints:1 subset:2 domain:2 aa:3 england:1 directly:1 arbitrariness:1 ed:2 energy:3 directions:1 reduce:1 principles:3 accidentally:1 unitarity:1 wires:2 static:1 knill:1 measure:2 quantum:59 our:1 operation:2 beyond:1 eq:13 haifa:1 brings:2 out:2 divincenzo:2 shown:4 fundamentally:1 space:3 oxford:1 restricted:2 irony:1 since:5 rev:8 projected:2 astray:1 research:1 particles:3 re:1 aharonov:1 performs:1 denoted:1 adaptive:1 cause:2 correct:16 restoring:1 foundation:1 linear:3 barrier:2 written:6 replicas:3 enforcing:1 seventh:1 given:3 free:4 standard:5 completely:5 toy:1 california:1 execute:1 wanted:1 jozsa:3 finite:3 care:1 definition:1 pairs:3 interaction:3 benioff:2 created:1 geometry:1 determining:1 could:2 bistability:1 programming:1 times:2 creates:1 turn:1 circuit:7 phy94:1 consequence:2 barenco:1 onto:2 first:4 initial:5 meas:2 probability:7 encoding:7 radical:1 variables:1 coding:1 number:3 thereof:1 xz:1 erroneous:1 done:3 stop:1 another:6 vote:1 illustrating:1 array:1 stage:2 engineer:1 aborting:1 perturbation:5 needed:4 introduction:2 unknown:11 interact:2 system:7 analog:1 1a:2 their:15 returns:1 perturbations:2 brevity:1 quanta:1 perfectly:1 bits:5 final:2 gives:3 imperfect:1 trapped:2 asymmetric:3 bit:5 continuous:4 serve:2 za:13 part:8 surviving:1 eliminated:8 representing:3 than:11 coefficients:2 clarifying:1 plausible:3 kind:2 wootters:3 ben:1 unfortunately:1 cyclic:5 measured:2 namely:4 distill:1 matter:1 individual:3 pairwise:3 amplitude:2 were:3 iωt:1 enforced:1 avoided:1 correction:25 bitwise:1 interrupted:1 randomly:1 already:1 contrary:1 braunstein:1 need:3 seem:1 constrained:1 any:21 vulnerable:1 she:1 symmetrized:1 paths:3 zero:1 efficient:3 convenient:2 latter:9 cope:1 able:1 isolated:6 mechanism:2 note:4 majority:1 ideal:2 potential:8 take:3 forces:1 essential:3 effectiveness:1 even:4 exactly:1 allow:1 shall:11 molecule:2 phases:1 singlet:4 most:6 preset:1 eight:1 codeword:26 pair:5 iǫt:2 intrinsic:1 singled:2 revzen:1 workshop:2 found:1 technion:1 considered:1 average:4 sometimes:1 drifts:4 investing:1 proceedings:1 definitely:3 principle:1 mechanical:2 left:1 typically:2 review:2 lying:1 laws:3 called:2 shor:7 gf:1 disturbances:2 random:6 scattered:1 notations:1 bring:2 gauge:2 carefully:1 longer:1 trivial:1 find:1 ground:1 completion:1 partners:1 electromagnetic:1 slow:2 knowledge:2 spite:1 irreversible:1 enough:7 supported:1 should:3 only:14 explicitly:2 pairing:1 molecules:1 indeed:4 supernatural:1 reminiscent:1 he:2 local:1 achieve:1 pj:4 do:4 hit:1 above:1 notation:3 means:8 secular:1 simplest:1 overall:1 addison:1 soon:1 joint:4 cannot:11 probably:1 report:1 during:2 disadvantage:1 produced:1 evolution:8 reading:1 arxiv:1 zs:2 method:8 circuits:3 bad:2 common:2 contain:3 london:2 discussing:1 view:1 satisfy:1 set:2 achieved:1 undergoes:1 national:1 testing:1 j2:2 transferred:1 detection:1 opposite:2 depends:1 computer:36 bare:1 result:7 fail:2 close:1 ur:1 uncorrelated:1 best:2 subject:4 closer:1 fails:1 welsh:1 tensor:1 nightmare:1 missing:1 definite:4 yet:1 symmetric:15 initially:5 state:75 ua:3 various:2 between:5 affecting:1 invariant:2 subscript:1 before:1 conditions:1 available:1 chapt:3 check:1 triplet:3 jx:1 statistically:1 jz:1 nature:6 qubits:60 attention:1 however:11 teleportation:5 implementing:1 emitter:3 latin:1 subspace:9 ket:2 remaining:1 jb:2 improve:2 both:1 protect:2 parentheses:1 2n:7 efficiency:1 xz0:10 many:7 equal:1 against:1 quantization:1 involve:1 0a:2 figures:2 context:2 logic:1 distinction:1 qubit:29 expression:1 mann:1 kets:1 unitarily:1 among:1 relevant:1 point:3 simple:7 ca:4 others:1 discarding:1 corresponds:1 alone:1 instants:1 cirac:1 unsuccessful:1 moreover:1 mathematically:1 uncorrected:1 pp:1 singlets:1 fault:3 basis:4 syndrome:5 due:3 been:4 strategy:1 restarts:1 much:5 symmetrizing:2 combined:1 expected:2 ph:5 define:1 obtained:2 detach:1 corresponding:2 commutes:1 orthonormal:2 quantities:1 sufficient:4 grating:1 gas:3 andrew:1 new:12 coherent:4 coherently:1 spin:4 former:1 those:2 case:10 processes:1 miquel:1 value:4 transformation:6 will:11 while:4 lead:1 transactions:1 error:69 situation:2 property:2 procedure:2 program:1 jy:1 unitary:13 eventually:1 almost:3 thus:4 non:1 surface:1 hardware:5 sudden:1 turns:1 discarded:1 flipped:1 technology:1 binary:3 different:6 null:1 considerable:1 grant:1 generic:1 acknowledgments:1 make:3 belong:1 arbitrarily:2 poincar:1 shifts:1 parts:2 quant:5 mixtures:2 gets:4 difficult:3 independent:2 used:5 receives:1 putation:1 collective:3 conceived:1 effect:1 hand:8 ion:4 levels:1 potentials:1 entanglement:4 cr:1 contribution:1 eigenvectors:1 least:1 modes:1 nevertheless:1 zoller:1 well:1 deal:1 obviously:1 without:6 machinery:1 model:4 obtainable:1 know:10 restore:6 construct:2 protocol:2 they:5 just:3 less:3 being:1 grateful:1 rest:1 sources:1 stored:1 identify:2 thanks:1 immediately:1 alternative:1 eigenstates:1 copied:1 now:8 kluwer:1 field:3 bell:1 had:1 except:2 improvement:1 source:1 spread:2 lett:5 easy:1 technological:1 stable:1 occurring:1 solvable:1 excited:1 ought:2 generalized:2 identical:5 tests:2 around:1 alternatively:1 read:1 ampli:2 possible:10 successful:2 matters:1 five:2 entangled:13 vacuum:2 press:3 using:3 variants:1 replace:1 correcting:2 usually:3 formal:1 meaning:1 loss:1 bistable:2 necessary:3 like:1 particle:1 identifying:1 obvious:1 reduces:1 performing:2 noted:1 separately:2 steps:2 either:1 materialized:2 output:1 inter:2 reduced:5 terminology:1 accessible:1 because:7 old:3 methods:5 classical:17 sequence:1 sends:1 successfully:1 some:4 sure:2 b0:3 alamos:1 respect:1 oscillations:1 peter:1 investigating:1 ignore:1 gradually:1 describing:2 eiη:1 realistic:1 memories:2 leaving:1 unavoidable:1 legal:2 get:2 does:4 proc:3 minimal:1 refer:2 measuring:5 ba:1 disentangle:2 drift:2 arbitrary:1 continuing:1 conventional:2 wesley:1 step:2 santa:1 become:1 prepared:1 super:2 hilbert:3 simpler:2 comparison:2 rare:1 anything:1 impose:1 freedom:1 am:1 discussed:2 generated:1 o:1 quantal:1 compatible:1 mutually:2 carries:1 involving:5 mixed:1 discard:3 continually:1 automatically:3 software:2 considerations:1 perturbed:1 computational:1 real:1 presence:1 communication:2 h0:7 h1:8 calderbank:1 three:2 down:1 phase:7 appropriate:1 right:2 references:1 determine:1 stabilisation:2 conceptually:2 scenarios:1 span:1 additional:2 ao:1 comparing:1 assumed:1 there:24 unconscious:1 fight:1 los:1 describes:1 bosons:1 way:16 irrespective:2 was:8 naturally:1 function:1 considerably:1 emergence:1 complete:7 form:1 smolin:1 denoting:1 but:13 sophisticated:1 failure:1 repeated:3 recoil:1 elimination:1 encoded:4 dissipative:4 proposal:1 auxiliary:1 reset:1 made:3 arranged:1 consist:1 society:1 whether:1 wish:2 up:2 us:4 achieving:1 dordrecht:1 below:2 paz:1 restores:1 fluctuations:3 problem:5 similar:1 clear:2 selects:1 mechanics:1 ab:2 constant:4 zeno:1 computing:2 defined:1 likewise:2 abstract:1 measurement:5 influence:1 graphical:1 encode:4 general:3 peres:5 single:10 governed:1 formalism:1 internal:2 four:2 constructed:1 incorrect:2 again:2 compared:2 ideally:1 no:15 rains:1 ekert:1 when:4 vanishes:2 event:2 application:1 other:16 remarks:1 helpful:1 normal:1 digital:1 test:4 teleported:1 forcing:1 orthocomplement:1 arithmetic:1 poor:2 symposium:1 stat:1 elements:3 kinds:1 superposition:2 accidental:1 mismatch:1 symbol:1 hirota:1 uniformly:1 ultimately:1 epeau:1 stay:1 evolves:2 a0:4 chance:2 restoration:1 vectors:8 matrix:6 occurrence:1 bases:2 correlated:3 implies:1 coupling:2 assume:2 physics:3 proposed:1 required:1 diffraction:1 together:6 having:3 ments:1 fresh:2 homologous:1 time:3 failures:1 decoherence:1 requires:3 original:3 once:2
|
quant-ph9611047.txt |@word remarkable:1 results:1 illustrated:1 quadrature:5 grateful:1 go:1 compact:1 depend:1 attracted:1 noncompact:2 removal:1 kγ:5 squeezing:9 γn:2 γm:3 include:1 case:6 random:1 amplitudes:1 very:1 connects:1 affect:1 condition:1 leads:1 irreducible:2 leave:1 discrete:1 convenience:1 interpolating:1 small:2 optics:1 originally:1 smaller:6 nbs:21 chen:1 further:2 linear:2 index:1 sub:5 goes:1 supplies:1 increasing:1 acknowledgments:1 funtion:1 satisfy:2 multinomial:1 respectively:5 ranges:3 objects:1 china:2 november:1 equations:1 change:1 intersect:1 obtained:3 institute:3 involved:4 larger:5 via:1 9a:1 moran:1 lima:2 unit:2 silva:1 figure:4 positive:2 contains:1 negative:8 call:1 therefore:2 black:2 until:2 more:2 lowering:2 becomes:6 operators:1 appendix:1 normalized:1 known:2 cases:1 must:1 balls:4 quantized:2 deformed:2 science:3 equation:1 work:1 oscillator:1 fock:1 subpoissonian:1 publications:1 following:1 averages:1 example:1 weaker:2 indicated:2 share:1 states:50 minimum:1 numbers:1 degenerate:2 sense:1 verify:1 feature:3 how:1 acta:1 ordinary:1 ryu:1 parameter:5 description:2 algebra:10 ladder:4 different:8 changchun:1 inst:1 natural:1 su:23 so:5 fundamental:1 representation:4 sg:4 abstract:1 japan:2 satisfies:1 still:1 its:2 before:1 derive:1 chosen:2 glogower:3 decreases:1 forms:2 absence:1 fig:4 mail:1 defining:1 deformation:3 them:2 introduce:1 they:3 oxford:1 nov:1 eigenvalue:2 university:2 mode:2 each:2 found:1 side:1 associative:1 weight:1 29a:1 hypergeometric:3 reduce:1 related:3 society:1 investigated:4 quantum:2 our:1 out:1 large:4 space:1 furthermore:2 since:3 rev:1 increase:2 re:1 mη:10 mγ:6 attentions:1 foundation:1 theory:3 enveloping:3 put:1 just:1 counterpart:1 turn:1 promotion:1 fu:5 already:1 probability:9 number:10 another:1 reached:1 introduction:2 jsps:1 relations:1 their:9 intermediate:7 too:1 realization:1 white:3 part:1 pnm:12 x2:5 than:2 population:1 kind:3 namely:2 limiting:3 fluctuation:1 clearly:1 lie:2 degenerates:1 hgs:2 generalized:1 shall:1 algebraic:5 letter:3 successive:1 phase:7 urn:1 holstein:1 physics:3 fact:2 drastically:2 supported:1 find:3 northeast:1 knowledge:1 parameters:4 enough:1 ball:1 only:1 generators:1 factor:2 characterization:4 above:1 quantph:2 means:2 contracts:3 de:3 famous:1 words:2 fields:2 arxiv:1 qm:11 thanks:1 national:1 up:1 depends:1 individual:1 discussions:1 satisfying:1 please:1 tend:2 state:2 between:8 barranco:1 approach:1 complementary:1 jp:1 however:2 interpolate:4 jm:3 both:6 limits:9 region:1 sensitive:1 admit:3 figures:1 variance:2 disappears:2 among:1 point:3 appeared:2 poissonian:10 corresponds:3 sampling:1 dimensional:4 wider:1 considering:1 ps:17 been:1 ph:3 algebras:7 pn:2 ak:2 define:3 photon:3 coherent:19 present:1 p2:6 p0:1 variances:1 straight:1 value:2 50a:1 will:1 suppose:1 squeezed:7 stoler:2 opt:1 non:1 bargmann:1 hong:1 author:1 suggest:1 radiation:4 same:2 poincar:1 quant:3 finite:3 literature:2 see:5 effect:1 characters:1 infinite:1 fellowship:1 primakoff:1 well:2 obviously:2 coordinate:1 drawing:1 left:1 unified:1 teich:1 proposed:1 when:4 valuable:1 atomic:4 olya:17 character:3 except:1 quadratures:1 lett:2 easy:2 momentum:1 real:1 yukawa:3 easily:1 evaluate:1 showing:1 know:1 integer:1 mod:1 marques:1 because:1 sequence:1 some:4 normal:1 comments:1 connecting:1 tends:1 prof:1 replaced:1 kyoto:4 binomial:14 bs:25 plots:2 super:3 properties:7 mixes:1 range:7 introduced:3 perelomov:4 obtaining:1 hermitian:1 references:1 operator:7 statistics:4 there:1 accordingly:2 mandel:2 way:1 function:5 hp:2 line:6 highest:1 considerable:2 raising:1 he:1 made:1 maximum:2 us:1 theoretical:2 limit:8 distribution:12 called:3 ac:1 constant:2 2mη:1 defined:1 universal:3 single:2 saleh:1 formalism:1 distributions:4 check:1 sasaki:5 qγ:2 susskind:3 no:1 na:1 generally:1 detail:1 field:6 other:2 details:1 conclusion:1 nonclassical:7 generated:1 important:2 structure:1 faster:1 values:2 together:1 far:1
|
quant-ph9611048.txt |@word represent:3 concept:8 semantic:6 consider:2 magnetic:1 global:3 alternatives:7 results:3 leads:3 entropy:7 grateful:1 consists:2 subobjects:1 gl:2 decisions:2 hole:4 localized:2 row:3 content:2 iii:2 young:3 tn:5 finally:1 th:6 under:1 ontological:1 norm:1 p2:1 belonging:1 confirmation:1 straightforward:1 far:1 electron:3 αrs:2 every:3 decide:2 difference:1 illustrated:1 level:3 irreducible:4 t3:1 deals:1 vector:2 minimal:1 small:1 biological:1 mo:1 natur:1 estimates:1 measurable:1 approximation:2 fold:2 second:1 invention:1 further:2 correspond:3 zp:2 linear:2 index:2 appear:2 apparatus:1 n34:1 m35:1 cell:1 n36:1 above:3 international:1 falling:2 equivalent:3 filled:2 full:1 simultaneously:1 understanding:1 objects:27 separation:1 represented:3 consideration:1 equations:1 appears:2 interpret:1 obtained:4 remark:1 substance:4 holger:2 institute:1 vectors:2 allows:1 experience:1 amount:1 extremes:1 products:1 published:1 der:2 useful:1 leptons:1 classification:1 explained:2 logical:3 editors:1 analyzing:1 stern:1 condensates:2 neutrino:1 total:4 planck:1 linearly:1 eddington:2 use:1 would:2 abbreviations:1 contains:1 properties:2 n56:1 call:1 therefore:7 taken:1 generators:3 type:2 theoretical:1 today:1 more:4 flat:1 substances:1 operators:3 curvature:1 aufbau:1 basically:1 known:4 actual:2 cases:1 producing:1 must:1 ii:1 valued:1 animals:1 mc:1 originally:1 protons:1 tations:1 mu:1 remain:1 fock:2 values:1 mp:2 concepts:3 following:3 fulfill:2 example:5 stimulating:1 f2:1 cosmological:5 permutations:3 ann:1 states:6 anihilation:2 numbers:9 sense:4 distinguishable:1 information:51 soc:1 provide:1 verify:1 divided:1 get:2 tableau:2 kamefuchi:1 how:2 pure:1 ordinary:2 explains:2 ruhr:3 product:4 de:1 nph:1 transforming:1 philosophy:1 derived:2 different:3 diagram:6 microstate:1 physik:1 cambridge:1 representations:10 fk:2 types:2 bekenstein:3 short:1 natural:2 outline:1 effective:1 lost:1 su:6 element:1 s3:4 complexity:1 so:7 sn:3 fundamental:4 keeps:1 representation:6 increase:3 order:6 turns:1 typical:1 reproduced:1 interpretation:2 help:1 developed:1 pointed:3 satisfied:1 interpreted:1 paper:1 mentioned:1 existence:3 still:1 its:10 boosts:1 derive:1 group:19 thank:2 relativity:1 conjugation:2 production:1 hidden:1 main:1 correspondence:2 them:1 combination:1 τrs:1 τrr:1 operator:1 presupposed:1 2p:1 simply:1 they:1 half:1 front:1 feature:1 nov:1 now:9 structural:1 term:1 dirac:2 parameter:4 university:2 identified:1 reasonable:1 each:7 found:1 2n:1 higher:4 characterized:2 permutation:1 homogeneous:1 eo:2 ei:1 energy:14 related:2 inhomogeneous:1 parabose:13 measurement:2 quantum:31 wavelength:2 ev:2 ep:2 special:3 out:5 large:4 shown:1 matrix:1 space:40 since:4 rev:2 rz:1 angular:1 particles:9 m2o:1 formula:1 δrs:3 correct:2 indicating:1 shows:1 commutation:3 theory:70 localization:2 possibility:1 standard:6 admits:1 indices:2 reason:3 rows:3 formation:3 imagine:1 estimate:1 acker:12 additional:1 definition:2 enormous:1 interaction:3 language:1 r3:1 starts:1 could:8 cosmic:4 castell:4 m23:1 int:5 place:1 massive:4 consequence:5 first:6 twodimensional:3 symmetry:8 question:2 variables:1 supposing:1 number:13 tableaux:1 philosophical:1 done:5 relations:3 directly:1 between:9 size:2 manuscript:1 given:11 cartesian:1 exists:1 decrease:1 needed:4 introduction:3 test:1 top:1 system:2 least:1 priority:1 their:4 assumption:3 constants:1 calculations:1 realization:1 scheme:4 structures:3 frame:1 gives:4 lot:1 baryon:1 exactly:3 n45:2 regards:2 overwhelming:2 representing:2 semantics:2 distance:1 kind:1 bits:1 iteration:2 matter:8 classes:3 distinguished:1 deciding:1 unchanged:1 argument:2 generalization:1 trilinear:1 say:1 manner:1 seen:1 seem:1 cosmology:1 any:4 contents:1 lie:1 mik:1 strength:1 able:2 instance:1 empirically:3 potential:3 build:3 green:5 heisenberg:1 multiple:2 allow:2 investigations:1 object:11 reach:1 most:2 connected:2 phase:1 represen:1 fk2:1 mach:1 subspaces:1 consequences:1 considered:2 later:3 looked:3 part:2 principle:3 urs:35 subgroup:1 physics:11 fact:1 german:1 τst:1 iǫ:2 spaces:4 relation:1 gerlach:1 keywords:1 wigner:1 next:1 find:1 postulates:1 ratio:2 knowledge:1 situations:1 explain:1 m25:1 should:4 only:11 won:1 black:6 molecules:1 indeed:2 over:5 columns:1 do:1 his:3 gev:1 means:5 dependent:2 hopefully:1 aim:1 cannot:3 new:6 applying:2 evolution:8 die:1 arxiv:1 method:2 common:1 multiplicity:1 view:3 set:1 n16:1 n14:1 physically:2 violated:1 connections:2 depends:1 radius:1 result:3 discussions:1 close:1 theoretic:7 momenta:2 acquires:1 tensor:6 symmetric:3 state:10 smallest:1 simplest:2 invariant:3 conditions:3 email:1 naturforschung:1 terms:1 august:1 nature:1 arises:1 physicist:1 atoms:1 problem:1 suggested:1 both:1 collaborators:1 many:2 compton:2 hence:1 quantization:10 connection:4 und:1 logic:1 attributes:2 passing:1 whole:3 photons:1 experimental:1 logik:1 groups:1 cm:1 point:3 simple:2 corresponds:1 proton:5 dimensional:7 m13:1 m12:1 anti:2 iµ:1 moreover:1 presumable:1 considering:2 described:5 transformations:2 basis:3 locally:1 three:3 been:1 tensors:9 zph:2 change:3 hawking:2 basic:3 ph:1 pi:1 abstract:5 empty:2 direction:1 describe:4 sufficient:1 dismiss:1 subspace:2 essentially:1 n24:1 c2:2 spin:5 those:1 case:3 p3:3 p0:4 p1:1 look:1 expanded:1 appearance:1 empirical:2 value:3 will:6 bochum:4 conformal:2 procedure:7 maximal:2 unitary:1 vol:7 informational:2 von:12 thus:8 13a:1 according:1 obeying:1 characterize:1 αst:2 ni4:1 acknowledgments:1 binary:3 containing:2 verified:1 insofar:1 radiation:1 indistinguishable:1 same:4 poincar:5 complex:7 quant:1 pauli:1 uncertainty:1 defines:2 four:1 development:1 used:1 orderung:1 appearances:1 numerical:2 upon:3 effect:1 hand:2 levels:6 munich:3 uni:1 n26:1 subgroups:1 framework:1 try:1 well:5 finds:1 thought:2 comes:1 components:2 position:9 model:4 dimension:2 left:2 λp:1 proposed:1 lorentz:4 reviewed:1 aspect:1 world:5 alternative:7 bit:4 density:3 regarded:10 seems:2 interested:1 apart:1 generalized:1 identical:1 smax:1 motivating:1 decomposed:1 possible:5 spanned:2 smallness:2 boxes:2 know:1 background:1 vacuum:9 using:3 ams:1 formal:1 loss:1 theor:5 necessary:3 like:5 particle:16 follows:4 underway:1 yields:2 always:1 become:1 downward:1 nucleons:2 reduced:1 mathematical:2 exceed:1 right:2 often:1 classical:1 creation:2 some:2 back:1 deflection:1 understood:4 proper:1 lorentzian:1 informationtheoretic:1 describing:1 lead:1 bottom:1 decision:5 quarks:1 per:1 contributing:1 does:4 decomposition:1 provides:1 picks:1 prof:3 proc:1 demonstrated:1 refer:1 measuring:2 truth:1 journal:1 wavefunctions:1 step:2 br:2 bs:3 frg:1 hilbert:4 manufacturer:1 a1:6 about:3 central:1 column:2 universe:6 discussed:2 compatible:2 range:1 a2:2 weizs:12 horizon:1 act:1 mixed:1 considerations:4 astronomical:1 own:1 into:6 isomorphic:3 remarks:1 because:7 references:1 einstein:2 elementary:9 financial:1 conceptually:1 mere:1 statistics:2 deal:1 support:2 there:2 u1:1 u2:1 accordingly:1 way:5 was:4 iˆ:1 lowest:1 graudenz:1 complete:1 m15:1 forming:2 but:5 volume:2 understandable:1 atom:1 hc:2 nonvanishing:2 made:4 arranged:1 consist:2 minkowski:2 cells:1 up:1 devices:1 ur:64 below:1 diagrams:4 cosmos:3 similar:1 called:5 phil:1 constant:3 defined:6 certain:1 universal:2 measure:1 am:1 general:4 complementarity:1 single:2 ar:8 exist:1 planets:1 formulation:1 physical:16 again:1 raised:1 no:10 whereas:4 wavefunction:2 when:1 ne:1 event:1 field:3 other:3 spatial:6 np:2 ohnuki:1 nr:2 massless:2 briefly:1 repeat:1 photon:2 helpful:1 deriving:1 chance:1 important:2 invested:2 n1:2 structure:9 calls:1 holes:2 rule:2 mass:4 time:7 antilinear:1 n2:2 n3:2 n4:2
|
quant-ph9611049.txt |@word represent:1 consider:1 crucial:1 excellent:1 desirable:1 resistance:3 eds:1 mill:1 centimeter:1 localized:1 particles:4 certainly:1 inverse:1 alamos:2 equivalence:1 anglin:2 charge:9 far:1 wave:4 electron:10 difference:1 continued:1 encounter:1 paz:1 disturb:1 unlike:1 damped:1 large:2 hypothetical:1 ups:1 direct:1 approximation:1 rate:3 theory:1 even:2 sum:1 brief:1 current:3 experiment:1 above:1 new:2 body:1 full:3 here:1 understanding:1 behaviour:1 slow:1 free:1 separation:2 relaxation:1 path:1 along:2 strong:2 observing:1 leaves:1 shaded:1 makes:1 examining:1 adjustable:2 inducing:1 merely:1 plenum:1 highly:1 brought:1 passage:2 λdb:2 stream:1 would:1 remains:1 laflamme:1 predictions:1 ψt:2 few:1 therefore:3 taken:1 theoretical:3 today:1 ψe:5 resistor:1 conductor:9 diffracted:1 particular:1 known:1 must:4 states:5 room:3 mm:1 science:1 challenge:1 crossed:2 thin:1 ρv:1 believed:1 example:1 ions:2 figure:1 process:1 high:2 effectively:1 slit:1 end:1 varied:1 pure:1 rather:1 regions:1 fourth:1 familiar:1 instead:3 parameter:2 profile:2 product:3 may:3 overall:1 after:2 produce:3 designed:1 realized:1 effective:1 joint:1 lines:1 manganese:1 provide:1 negligible:2 allow:1 correlation:1 order:6 typical:1 constituents:1 over:12 vary:1 produced:1 thermal:3 through:4 statistical:1 still:1 its:1 before:1 rapidly:1 decay:1 interesting:1 τd:3 scully:1 actually:1 detected:1 systems:1 insulator:1 mail:1 τr:4 into:1 interference:4 greater:1 propose:1 frontiers:1 effects:2 nov:1 discuss:1 easily:1 fully:1 sufficiently:1 magnitude:1 reasonable:1 crossing:2 found:1 beneath:1 heavy:1 weighted:1 there:1 gaussian:1 used:1 expect:2 quantum:10 laboratory:1 space:1 since:2 induces:1 b288:1 formula:1 darling:1 occurs:2 linear:3 interactions:1 enforcing:1 possibility:1 like:1 completely:1 york:1 estimate:1 mimic:1 interaction:2 determining:1 could:2 motion:2 length:3 disturbed:1 conductors:2 first:1 flying:1 probability:3 number:1 passes:2 given:2 perturbation:1 temperature:3 their:1 introduction:1 top:1 system:6 indicate:1 rates:1 calculations:2 national:1 low:1 passed:2 wavelength:1 zeroth:1 took:1 begins:1 wide:2 double:1 second:1 final:4 preparation:1 were:1 treated:1 resistivity:4 recover:1 any:1 option:1 bohm:1 strength:3 zero:1 lumps:1 convenient:1 able:2 note:1 deconstructing:1 saturation:1 take:2 so:1 detector:2 play:1 towards:2 altered:1 though:1 measures:1 most:1 metal:1 feynman:2 electrons:2 principle:1 pattern:1 velocity:1 physics:3 3q:1 fact:1 shor:1 phenomenon:2 intensity:1 show:1 probe:3 fleming:1 chuang:1 trivial:1 q2:1 state:6 should:4 only:1 indeed:1 plate:22 means:1 beams:1 zurek:5 de:1 stop:1 beam:2 october:1 nearly:1 probably:1 lattices:1 evolution:2 densities:2 ohmic:3 investigate:1 qi:4 traverse:1 set:2 computed:1 clarified:1 sensitivity:1 depends:1 result:1 close:1 nonequilibrium:1 surfaces:1 mechanically:1 crystal:1 phonons:2 macroscopic:1 written:1 between:8 limit:1 approach:1 across:3 speed:2 ends:1 terms:1 distinguish:1 suppressed:1 both:1 heating:1 passing:1 boyer:2 among:2 presumably:1 simple:2 kilometers:1 proton:1 height:5 dimensional:1 non:2 considering:1 decohere:1 finally:1 described:1 stretch:1 trajectory:8 due:2 been:3 pc:1 arxiv:1 deliberately:1 ph:1 flight:2 concerning:1 gas:6 precision:7 bulk:2 coherent:1 wake:1 metals:1 present:1 case:2 contemplated:1 might:1 value:1 will:16 suppose:1 characterizing:1 layer:1 unitary:1 concomitant:1 mexico:1 thus:5 them:1 surface:1 according:1 currents:4 different:3 perhaps:1 make:1 cross:1 same:1 orders:1 unity:1 quant:1 units:1 higher:1 calculation:1 investigated:2 trajectories:9 effect:1 driven:1 ion:2 moving:1 contribution:1 electromagnetism:1 suitable:1 discounted:1 possessed:1 thought:1 patterns:1 without:1 greatest:1 position:2 model:1 charged:9 distances:2 stringent:1 proposed:1 resistive:1 cease:1 predicts:1 scattering:1 adding:1 disturbance:2 slits:1 treatment:1 role:1 mod:1 real:1 tests:1 aspects:1 sums:1 using:2 advanced:1 apart:1 particle:25 semi:1 adiabatic:1 facing:1 arbitrary:1 sketch:1 because:2 classical:6 some:2 broglie:1 proper:1 specific:1 scale:4 describing:1 electromagnetic:1 extensively:1 per:1 does:1 2mkb:1 measuring:1 varying:3 noise:1 power:1 expansion:1 singly:1 joule:1 properties:1 conducting:11 dependence:3 o:1 distinct:1 range:4 rev:6 communication:1 image:6 within:2 references:1 primarily:1 proportional:4 classicality:1 theoretically:1 classically:1 suffice:1 initial:2 los:2 inner:3 astrophysics:1 function:3 alloys:1 but:5 ford:1 technologies:1 made:2 compute:1 places:1 characteristic:1 inside:1 up:1 record:1 ωm:1 distribution:2 more:1 distance:3 mechanics:2 constant:2 moore:1 flow:1 abstract:1 textbook:1 general:2 single:1 our:4 moves:1 dashed:1 when:1 detail:1 field:1 electrical:1 spatial:2 test:7 conclusion:1 picture:1 superposition:1 models:2 important:1 allowing:1 dissipation:4 nuclei:1 implies:1 assume:2 required:1 diffraction:1 together:1 dragged:1 phonon:1 mass:3 time:5 serious:1 decoherence:24 coherently:1
|
quant-ph9611050.txt |@word represent:1 partial:1 consider:3 caused:1 magnetic:2 results:6 illustrated:1 eds:1 follow:2 zinn:8 whose:1 depend:2 calculate:1 technique:1 γv:1 rg:3 giso:3 stable:5 anharmonic:11 divergent:2 applied:1 very:9 implicitly:1 rise:1 wave:1 αmin:3 sensitivity:2 experimentally:1 difference:1 exact:10 condition:3 quartic:2 presented:2 cause:1 anisotropy:6 solution:5 fewer:2 large:9 vector:4 demonstrated:1 indices:1 eigenvalues:3 upper:2 zn:2 smaller:1 pms:1 arnimallee:1 10g:1 approximation:17 elegant:1 second:6 zu:1 zv:1 scientific:3 employ:1 appear:1 brackets:1 trivial:1 section:1 expressed:1 above:4 new:3 increasing:4 3d:1 coefficient:1 fiz:1 respectively:2 never:1 component:4 here:1 objects:1 free:1 represented:1 ratio:4 along:1 strong:13 z0:1 deduced:2 obtained:11 great:1 study:1 studied:1 simultaneous:2 loop:5 suggestion:1 published:1 action:2 studies:1 plotted:9 nmax:10 via:5 br:1 brezin:1 extra:1 explained:2 ipn:5 9g:1 apn:4 use:3 figure:19 positive:1 contains:1 negative:1 next:1 aharony:1 going:1 therefore:1 type:2 more:1 chapter:1 composite:3 becomes:1 under:3 curvature:2 14g:1 berlin:3 observations:1 particular:1 known:11 cases:1 must:1 account:1 mc:7 permits:1 recall:2 equation:2 work:2 oscillator:17 extremum:1 values:7 following:4 example:2 renormalization:10 indicated:1 chosen:4 calculation:1 permutations:1 sokolov:2 indicates:2 minimum:5 numbers:3 regularization:1 biso:2 nontrivial:3 criterion:3 justin:8 optimal:17 parameter:16 φ2b:2 fu:1 frohlinde:3 may:2 derived:1 applications:1 fundamental:1 plane:2 physik:1 magnetizations:1 choice:3 constants:10 schulte:3 short:1 natural:2 third:1 plateau:1 interpolates:1 so:3 allow:1 taking:1 amit:1 order:25 βk0:1 βk1:2 βk2:2 pointed:1 eqs:3 indistinguishable:1 stability:8 paper:4 resummed:11 captions:1 its:1 before:1 le:7 group:4 wallace:1 somewhere:1 interesting:2 vicinity:2 decreases:1 systems:1 pad:5 defining:1 versus:3 cusp:2 universality:3 scaling:1 mention:1 subtraction:2 they:1 half:2 oxford:2 nov:1 now:4 represents:1 term:4 university:1 accompanying:1 2e:1 2g:2 reasonable:1 each:4 crossing:1 found:14 universit:1 reproducing:1 square:1 prompted:1 series:9 energy:11 hard:1 idea:1 related:3 used:4 combining:2 loops:2 zm2:1 approximated:2 transitions:4 eq:14 special:2 out:2 shown:6 matrix:2 res:1 since:4 rev:7 rameter:1 contained:1 investigation:1 izv:1 denoted:2 ref:8 plotting:1 shows:1 numerical:2 turning:5 theory:19 interactions:1 little:1 possibility:1 small:5 formation:1 york:1 dx:2 nitskii:1 beginning:1 e0:2 βu:1 βv:1 interaction:8 sijkl:3 transition:1 δil:1 βg:1 iso:2 isotropic:17 δij:3 δik:1 βn:3 eexact:1 exhibited:1 first:3 origin:2 informations:1 initial:1 symmetry:5 powerful:1 number:5 theoretische:1 restrict:1 simplified:2 another:2 carry:1 compared:2 ser:1 interchange:2 given:6 perturbation:14 integrals:1 their:2 introduction:1 zφ:6 system:3 relations:1 indicate:1 zeros:3 too:1 calculations:1 scheme:3 exponents:5 gives:1 1g:2 estimates:3 exactly:4 zeroth:2 measurable:1 x2:3 than:2 coefficients:2 wide:1 variational:3 unfortunately:1 accordance:1 gotten:1 approximations:2 rate:2 preparation:1 determined:2 were:1 powers:1 exhibit:1 lowest:2 fluctuation:1 summable:1 curves:2 already:2 close:6 principle:1 pokrovskii:3 orders:2 symmetrized:1 lie:3 strength:2 minimally:1 zero:2 depending:1 physique:3 isolated:1 potential:2 zφ2:4 negligible:1 coincide:1 mayer:2 becoming:1 accuracy:3 heisenberg:2 formulas:1 akad:1 gβ:1 shall:3 object:1 most:6 guillou:7 letter:1 phase:5 class:4 stands:1 don:1 consequences:1 calculated:2 flow:1 points:5 diagonals:1 exp:3 physics:1 fact:1 slope:2 show:2 infrared:4 implying:1 hypercube:1 ground:14 based:3 knowledge:1 parameters:4 only:5 explicitly:2 employed:1 over:2 dd:1 closely:1 dw:1 procedures:1 symbols:1 arxiv:1 expansions:9 2b:1 nauk:1 fixed:35 favoring:1 approaching:1 green:1 set:1 statistical:1 exists:2 physically:3 δjk:1 δjl:1 lett:6 edition:3 see:10 bare:3 result:8 recently:1 theoretic:1 vint:1 best:1 techniques:1 zkn:3 detect:1 interacting:2 discretized:1 review:1 symmetric:10 state:14 various:7 correctly:1 between:4 approach:2 available:1 attention:1 terms:3 intending:1 domb:1 restricting:1 however:2 reproduces:2 invisible:2 ferromagnet:1 tensors:1 suggested:1 both:3 x2i:1 strongcoupling:2 numerically:1 qft:1 many:1 region:6 uncertainty:1 σg:2 cub:2 against:2 ln:2 γij:2 expression:1 experimental:1 otherwise:1 ck:1 relevant:1 destabilized:1 conclude:3 simple:7 complies:1 corresponds:3 dimensional:2 path:1 constant:11 crystalline:1 extrema:2 described:1 transformations:2 addition:1 due:2 been:7 interest:1 anisotropic:6 ph:2 choose:2 graphical:2 corresponding:9 6g:1 itzykson:1 sufficient:2 coincides:1 relevance:1 determination:4 derivative:1 spin:1 present:1 case:11 reliable:1 resummation:18 value:22 will:5 euclidean:2 while:1 viii:1 behavior:8 error:2 φbk:1 φbj:1 φbi:4 couplings:1 procedure:1 polymer:1 vb:8 vol:2 refs:3 thus:4 equal:2 reads:1 itself:1 converts:1 around:3 different:2 sensitive:1 make:1 renormalize:1 cross:1 same:4 any:1 shorter:1 φb:3 quant:2 arguments:1 largest:1 φi:6 finite:1 higher:1 independent:1 extended:1 singapore:1 cubic:35 comprehensive:1 trajectories:1 hand:1 edges:1 purpose:1 infinite:1 kleinert:13 recent:1 lower:1 off:1 reflection:1 sssr:1 well:2 analysis:1 academic:1 without:1 does:1 components:10 easily:1 model:3 usual:1 ferroelectrics:1 less:2 increasingly:1 percent:1 accurate:3 resolution:2 freie:1 jetp:1 world:3 βkn:5 previous:1 preprint:2 γijkl:1 field:22 point:40 seems:1 bnv:1 bnu:1 other:1 combine:1 δijkl:3 prominently:1 real:3 saturation:4 fluctuating:1 increased:1 depends:1 eigenvalue:1 read:1 breaks:1 sums:1 possible:1 smallness:1 five:5 know:1 similarly:1 press:5 using:8 intersection:2 loss:1 success:1 δv:10 follows:2 δu:10 isotropy:1 continue:1 yields:4 either:1 janke:7 become:1 indications:1 old:1 methods:1 classical:1 truncated:1 phenomena:3 unnecessary:1 corroborate:1 b0:9 b1:3 b2:2 table:7 neglecting:1 ourselves:1 ezin:1 anisotropies:1 dimensions:3 critical:11 exposition:1 unstable:1 minimal:4 inaccurate:2 power:7 convincing:1 bn:1 confluent:1 expansion:4 clarendon:1 ratios:1 instability:1 optimize:1 gained:1 comparison:4 carried:1 certainty:1 dependence:7 o:15 sufficently:1 ensure:1 efforts:1 introduced:1 cambridge:1 significant:1 pergamon:1 into:1 integral:3 functional:1 three:1 accommodate:1 lies:9 en:4 references:1 determine:3 sov:1 operator:1 statistics:1 institut:1 drouffe:1 there:2 long:1 pochhammer:1 borel:5 way:1 l137:1 was:4 function:12 considerably:1 hypergeometric:1 form:3 energies:5 forming:1 δkl:1 differences:3 but:1 khmel:1 expected:1 convergence:7 highest:1 persisting:1 made:2 up:7 us:2 ur:1 crystal:1 below:2 convince:1 limit:1 problem:1 ub:8 mechanics:2 associated:1 vpt:4 defined:2 certain:1 abstract:1 measure:1 influence:1 evidence:2 quantum:7 single:1 exist:3 our:2 crystals:3 proceeds:1 physical:2 again:2 functions:19 beyond:1 no:4 index:1 when:2 detail:2 application:2 definitely:1 ns:13 conclusion:1 draw:1 permitting:1 calculating:4 models:1 vertex:1 variation:1 important:1 structure:1 ago:1 implies:1 coupling:32 algorithm:6 practically:1 4w:1 curve:1 governed:1 mass:3 time:1 4g:1 starting:1 having:2 once:4
|
quant-ph9611051.txt |@word sergei:1 darboux:5 consider:1 remarkable:1 funct:1 results:2 leads:1 eds:1 scalar:2 commute:1 grateful:1 devoted:1 whose:1 γx:1 const:3 celeghini:1 helps:1 under:1 anharmonic:2 δca:1 case:4 straightforward:1 tends:1 zachos:1 entire:1 hamiltonian:4 turns:3 sklyanin:1 solution:1 solved:1 tomaras:1 eigenvalues:1 anal:1 degeneracy:1 consistent:1 arnimallee:1 second:8 rigorous:1 dynamics:5 volovich:1 aˆi:2 established:1 appear:3 brackets:1 interactions:1 batalin:2 ˆb:8 above:2 ˆi:5 ˆj:1 ˆk:1 method:2 contrast:1 coefficient:3 compact:1 simultaneously:2 respectively:3 hq:1 never:1 here:1 inverse:1 path:1 equations:2 obtained:5 remark:1 rigorously:1 institute:1 leaves:1 changed:2 allows:1 approaches:1 eva:1 resulting:1 poisson:5 action:1 makes:1 via:1 regardless:1 kinematically:1 manage:1 floratos:1 texts:1 ipp:1 planck:1 readily:1 use:1 would:1 commun:1 remains:1 positive:2 negative:1 nucl:2 therefore:7 taken:1 type:2 theoretical:1 becomes:1 operators:4 validity:1 berlin:2 virtue:1 particular:3 known:2 must:1 springer:1 chaichian:2 deformed:23 recall:1 equation:2 oscillator:8 obvious:1 following:7 arrive:1 example:4 qdeformed:1 renormalization:1 shabanov:2 give:1 πj:1 ckn:1 degenerate:2 irreducible:1 unphysical:1 occur:3 absolute:1 goal:1 ahler:11 rather:3 describes:1 means:2 xˆ:9 how:1 nontrivial:2 answer:1 ordinary:2 parameter:2 l873:1 algebra:19 may:4 oscillators:2 after:1 plane:2 dokl:1 representations:1 constants:1 natural:1 dynamical:5 effective:1 explicit:1 correspond:1 provide:1 ones:1 so:5 representation:1 order:1 interpretation:1 ϕk:1 indeed:3 pointed:1 satisfied:1 interpreted:1 course:1 mathematicians:1 paper:1 through:4 looks:1 mentioned:1 existence:2 excitations:3 diagonalized:1 group:2 chosen:1 ϕa:4 solving:1 coordinates:11 actually:1 degrees:2 systems:10 jacobi:7 ϕb:2 might:3 deformation:9 correspondence:2 non:9 ya:1 introduce:1 framework:2 they:1 nov:1 now:2 yu:1 possess:1 dirac:5 university:1 level:1 hermitian:1 2z:5 establishing:1 mode:2 each:2 2m:1 side:2 associative:1 constraints:8 ϕi:1 weyl:11 energy:3 hard:1 related:3 elementary:1 frequency:1 quantum:21 our:1 operation:1 eq:1 special:1 out:4 emerges:1 shown:2 matrix:3 space:19 since:1 rev:1 projected:1 particles:1 attracted:1 izv:1 induced:5 correct:2 math:9 theory:12 found:1 kulish:3 given:2 free:2 standard:1 admits:1 reason:1 complicated:1 muller:1 definition:1 interaction:1 ds2:1 motion:4 turn:2 int:1 δik:1 hence:1 first:5 xk:1 initial:2 humboldt:1 variables:9 another:1 schwenk:1 xp:1 appl:1 guess:1 necessarily:1 iak:2 ordering:7 πk:2 πi:2 system:7 relations:5 assumption:1 manifolds:3 postulate:2 cycle:1 structures:2 gives:1 holomorphic:3 representing:1 than:1 coefficients:1 tarlini:1 kindly:1 gik:4 see:4 yang:1 naturally:1 treated:2 distinguished:1 result:1 exhibit:1 bridge:1 symmetries:1 biedenharn:1 dynamically:2 spectrum:1 generalization:1 curved:1 constrained:8 any:5 conversion:2 latter:3 instance:1 potential:3 generalized:1 analogy:1 coincide:1 canonical:10 heisenberg:16 lectures:1 sure:1 shall:3 algebraic:1 regular:1 renormalizing:1 but:1 phase:18 class:10 tensor:1 ka:1 observation:1 considered:2 ki:1 sometimes:1 coincides:1 kn:7 bracket:6 li2:2 physics:2 fact:1 arnol:1 show:1 friction:3 relation:7 substituting:1 trivial:3 giachetti:1 proposed:2 should:3 explicitly:2 ambiguity:1 developed:1 circle:1 local:1 suq:3 get:1 familiar:1 simplest:1 mignani:1 ϕn:1 dz:2 words:1 new:1 ahlerian:1 gen:4 alexander:1 exhibiting:1 approach:2 arxiv:1 yield:1 fixed:1 view:1 set:2 δjk:1 depends:1 p20:1 eliminating:1 violet:1 discussions:1 macfarlane:1 quantizing:4 said:1 commutation:10 various:1 between:1 invariant:1 mathematical:2 encounters:1 notice:3 terms:1 extend:1 attention:1 however:3 untouched:1 jk:4 phasespace:1 last:1 taking:1 equal:1 quantization:9 fulfilled:1 symplectic:32 casimir:1 otherwise:1 point:2 simple:1 harmonic:2 leading:1 dimensional:1 conjugation:2 consideration:1 associated:4 hoissen:1 pp:2 configuration:1 commutative:5 aˆ:3 associativity:2 locally:1 due:4 been:2 defined:2 much:1 basic:1 ph:1 algebras:5 ak:3 xxvi:1 θj:9 θk:2 θi:3 corresponding:2 commutes:1 convert:1 berezin:1 general:2 irrelevant:1 present:1 p2:1 p0:2 frozen:1 choices:1 while:2 replaced:1 euler:1 lukierski:1 exist:1 property:1 procedure:1 real:2 von:1 thus:5 surface:3 obeying:1 reads:2 ij:11 ia:2 ig:1 cjk:2 different:2 author:1 make:2 same:1 complex:4 quant:1 diagonalize:1 extended:2 infinity:1 imply:1 upon:6 kokkotas:1 hand:3 potentials:1 illustrated:1 identity:7 destruction:2 modes:1 acknowledgement:1 modeled:1 academic:1 without:1 coordinate:2 arising:1 manifold:7 just:2 being:1 obtain:4 2ˆb:1 drinfeld:1 useful:1 yet:1 adding:1 lattice:1 transformed:2 lett:12 mod:2 transformation:3 momentum:2 resolved:1 desy:1 spanned:2 press:1 formal:5 fradkin:1 appearing:1 like:1 particle:7 follows:1 serves:1 specific:1 yields:1 arbitrary:1 works:2 gauge:3 depend:1 therein:1 right:2 methods:1 classical:13 sequent:1 creation:2 some:4 examples:2 oscillations:1 curious:1 provided:1 lead:1 eiθ:1 avoid:1 footing:1 pep:1 does:2 assuming:3 prof:1 proc:1 ωij:4 faddeev:1 obey:1 bb:1 bc:1 equivalent:2 symp:1 qˆ:4 raise:1 freedom:2 fairlie:1 discussed:1 o:4 covariant:2 obeys:1 woronowicz:1 germany:2 introduced:1 baxter:1 h2:3 into:5 within:1 integral:3 appropriate:1 because:2 references:2 wess:1 determine:1 sov:3 operator:8 accumulated:1 reducing:1 aref:1 there:3 question:1 long:1 dilogarithm:1 quadratic:6 physicists:1 way:3 ixp:2 analyze:1 was:1 assumes:1 iˆ:1 function:4 form:8 regard:1 δkj:1 amongst:1 construction:1 cij:2 variations:1 us:3 below:2 sorace:1 limit:5 demonstrate:2 problem:3 ωb:1 called:2 mechanics:9 ab:3 constant:3 ai:2 abstract:1 aj:6 fellow:1 pˆ:12 formalism:1 metric:4 physical:10 functions:1 no:1 whereas:1 when:1 cˆ:1 graduate:1 application:2 other:4 mathematics:1 naive:1 describe:1 curvature:1 structure:27 multimode:1 ago:1 assume:1 pusz:1 interval:1 rule:8 time:1 observables:2 daskaloyannis:1
|
quant-ph9611052.txt |@word consider:5 remarkable:1 ali:1 depends:2 caused:1 magnetic:13 results:4 leads:7 killam:1 commute:1 generalize:1 computation:1 parameterization:1 reasoning:1 whose:1 certainly:1 inverse:2 depend:2 calculate:1 re:1 exponentiation:1 monotonically:1 present:1 marks:1 alberta:3 te:1 straightforward:1 very:2 springer:1 geometrical:1 corollary:1 every:3 redefinition:3 exact:15 condition:5 level:2 zeit:1 irreducible:1 solution:19 integrated:1 try:1 solved:1 vector:6 differentiates:1 razavi:1 manifestly:1 eigenvalues:3 enforce:1 kato:2 sin2:1 direct:3 approximation:10 zero:2 eiαn:2 pass:1 further:3 dynamics:3 canonical:13 spectral:1 appear:1 section:2 expressed:1 reminiscent:1 experiment:1 intersect:1 new:2 3a:1 increasing:1 method:3 simultaneously:1 component:2 here:4 simon:1 inversion:1 const:5 november:1 quite:2 equations:1 change:1 obtained:3 institute:1 involved:1 study:4 resulting:1 procedure:2 resonance:1 implement:1 spacetime:1 via:1 projection:3 requiring:3 namely:1 replace:1 total:2 unit:2 use:4 takes:1 would:1 recalling:1 positive:1 bundles:3 negative:4 next:4 derivation:1 therefore:6 associated:2 type:1 theoretical:2 more:4 knows:1 suggestions:1 dxµ:1 odinger:27 everywhere:1 hilger:1 particular:5 known:3 foundations:1 cases:4 must:3 parameterize:1 γn:4 valued:5 quantized:1 indicates:1 recall:2 equation:32 london:1 fock:2 renders:1 following:3 making:2 abelian:4 calculation:5 relativistic:1 neglected:1 states:2 sphere:2 degenerate:1 sense:1 tan:3 axis:5 rather:1 holds:1 feature:1 write:2 pure:1 simplifies:2 verlag:1 parameter:3 sin:19 circular:1 simplicity:1 product:2 algebra:1 may:4 after:2 different:1 consequence:2 levi:1 plane:2 choice:1 parallel:5 natural:1 dynamical:1 effective:2 resemble:1 correspond:2 su:6 cosmology:1 switch:1 so:1 enter:2 representation:3 order:4 δmn:1 dx:1 zee:1 indeed:1 pointed:1 satisfied:1 course:1 paper:4 through:1 during:2 japan:1 still:1 its:6 derive:1 group:3 thank:1 acknowledge:1 chosen:1 solving:2 coordinates:2 actually:1 forms:1 h2:2 systems:5 jacobi:1 derivative:1 h0:1 non:7 views:1 hamilton:1 effects:1 half:1 arriving:1 nov:1 now:2 easily:4 term:1 always:1 university:1 hamiltonian:38 identified:1 orthonormal:1 magnitude:3 turns:2 found:1 repeating:1 traces:1 side:2 em:1 holonomy:3 financial:1 series:1 energy:1 idea:2 frequency:2 obtains:2 quantum:16 eq:9 special:2 out:4 canada:2 large:4 shown:3 matrix:1 space:5 furthermore:2 induces:1 denotes:2 transforming:2 ra:5 induced:2 occurs:1 foundation:1 fiber:1 theory:7 terminated:1 enforcing:1 standard:1 applications:2 base:1 york:1 remainder:2 r0:4 r1:1 r2:1 r3:2 geometry:1 iterative:2 times:1 introduction:1 length:3 hence:7 onto:2 first:3 origin:3 initial:1 symmetry:1 relate:1 variables:2 number:1 transform:1 restrict:1 relations:1 another:6 precisely:1 angular:5 wilczek:1 given:6 similarly:1 ordering:1 unknown:1 eqs:1 system:4 least:1 nian:1 scheme:1 collapse:1 centered:2 reversed:2 exactly:9 optical:1 because:2 representing:1 peculiar:1 determines:1 third:1 was:1 iteration:1 computes:1 project:1 nakahara:1 determined:1 perturbative:1 generality:2 ann:1 concludes:1 turned:1 curves:1 seen:2 seem:1 clearly:3 lie:1 wilson:2 pursued:1 latter:2 mills:5 note:9 potential:2 sufficiency:1 finding:1 negligible:2 even:1 begin:1 unless:2 shall:7 phases:1 simplify:1 successive:2 phase:5 acknowledgements:1 class:2 observation:1 considered:2 yang:5 exp:2 physics:3 fact:4 eiℓ:1 particularly:2 show:3 timedependent:1 ϕj1:1 chapters:1 rotating:1 gauge:11 civita:1 trivial:1 find:1 principal:2 ualberta:1 parameters:2 state:5 than:1 lemma:9 only:4 explicitly:3 generators:1 hamiltonians:9 local:2 over:2 do:2 above:2 means:1 dependent:7 express:1 cannot:2 words:1 portions:1 dt:8 dr:1 adiabatically:1 evolution:14 arxiv:1 ja2:1 yield:1 patch:1 nα:1 nγ:1 nδ:1 valid:3 view:3 set:4 exists:2 frame:6 j1:11 j2:4 j3:11 see:7 result:1 transportation:4 analog:1 hilbert:5 nuclear:1 dipole:8 symmetric:1 written:1 closed:1 probably:1 geometric:5 conditions:2 αn:4 preserve:1 terms:4 nature:1 however:4 article:3 ja:6 jb:2 jc:1 both:2 cos:12 last:1 deals:1 ir2:1 ir3:4 according:3 muriel:1 hψ:1 berry:2 casimir:1 uni:1 expression:6 finds:2 arbitrarily:2 mechanics:4 cn:2 cm:3 point:1 simple:2 ca:1 corresponds:6 a392:1 dimensional:3 anti:1 iterations:1 path:1 constant:6 ǫabc:2 most:3 transformations:14 second:1 basis:2 due:2 springerverlag:1 reduction:3 describes:3 treat:1 pe:2 expected:1 combine:1 ph:2 topology:1 dℓ:2 choose:2 direction:4 corresponding:1 quantities:1 royer:1 generalization:1 systematic:1 mail:1 c1:2 repetition:1 spin:2 iσ:3 those:3 case:17 traced:1 guided:1 will:3 angles:2 leaves:1 property:1 iℓ:2 loop:2 planar:3 unitary:7 approximate:1 played:1 refs:1 thus:1 encountered:3 sudden:1 vanish:3 lengthy:1 perform:1 make:2 amn:3 connection:1 same:7 unity:2 quant:2 arguments:1 widely:1 units:1 finite:1 difficult:1 evolve:1 used:7 upon:1 effect:1 hand:3 driven:1 moving:2 purpose:1 changing:3 totally:1 recent:1 eigenvectors:8 schr:27 thy:1 makes:1 variety:1 well:1 analysis:1 bohm:2 without:2 solve:2 components:1 sets:1 coordinate:1 termination:1 spherical:1 manifold:1 tip:1 edmonton:1 identically:1 obtain:2 intervals:1 alternative:1 eigenstates:3 aaµ:4 like:1 preprint:1 application:4 iϕ:3 except:1 iψ:1 priori:1 transformed:7 lett:2 easy:3 extensive:1 solvable:7 transformation:13 momentum:3 real:2 iθ:1 2j1:1 eigenvalue:1 possible:1 period:1 possibly:1 confined:1 using:3 unique:1 mod:1 loss:2 replacing:1 particle:1 alternatively:2 reduces:2 adiabatic:9 δn:4 δm:4 yields:7 either:1 integrals:2 arbitrary:2 simply:1 stationary:4 essential:1 right:3 methods:1 classical:1 some:5 born:2 choosing:1 moreover:1 extended:2 transport:1 eiα:1 provided:3 dimensions:1 lead:2 avoid:1 comments:1 does:5 provides:1 proc:1 ij2:1 eiϕ:1 equivalent:3 notable:1 expansion:3 eiσ:1 invaluable:1 approximating:1 properties:3 handled:1 hamilto:1 constraint:1 dependence:1 convenient:1 larmor:1 consequently:1 soc:2 rev:4 rj3:1 presence:1 previously:1 h3:1 into:1 h1:7 three:3 down:2 variable:3 appropriate:3 en:9 references:1 operator:16 proportional:1 utility:1 performing:1 area:1 support:1 there:5 u1:8 u0:11 u3:4 u2:3 inner:1 way:4 ed:1 adam:1 sections:1 combined:1 function:2 considerably:2 form:14 basic:3 but:1 atom:1 line:1 especially:1 made:1 compute:1 up:1 us:7 complications:1 demonstrate:2 problem:5 aa:2 intersects:1 defined:5 recognize:1 abstract:1 general:11 single:4 exist:1 periods:2 dθ:1 functions:1 no:2 mostafazadeh:3 when:1 vanishes:3 field:10 other:1 role:1 nr:1 operators:1 conclusion:2 happens:1 elements:3 symbol:1 bundle:2 includes:1 zwanziger:1 included:1 t6g:1 sides:2 assume:2 curve:12 dσ:1 original:6 dot:1 time:31 dϕ:2 roy:1 having:1
|
quant-ph9611053.txt |@word consider:2 ali:2 magnetic:3 particular:2 results:4 leads:5 killam:1 expressions:1 whose:6 inverse:1 const:1 equivalence:1 finally:1 γn:3 under:1 alberta:2 analogous:1 p2:6 very:1 kanai:1 redefinition:3 difference:1 exact:3 condition:4 hamiltonian:9 turns:2 solution:5 try:1 discrete:2 razavi:1 eigenvalues:1 dutra:1 consistent:1 sin2:1 sign:3 approximation:3 further:1 canonical:9 even:1 what:1 appear:1 expressed:4 above:7 new:2 consisting:1 satisfy:1 respectively:1 here:3 canonically:5 groups:1 november:1 equations:1 obtained:7 institute:1 study:1 larger:1 allows:1 suggests:1 resulting:1 action:1 changes:5 jackiw:1 orthonormality:1 summation:1 apply:2 total:1 establish:1 linearly:1 plot:3 use:5 would:4 remains:2 positive:8 brittin:1 negative:2 next:2 therefore:3 theoretical:1 operators:3 odinger:7 aware:1 riesenfeld:2 known:3 cases:3 must:2 kumar:1 recall:1 equation:8 oscillator:31 values:1 following:3 making:2 example:3 figure:1 indicates:1 performed:1 degenerate:1 sense:1 e2t:2 decaying:1 holds:1 maps:1 ordinary:2 parameter:1 sin:8 product:2 de:3 description:1 replacing:1 oscillators:10 applications:1 berg:1 constants:2 man:1 dynamical:2 su:2 order:2 least:1 developed:2 over:1 satisfied:2 during:1 mentioned:1 satisfies:2 still:2 its:2 thank:1 how:1 ln:3 interesting:3 late:1 systems:1 mail:1 main:1 might:2 theo:1 non:1 identically:1 souza:2 nov:1 now:1 articles:1 inversion:1 always:1 university:1 e2κ:1 each:1 2m:3 side:4 em:1 en:5 transforming:2 directly:2 series:1 energy:1 reduce:1 idea:1 related:1 frequency:30 obtains:1 quantum:1 eq:21 special:1 out:2 canada:2 shown:3 space:3 furthermore:2 since:4 rev:8 may:3 investigation:1 ref:2 math:5 shows:1 foundation:1 eiαn:1 fluctuates:1 albuquerque:1 free:2 reason:1 transition:1 tempting:1 hence:3 first:2 xc:2 e2iδ:2 transform:5 done:1 relations:1 another:3 xp:4 given:4 similarly:2 unknown:1 eqs:1 system:8 construct:1 their:1 allahverdi:1 scheme:1 reversed:2 continuous:3 x2:7 wide:1 determines:1 showed:1 iteration:1 see:2 annihilation:1 arun:1 generality:1 ann:2 spectrum:3 generalization:1 greenberger:1 seen:1 seek:2 clearly:1 depending:1 latter:3 able:1 ideas:1 note:5 potential:2 generalized:3 analogy:1 play:1 exactly:8 most:1 phase:2 acknowledgements:1 class:5 considered:1 implications:1 inferred:1 points:1 principle:1 exp:3 physics:1 fact:5 particularly:2 show:1 lewis:2 relation:2 solutions:1 substituting:4 ground:1 ualberta:1 parameters:1 universal:1 should:1 analytic:1 only:2 hamiltonians:2 do:1 cheng:1 dh:1 means:2 dependent:12 express:1 applying:1 dt:8 dr:1 gen:2 differentiating:1 adiabatically:3 evolution:11 arxiv:1 method:5 zhu:1 dodonov:1 analog:1 view:2 undergoes:1 frame:2 klauder:1 namely:3 result:2 discussions:1 recently:2 best:1 subject:2 fails:1 satisfying:3 µt:2 dipole:3 state:1 identification:1 closed:2 between:5 invariant:1 geometric:1 αm:1 αn:4 terms:6 missing:1 however:3 jr:1 concentrate:1 ji:2 article:2 both:1 cos:3 reverse:1 desired:1 acknowledge:1 according:4 chosen:1 hψ:1 expression:3 finds:1 otherwise:1 simple:4 ca:1 corresponds:3 associated:2 described:2 transformations:3 px:4 due:1 been:3 int:1 much:1 interest:1 basic:1 ph:1 dozens:1 tan2:1 fig:1 corresponding:3 fung:1 derivative:1 case:11 indefinitely:1 while:1 korsch:1 procedure:1 eκ:1 unitary:9 approximate:3 refs:1 ir:5 thus:1 vanish:1 ie:1 agarwal:1 perform:1 amn:6 same:1 quant:1 emphasize:1 grows:1 difficult:2 independent:4 arrives:1 hand:4 moving:1 purpose:1 kim:3 changing:1 identity:1 eigenvectors:1 schr:7 nevertheless:1 well:2 analysis:4 without:1 left:1 being:2 edmonton:1 obtain:1 immediately:1 yet:1 field:1 iψ:1 other:1 transformed:3 lett:2 versa:2 solvable:7 transformation:14 real:24 iκ:2 2j1:1 eigenvalue:1 iβ:1 possible:2 harmonic:13 using:2 mod:1 loss:1 necessary:1 like:2 particle:2 reduces:1 adiabatic:6 δn:3 abdalla:1 δm:2 yields:2 arbitrary:3 invaluable:1 reduced:3 right:3 classical:1 2iδ:2 creation:1 some:6 back:1 lead:3 does:1 expressing:1 tends:1 prog:1 equivalent:5 expansion:2 step:1 although:1 found:2 imaginary:12 hilbert:3 simpler:1 range:1 introduced:1 presence:1 previously:1 because:2 references:1 inverting:1 operator:11 financial:1 performing:2 additional:1 support:1 there:2 u0:6 hasse:1 m0:14 function:3 form:3 but:2 repeated:1 m02:1 repeatedly:2 made:2 compute:1 us:2 problem:4 called:1 constant:5 defined:1 ko:1 abstract:1 proven:1 general:2 single:1 exist:2 periods:1 dδ:1 physical:1 functions:5 mostafazadeh:2 whereas:1 vanishes:1 application:2 valid:1 role:1 repeat:1 a2:1 variable:2 t6g:1 sides:1 vice:2 assume:1 dτ:6 indirectly:1 mass:13 time:32 original:5
|
quant-ph9611054.txt |@word represent:3 monte:1 measurements:1 homomorphism:1 consider:19 global:4 splitting:1 integration:1 sαk:1 entropy:14 controversial:1 consists:4 gr:4 compact:1 increase:1 depend:3 referring:1 albrecht:3 tr:10 interactions:25 tn:6 uniqueness:1 indicate:1 tk:6 th:7 under:6 nodes:2 include:2 case:8 conjecture:1 iuj:1 risk:1 orthogonal:9 far:3 rise:2 differently:1 choice:4 every:2 orientations:1 ui:14 little:1 matrices:2 condition:5 generalised:2 dim:4 propagating:1 beginning:1 hamiltonian:6 ref:7 list:1 solution:1 t1:3 hartle:13 vector:4 ml:6 small:8 eigenvalues:2 barbara:1 proof:4 degeneracy:3 prevent:1 pragmatic:1 consistent:39 sin2:2 prediction:2 past:1 fold:1 zero:18 street:1 mk:1 further:3 dynamics:1 carlo:1 eigenspaces:3 linear:5 even:1 aim:1 what:2 λij:2 giving:1 trivial:14 section:6 selected:18 kent:5 version:3 en:2 goes:1 new:3 consisting:4 contrast:1 satisfy:4 relationships:1 give:1 degree:1 whose:2 respectively:1 never:1 equals:1 here:4 understanding:1 ranges:1 following:4 test:1 others:1 represented:2 path:3 november:1 strong:1 equations:1 change:1 obtained:2 incoming:1 parameters:1 wesley:1 study:1 larger:4 reason:3 experience:1 suggests:4 maximising:3 products:1 pick:1 usually:3 surely:1 suitable:1 spacetime:1 involves:1 genuinely:1 formulated:1 useful:2 projection:40 classification:7 requiring:1 merely:1 explained:1 highly:1 nk2:1 unitary:1 rπ:2 tp:1 apply:2 total:6 select:3 environment:20 use:9 takes:1 would:8 prove:1 probabilities:17 positive:4 pluses:1 contains:2 predictions:3 hilbert:13 comparing:1 call:4 therefore:8 criteria:5 taken:1 themselves:1 selects:11 theoretical:1 λmi:2 more:10 linden:7 flaw:1 vk:3 excluded:1 successful:1 becomes:2 operators:10 stable:3 constructs:1 odinger:2 studies:1 science:1 particular:4 projective:1 cases:5 hold:1 iii:4 must:10 extension:4 recall:1 work:2 mi:19 measures:1 theories:1 remain:3 ρr:4 values:3 minimisation:2 cam:1 those:2 making:1 root:2 example:13 history:18 grained:1 stated:1 calculation:1 introduces:1 allowed:5 suggestions:1 generically:9 πj:13 states:13 minimum:4 degenerate:2 arise:3 unphysical:1 sharp:1 subsystem:2 conversely:1 occur:2 subtrees:4 influenced:1 needs:1 end:8 compactify:1 rather:2 s2:2 discussion:3 holds:3 off:6 orthogonality:1 write:3 how:1 varies:1 criterion:6 pure:4 simplifies:1 instead:3 sin:21 falsifiable:1 product:2 description:4 information:68 may:6 max:3 after:3 variant:1 containing:1 substitute:1 hence:3 wrong:1 produce:8 designed:1 date:1 fk:5 unentangled:1 parallel:6 iθj:2 iθk:2 changes:1 natural:7 whenever:1 sq:2 sp:2 summing:1 su:1 element:2 sk:5 provide:3 2d:1 ones:1 so:30 specifying:1 allow:1 subsequently:1 z2k:1 s1:3 restricted:3 restriction:2 maximisation:1 interpretation:2 help:1 produces:3 minimising:3 over:9 insight:1 vary:2 satisfied:1 stability:2 course:1 paper:12 through:1 thesis:1 mentioned:1 satisfies:1 still:1 pointer:1 its:7 tendency:1 before:3 2mi:1 forwards:1 chosen:3 interesting:5 fix:1 jim:1 coordinates:1 writing:1 forms:3 previously:1 window:3 degrees:2 systems:6 tors:1 mail:1 schmidt:33 might:5 overcome:1 maximal:2 measurement:14 them:4 within:5 greater:3 combination:1 entire:4 introduce:1 mention:1 they:21 half:3 own:1 formulating:1 nov:1 now:8 silver:1 represents:1 term:3 finite:7 adjacent:3 goldstein:1 always:5 university:5 classified:1 a1n:5 orthonormal:2 realistic:6 good:2 finely:1 reasonable:2 each:19 done:3 entirely:1 uninteresting:1 vec:1 2k:1 homogeneous:1 lifted:1 square:1 directly:1 ek:6 evolve:1 series:5 hard:1 idea:3 inhomogeneous:1 used:17 expect:1 measure:5 quantum:17 laboratory:1 differ:4 eq:35 shannon:7 out:2 large:4 shown:2 matrix:20 space:19 unnatural:2 since:26 rev:12 projected:2 content:4 ajk:1 mα:8 dowker:3 mβ:5 formula:2 get:1 issue:1 correct:2 math:3 shows:5 occurs:3 earlier:2 theory:7 written:8 8a:1 diagonal:7 monotonic:1 completely:2 complicated:6 imperial:1 earliest:2 remainder:1 9ew:1 definition:2 pairs:2 interaction:31 r3:2 simulations:1 starts:2 could:7 times:23 turn:1 place:3 due:1 assumed:3 corrections:1 investigates:1 omits:1 onto:8 eqs:2 first:13 intuition:1 initial:24 xn:2 features:1 probability:18 variables:1 assumptions:1 number:7 rank:4 u0:3 restrict:1 infinite:1 devices:1 simplified:4 approximately:5 another:1 type:1 precisely:1 xt:6 size:1 complexity:2 given:1 perturbation:2 e1:1 rewritten:1 similarly:2 introduction:1 πk:2 interact:1 πi:8 πn:1 system:33 least:2 their:7 attack:1 perturbations:2 rooted:1 too:2 calculations:1 ordered:2 scheme:1 branches:2 final:4 speaking:2 gives:1 relies:1 imperfect:1 m0:1 relationship:1 completed:1 exactly:7 contribute:3 plus:1 part:6 authors:1 attempt:2 believe:3 than:7 specify:1 begins:2 approximation:1 princeton:2 was:1 pointers:1 tree:2 likely:6 submitted:4 halliwell:1 classes:3 were:2 enables:1 result:4 lowest:1 parameterised:1 symmetries:1 generality:1 ann:1 idealised:1 argument:2 roughly:2 say:1 unlikely:5 qualitatively:1 disjoint:1 seem:2 cosmology:1 any:18 generic:2 angle:1 dαα:6 dαβ:3 min:2 convenient:2 ideas:6 ucsbth:1 note:5 instance:1 take:8 analogy:1 indexed:2 algorithms:14 sn:2 heisenberg:2 continuous:3 unless:5 fundamental:1 investigations:2 trρ:1 xπ1:2 sets:50 extending:1 satisfying:1 experiences:1 ensure:3 letter:1 sfi:1 nothing:2 subset:1 future:1 intrinsic:1 class:20 es:1 interacting:2 cause:1 synonym:1 especially:2 considered:11 clear:3 later:6 stronger:3 inferred:1 typeset:1 looked:1 bracket:2 electrons:1 principle:2 exp:1 physics:2 xπ:8 incomplete:1 choose:1 precise:3 5th:1 selection:13 particularly:1 show:7 random:1 page:1 utk:4 spaces:1 solutions:1 california:1 d2:2 find:1 jaynes:1 d1:3 finally:1 urbana:1 eigenstates:2 situations:2 explain:1 histories:107 start:1 should:5 terminal:1 lemma:2 only:33 experiment:2 factor:1 attained:1 isham:8 local:2 axiom:1 discuss:1 dn:2 do:4 dj:1 above:1 notation:5 means:1 dependent:9 zurek:2 addison:1 generalise:1 αi:4 cannot:3 nearly:1 distinctly:1 combinations:1 during:16 quantifies:1 2ml:1 depending:2 eiθj:1 evolution:7 intuitive:1 conditions:11 arxiv:1 method:1 sum:7 utj:1 qc:4 qe:1 contain:3 mathematically:1 weaver:1 fixed:3 gell:6 valid:1 requirement:3 set:96 constructing:2 exists:2 edited:2 physically:9 correlations:1 quasiclassical:2 up:1 edition:1 see:7 individual:4 sec:2 projections:52 terms:6 iu:1 particle:10 best:2 subject:2 appear:2 said:4 computer:1 tensor:1 ways:2 pictures:1 missing:5 definite:2 tend:1 state:18 difficulties:1 various:1 closed:11 between:20 affecting:1 consecutive:1 αk:16 reading:1 approach:5 αl:2 αn:4 available:1 αt:4 recently:1 commence:1 complementary:1 initially:3 qπ:4 weak:5 however:9 wi:6 ωp:1 continuously:1 distinguish:1 ascribes:1 interfere:1 behaviour:1 cos:14 last:6 tractable:1 many:4 taking:1 conclusions:1 equal:1 constructed:1 agree:2 mathematical:1 negative:1 context:1 sense:1 estimation:1 expression:1 photons:2 mann:6 kets:1 arbitrarily:1 among:4 undone:1 timescale:1 supply:1 simple:12 favouring:1 corresponds:2 plusses:1 directions:5 minuses:2 simply:2 decreases:1 sequences:1 respect:5 throughout:2 considers:5 considering:2 combines:1 described:2 second:5 basis:4 three:4 been:1 ai:2 describes:3 coarse:2 pe:1 pj:5 pk:4 ph:22 pi:5 pn:2 ak:5 define:16 θj:10 θk:11 direction:6 senses:1 corresponding:3 finishes:1 both:2 mind:1 concerning:1 formed:9 analytic:1 modelling:1 finished:1 understand:1 general:6 spin:19 present:1 applied:5 p1:2 bπ:11 developing:1 defining:1 λ0j:1 value:1 choices:2 will:26 tre:1 suppose:4 viii:1 aid:1 ill:2 bπ1:5 vectors:5 almost:1 vi:3 refs:1 damtp:7 thus:3 non:17 vn:2 iv:2 ii:2 need:2 ik:3 itself:2 vanish:1 interacts:2 different:5 moves:1 projector:1 perhaps:3 suggest:3 make:4 dhc:1 same:16 clearly:1 drawback:1 quant:4 split:4 omn:1 largest:4 avoids:1 proved:2 defines:2 events:5 difficult:2 development:1 independent:9 literature:2 trivially:3 i1:3 optimisation:2 i2:2 nj:12 v1:1 nk:12 uses:2 along:1 computationally:1 a2j:1 a2k:1 identity:1 recent:1 numbered:1 schr:2 unconditionally:1 no:12 well:4 subtree:4 analysis:2 picks:1 concrete:1 without:3 greatest:2 consistency:19 very:3 quantitative:1 model:18 otherwise:2 dimension:3 schreckenberg:1 moving:1 proposed:2 less:1 being:3 generally:1 invariant:2 rest:1 intervals:1 predicts:2 immediately:1 λj:1 singularity:1 alignment:1 previous:1 progressed:1 nǫ:1 preprint:1 density:9 regarded:1 point:3 seems:5 except:1 δαk:1 reasons:3 interested:1 lett:2 easy:1 theorem:4 apart:1 remaining:1 real:4 iλ:2 vii:1 motivating:1 depends:5 easily:1 situation:1 replaced:1 gellmann:1 results:9 possible:9 additivity:1 early:1 interior:1 increases:1 embedded:1 press:1 using:17 unique:3 string:2 disadvantage:1 counterintuitive:2 necessary:5 like:2 excluding:1 deta:2 follows:1 picking:2 either:6 become:1 ie:1 reduced:4 spins:3 specifies:1 reidel:1 satisfactory:1 because:8 dordrecht:1 often:1 sequence:1 pαk:1 some:12 pαn:1 understood:1 examples:4 28th:1 moreover:1 extended:3 ourselves:1 nonzero:1 possibilities:1 vol:1 proceeding:1 sufficiently:1 though:6 2f:1 comments:1 minimises:1 does:7 decomposition:10 unit:2 tends:1 uml:1 particles:5 umi:5 augmenting:1 refer:2 measuring:1 process:1 experimental:1 algorithmic:1 selecting:3 equivalent:13 aj:7 ensures:1 nj2:1 revtex:1 santa:1 2m:2 cβ:2 cα:7 refers:1 properties:2 simpler:1 chapter:1 integers:1 about:6 pα:14 griffiths:1 carried:1 anything:1 constraint:1 freedom:3 triviality:2 discussed:2 o:5 essential:1 distinct:1 range:1 extensions:4 constraints:1 projectors:3 em:1 cambridge:3 statements:1 h2:4 communication:1 into:3 h1:5 bound:3 ut:2 pair:3 hermitian:1 right:1 references:1 operator:6 consecutively:1 next:3 relativistic:1 statistics:1 span:1 log:24 normalised:4 refinements:1 strictly:2 there:11 u1:2 approximate:2 long:1 why:2 lost:1 much:3 way:1 perform:1 sections:1 ensured:1 function:2 medium:4 complete:11 form:6 enough:2 regard:1 but:11 hj:1 hk:2 repeated:2 exact:3 line:2 removed:1 true:3 proposal:2 he:2 maximised:2 made:5 rotation:2 algorithm:47 consist:4 wπ:47 whether:1 prevents:1 probabilistic:1 maximum:22 us:1 ranks:1 below:2 un:2 limit:4 maximises:1 uk:71 uj:77 approaches:2 problem:7 similar:1 calculated:3 nature:1 mechanics:6 separated:5 ac:1 associated:2 choosing:4 computing:1 defined:16 abstract:1 describe:6 denote:2 single:2 θi:11 exist:1 rule:1 our:3 formalism:4 identities:1 physical:5 qα:2 functions:8 qβ:8 completeness:1 tentative:1 whereas:1 when:18 detail:2 illinois:1 preventing:1 started:1 other:12 special:3 branch:16 papers:1 department:1 mathematics:1 most:2 sufficient:5 node:4 picture:2 stat:1 elements:7 intend:1 generates:1 calculating:1 separate:1 models:2 preceding:1 problems:6 ultimately:1 includes:2 a1:3 cb3:1 meaning:2 important:2 bounded:5 yields:1 structure:1 searches:1 independently:2 implies:1 calls:1 assume:3 statistical:1 interval:1 together:4 graining:2 4n:2 weights:3 time:43 serious:1 decoherence:13 starting:1 having:1 augmented:1
|
quant-ph9611055.txt |@word represent:1 gu:2 consider:3 remarkable:1 rev:2 lack:1 concern:1 results:4 proposition:2 montr:2 consists:1 soc:1 devoted:1 whose:1 spin:2 equivalence:1 tr:10 passage:1 presents:1 finally:3 gu0:2 those:1 under:4 must:2 ın:3 applied:3 advantage:1 translations:2 springer:1 splitting:1 p1:6 every:1 ln:2 difference:1 condition:5 tri:1 did:1 irreducible:2 permits:1 solution:2 hereafter:1 leave:1 solved:3 vector:1 possibilities:1 lines:1 uva:3 za:1 zb:1 approximation:1 second:3 dynamics:1 fonction:1 linear:4 even:1 eia:1 stands:1 invertible:1 section:4 brief:1 henceforth:1 version:2 above:3 new:6 method:4 satisfy:3 notions:1 respectively:4 loose:1 nena:1 here:1 understanding:1 les:1 ansatz:3 groups:9 situation:1 represented:2 consideration:1 along:1 equations:1 appears:1 interpret:1 contraction:4 obtained:2 great:1 restrictive:1 study:2 studied:4 allows:4 completely:1 leaving:1 p2:6 accomplished:1 commutators:1 usually:3 hospitality:1 conveniently:1 suitable:3 honor:1 65th:1 subsect:1 family:1 requiring:1 explained:1 cylinders:1 unit:1 readily:1 ıa:4 use:2 commun:1 covariant:5 contains:1 next:2 assuring:1 program:1 therefore:1 taken:1 associated:7 type:1 ciencia:1 more:5 flat:1 remark:1 operators:15 odinger:1 berlin:1 particular:2 known:2 projective:4 cases:4 iii:3 hints:1 gadella:3 account:2 isomorphism:1 r2:1 quantized:1 integrating:2 work:4 reviews:1 infinitesimal:2 del:7 following:9 making:2 ingredient:1 averages:1 example:2 proof:1 dedicated:1 transition:1 give:3 process:1 relativistic:2 organized:1 purposes:1 states:2 14b:1 sense:3 inθ:1 orbits:8 simple:2 axis:2 requirements:1 verify:3 s1:1 acts:1 maps:2 nontrivial:1 guarantee:1 sin:6 product:12 proc:1 algebra:4 transforming:1 philosophy:1 mapping:5 consequence:1 plane:4 representations:7 choice:1 compatibility:1 fn:1 short:1 attempt:1 third:1 sw:31 correspond:1 element:1 so:3 representation:6 order:4 origin:5 holds:1 wigner:5 over:1 choose:2 years:2 paper:2 through:2 statistical:3 mentioned:2 existence:1 still:1 its:3 du:2 group:22 forme:1 till:1 chosen:1 interesting:1 lm:1 coordinates:6 complex:1 lr:2 systems:7 mail:3 dges:1 easier:1 correspondence:16 non:5 greater:1 rotations:2 introduce:1 reciprocally:2 ǫij:2 they:4 nov:1 now:2 association:2 kirillov:4 easily:1 inversion:1 finite:2 dirac:1 2q:1 verifying:1 invariants:1 classified:1 identified:1 quantizing:1 2d:2 l2:5 reasonable:1 each:3 found:1 2n:10 pb95:1 associative:1 reproducing:1 homogeneous:1 tensor:1 lifted:1 weyl:13 successively:1 reduce:1 idea:1 related:1 tracial:1 contracting:1 extended:1 factorization:1 measure:2 quantum:8 our:2 avoided:1 es:3 out:2 accomplish:1 matrix:1 space:25 rep:1 since:1 induces:2 particles:3 may:1 acting:2 reader:1 denoted:1 formula:2 get:5 induced:2 ref:5 math:6 theory:12 interactions:1 ısica:1 free:1 standard:7 admits:2 difficulty:1 isotopy:2 cari:1 york:1 beginning:1 definition:1 interaction:1 language:1 oscar:1 impose:3 eis:2 length:1 birthday:1 βa:1 incorporated:1 universidad:2 linearizes:1 assign:1 first:3 separable:1 symmetry:2 reflected:1 twisted:5 phil:1 relations:2 another:2 open:1 h2n:2 given:4 law:2 bracket:2 rewritten:1 introduction:1 adjoint:2 behaves:1 system:6 construct:3 parallel:1 their:4 normalization:1 calculations:1 arratia:4 speaking:1 olmo:8 statement:1 relationship:1 mariano:1 tool:1 took:1 immediate:1 nieto:1 imposing:2 than:2 coefficients:1 kind:5 unicity:2 unfortunately:1 showed:2 zero:4 project:1 elementary:3 departamento:2 were:3 grossmann:2 seminal:1 symmetries:2 explicit:2 ann:1 matem:1 generalization:1 say:1 take:2 demonstration:1 any:3 eal:2 lie:7 angle:1 depending:2 essentially:1 latter:1 able:1 ideas:1 note:4 generalized:3 forces:1 γu0:7 coincide:1 canonical:5 heisenberg:2 trace:7 established:1 object:1 techniques:1 most:1 connected:4 remarks:2 commutation:2 considered:3 calculated:1 later:1 feynman:1 points:1 exp:2 camb:1 une:1 fact:1 dover:1 nψ:3 supported:1 spain:2 attempts:1 spaces:2 relation:1 substituting:1 find:2 orica:1 based:2 just:1 aφ:3 aω:1 situations:3 should:1 failed:1 only:1 generators:2 subsection:1 equivalents:1 ministerio:1 local:1 pointed:1 do:1 his:1 handle:1 notation:1 means:7 quantique:1 de:12 ones:1 rest:1 words:1 progress:1 dv:2 dw:2 interpreted:1 gen:3 dp:1 dq:1 bar:1 conditions:5 arxiv:1 yield:1 investigate:1 qi:2 qm:7 view:1 kernel:31 set:7 constructing:2 reference:1 achieved:2 clarified:1 espa:1 j0:2 aplicada:1 see:1 βa2:1 result:2 arg:1 tulczyjew:1 dµ:9 analog:1 subject:1 appear:2 satisfying:1 wa:4 subsequent:1 review:2 educaci:1 marmo:1 written:3 difficulties:2 between:3 invariant:2 geometric:1 approach:1 hence:1 ends:1 terms:4 wb:2 extend:1 nature:1 einθ:1 wn:5 wl:1 wk:1 however:3 moyal:18 jn:1 jetp:1 problem:9 improve:1 both:2 cos:4 last:2 universit:1 many:3 taking:3 la:4 according:1 quantization:14 deduction:1 etc:1 symplectic:1 summarizing:1 expression:4 strongly:1 point:12 appeared:1 corresponds:1 dimensional:2 simply:1 conjugation:1 quantizations:1 respect:2 considers:1 selfadjoint:2 kernels:7 commutative:2 basis:4 addition:1 af:1 three:2 been:10 mart:4 int:1 much:1 interest:1 basic:4 expected:1 ph:1 pi:2 pn:2 define:2 direction:1 corresponding:3 θm:1 sufficient:1 covariance:9 royer:2 fortschr:2 noncommutative:1 2ij:1 assigning:1 2j:1 present:2 case:9 presses:1 main:1 splits:1 value:2 will:6 euclidean:9 while:1 ought:1 aid:1 skewsymmetric:1 property:10 procedure:2 computed:1 maximal:1 cylinder:11 unitary:4 2βj:1 played:1 endowed:3 ir:12 thus:2 them:3 equal:2 ii:4 properties:1 dual:3 mod:1 simoni:1 different:3 develop:1 generic:2 make:2 same:2 verifies:2 quant:1 littlejohn:1 proved:1 several:1 composition:1 difficult:1 hermiticity:1 independent:1 used:2 counterparts:1 hand:2 action:5 interested:1 totally:1 identity:2 recent:1 fourier:1 schr:1 l2s:2 nevertheless:1 whole:3 motions:1 valued:1 well:3 roughly:1 obtaining:1 without:2 position:1 dimension:2 exploits:1 proposed:1 obtain:6 symplectomorphisms:1 thanks:1 alternative:1 rotation:1 stratonovich:5 previous:2 generator:1 conclusions:2 nilpotent:3 had:2 reasons:1 belongs:1 transformed:2 easy:2 bond:3 guarantees:1 transformation:1 momentum:1 useless:1 around:1 term:2 spanned:2 valladolid:4 using:7 u0:15 injectivity:1 necessary:1 like:5 success:2 follows:3 reduces:1 yields:1 arbitrary:4 reinterpreting:1 works:1 reduced:1 parity:2 satisfactory:2 because:2 classical:8 discrete:1 some:7 self:2 deduce:1 elements:1 pφ:2 choosing:1 specified:1 gracia:3 provided:1 paraboloids:1 lead:1 prop:2 provides:1 steps:1 bessel:2 symbol:1 minimal:1 considering:2 eiϕ:1 equivalent:1 perpendicular:1 constructive:2 how:2 br:1 worthy:1 atica:1 hilbert:7 injective:2 transformations:1 about:6 kinematical:3 central:5 carried:1 extension:4 o:24 nonvanishing:1 sake:1 carrier:1 extensions:2 stand:1 act:1 introduced:2 researching:1 contractions:1 statements:1 ecanique:1 into:6 integral:4 isomorphic:1 phase:15 appropriate:2 references:1 inverting:1 sov:1 operator:10 assumed:1 eηi:1 there:1 wab:1 start:1 way:4 ingenier:1 was:3 naturally:1 function:11 complete:1 but:5 pj:2 construction:6 link:1 delta:1 eap:1 trying:1 hg:1 partially:1 made:2 compute:1 whether:1 us:1 theoretical:1 te:1 miguel:1 coadjoint:16 called:3 varilly:3 mechanics:5 ab:1 constant:2 computing:1 defined:14 abstract:1 meaningless:1 general:4 single:1 ar:2 together:2 dθ:1 formulation:7 θn:1 check:1 physical:9 functions:19 completeness:1 no:2 na:1 when:3 other:7 role:1 papers:1 ur:2 star:2 preceding:3 problems:1 generated:2 allowing:1 included:1 structure:2 ago:1 ballesteros:1 implies:1 factorized:1 values:1 cpd:1 orbit:15 rule:1 4n:1 reproduce:1 groot:1 presenting:1 observables:1 once:2
|
quant-ph9612001.txt |@word limited:1 externally:2 optic:1 consider:5 illustrates:1 plots:1 squared:1 magnetic:5 concern:1 results:6 integration:2 illustrated:1 unmixed:1 knows:1 edu:1 consists:1 shot:2 expressions:1 adjustment:1 transits:1 poorly:1 extra:1 watt:1 fokker:18 tr:5 posteriori:2 supported:1 charge:5 program:1 those:2 th:1 text:2 slowest:2 include:1 sent:1 apparatus:1 case:4 probe:1 provides:1 reader:1 induce:4 readout:4 every:1 figs:4 experimentally:3 difference:1 matrices:2 condition:2 splitter:1 school:1 regarding:1 contemplated:1 immediately:1 presented:3 did:1 t2:4 solution:3 occurs:2 large:4 solved:1 insights:1 progress:1 succession:2 small:3 markov:1 shows:1 inspection:1 noted:1 related:1 upper:1 smaller:2 force:5 zi:2 findings:1 concise:1 oscillator:1 consistent:4 invariably:1 direct:1 pulse:1 sign:1 past:1 go:1 zero:5 design:9 pass:4 rigorous:1 dynamics:1 targets:1 substitute:1 linear:1 even:6 reviews:2 what:2 plays:2 appear:1 rate:14 exploration:1 exactly:1 unwieldy:1 near:2 supplied:1 launch:1 henceforth:2 experiment:5 above:3 new:2 technology:1 change:1 jumps:2 contrast:1 paradoxical:1 satisfy:3 millisecond:1 outgoing:3 full:1 evaluating:1 respectively:1 never:1 commercial:1 residual:1 here:6 behaviour:1 desired:1 separation:4 relaxation:11 directions:1 path:4 standard:4 equations:20 appears:1 z2:3 obtained:6 remark:4 tunneling:2 incoming:2 technical:1 shift:13 inspired:1 reminiscent:1 reason:1 experience:1 scatter:1 prior:2 amount:1 simultaneous:1 resulting:1 resonance:9 narrow:2 delays:1 golden:1 via:3 useful:1 randomness:1 scales:1 requiring:1 visible:1 addressed:1 achievable:1 stern:17 apply:1 total:1 planck:16 readily:13 conventional:2 dna:1 asymptotic:3 would:7 dnb:1 remains:1 positive:1 nexp:4 finally:1 army:1 next:3 calculation:1 duplicate:1 noting:3 therefore:4 memory:2 taken:1 scope:1 themselves:1 compactly:1 theoretical:2 more:5 separated:1 rich:1 relax:1 becomes:2 operators:1 apparent:4 emission:3 aware:2 interacted:1 proton:1 backwards:1 normalized:3 particular:2 provide:2 dependance:1 hold:1 must:6 evolves:3 account:3 uger:1 defines:1 characterize:1 science:1 equation:18 averaged:1 rθ:28 modified:1 other:1 values:8 three:5 following:2 applies:1 perturbs:1 spontaneous:10 example:5 dropped:1 control:1 ions:1 computers:1 incrementally:1 figure:3 photocurrent:3 process:10 states:16 assumptions:2 numbers:1 sense:1 sought:1 quantummechanical:1 conversely:2 occur:4 information:1 vanish:1 end:2 relaxes:4 photodiode:9 σz2:1 verify:1 discussion:1 acts:1 conducted:2 regions:1 numerous:1 surely:1 pure:3 simplifies:1 instead:1 strong:1 parameter:1 sin:4 proof:1 greatly:1 description:2 may:1 designated:1 after:4 derived:2 reflect:1 hence:1 stipulate:3 empirical:1 computation:1 choice:7 data:8 plank:2 included:1 sy:10 sx:10 dynamical:1 imply:2 sets:1 whenever:3 author:2 explicit:1 yielding:1 ghz:1 extremal:1 rather:3 si:5 so:3 correlation:1 order:8 typical:2 holds:1 interpretation:1 feedback:3 office:1 over:2 despite:1 mainly:1 soon:1 installed:1 course:1 thermal:5 experiments:17 through:4 statistical:5 differs:1 belavkin:2 still:3 its:2 before:1 delay:1 rapidly:1 shifts:3 ln:1 exact:1 encompasses:1 stimulated:3 decreases:1 forms:1 wineland:3 absence:4 complex:3 microscopic:10 systems:4 derivative:2 main:1 work:3 alter:1 photodiodes:4 correspondence:1 them:1 motivated:1 thereby:1 entire:2 polarizations:2 practice:1 heinzen:1 evolution:6 primary:1 scaling:1 band:3 effects:16 they:3 half:1 grows:1 nov:1 now:2 discuss:2 nor:1 represents:1 february:1 finite:3 equality:1 verifying:1 always:3 university:2 hamiltonian:2 perturbing:1 2z:1 ensemble:4 1x2:1 realistic:1 inequality:4 mode:1 each:7 found:3 traces:4 side:3 characterized:1 mean:2 differential:1 rugar:2 weight:1 due:2 short:1 energy:4 idea:1 know:1 interferometer:6 frequency:8 yield:1 begun:1 measurement:36 closedform:1 our:8 transitions:21 eq:38 special:1 out:1 rt:2 respects:1 shown:11 matrix:5 driving:1 space:2 furthermore:2 since:2 induces:1 wholly:1 acting:1 investigation:1 rc:3 medicine:1 newly:1 induced:7 u2x:3 correct:1 singlemode:1 biomedical:1 fiber:3 theory:7 interactions:4 contain:1 guess:1 possibility:2 differing:1 completely:1 complicated:1 york:1 imagine:1 ask:1 estimate:1 hand:3 generate:2 lag:1 interaction:10 derivation:1 ion:6 simulations:1 transition:4 used:1 times:6 filter:5 turn:1 length:1 place:1 exponentially:5 δij:2 consequence:1 retain:1 think:1 first:2 aρa:1 there:4 probability:9 striking:1 wave:3 number:5 linger:1 simplified:1 long:3 directly:1 impossible:3 fluxes:1 several:1 passes:1 given:2 perturbation:3 similarly:3 introduction:1 leading:1 eqs:7 system:13 construct:1 their:2 assumption:1 rates:2 too:1 calculations:1 white:5 perfectly:1 behaved:1 final:12 speaking:2 shifted:1 fraction:2 behind:1 centered:1 continuous:3 agree:1 transverse:7 optical:42 arctanh:1 than:6 specify:2 diffusion:4 relative:1 wootters:1 unfortunately:1 fold:1 require:1 see:3 limiting:1 individual:2 amplitude:1 were:3 embody:2 toward:3 descriptions:1 behaviors:1 hz:2 generality:1 fluctuation:1 modern:3 mind:1 measure:1 randomly:3 already:1 substantial:1 z0:31 close:1 need:2 confirms:1 orders:2 paths:1 minimally:1 depending:1 efficient:1 convenient:2 trapped:3 isolated:1 mechanism:1 arm:1 polarization:19 trθ:4 ideal:1 subjects:1 absorbed:1 take:2 forces:1 observationally:1 finding:1 green:7 detector:1 techniques:1 relaxed:1 channel:14 spectral:3 begin:1 added:2 beyond:1 saturated:1 trace:2 shall:5 swiftly:1 most:3 visually:1 involving:1 connected:1 significant:2 preliminary:1 device:3 cloned:1 measured:4 manifested:1 causality:2 prove:3 parametrize:1 observation:1 consequences:1 considered:2 average:1 later:3 differ:1 drive:1 physica:1 hi:5 trajectories:1 principle:5 exp:3 nuclear:1 velocity:4 left:1 physics:6 away:3 fact:2 choose:1 unnecessarily:1 particularly:4 intensity:2 show:1 violation:1 timedependent:2 random:2 least:1 rotating:2 purely:1 attempts:2 relation:3 gerlach:17 substituting:1 consequent:1 help:1 current:3 based:1 knowledge:1 dehmelt:2 ment:1 square:1 folded:1 written:3 negligible:2 should:5 only:8 coefficients:1 suppresses:1 factor:5 achieve:1 do:2 mrfm:2 dominant:1 notation:1 oscilloscope:4 dependent:1 dd:1 overall:2 expectation:6 preferred:1 satisfied:1 beam:2 cannot:3 dz:5 legitimate:1 closely:1 competing:1 during:5 dt:11 major:1 target:1 processes:6 precession:1 continuum:2 multiple:1 textbooks:1 fields:5 arxiv:1 alteration:1 microscopy:4 summary:1 naked:1 underlying:1 bab:3 predicted:5 characteristic:1 qi:5 inside:1 view:4 coefficient:1 set:3 reference:4 physically:6 frame:2 correlations:1 respect:5 detection:5 collectively:1 depends:1 computer:1 sec:1 result:3 lowpass:1 fail:1 unaltered:1 meet:1 satisfies:1 analog:1 subject:4 permuted:1 probable:1 macroscopic:8 review:4 eigenstates:1 initially:1 state:35 determined:1 closed:3 between:6 fermi:1 approach:2 email:1 available:3 accord:2 emitted:1 terms:7 statistically:2 wa:1 nature:3 qubits:4 component:1 sole:2 weak:1 however:3 efficiency:1 succeed:1 unnormalized:1 distinguish:2 article:10 detecting:1 suppressed:1 alters:1 restrictions:1 cos:2 improved:1 experimentalist:1 ua:4 region:6 hint:3 according:3 itano:5 σz:14 σy:2 σx:2 figures:1 context:2 interesting:3 section:1 divincenzo:1 qubit:67 expression:6 regarded:1 experimental:3 otherwise:1 detailed:3 adjusted:5 relevant:1 cm:2 point:5 simple:5 kilometers:1 harmonic:1 environments:1 dimensional:2 analyzed:1 pole:1 simply:1 framework:1 sequences:1 constant:5 investigator:1 noisy:3 second:3 late:1 ensures:2 combiner:1 described:6 leads:1 basis:3 observing:1 create:1 detected:11 been:7 strategy:1 dux:1 whom:1 duz:2 describes:2 combined:2 interest:1 expected:3 applying:1 ph:1 pi:3 fig:8 box:1 ranging:1 retrospective:3 both:5 maximal:1 designed:2 photon:26 essentially:2 gently:1 observe:1 zurek:1 external:1 spin:6 diffuse:1 present:4 applied:6 attractors:1 traced:1 laser:1 exponential:2 straight:1 single:9 value:7 will:7 while:3 behavior:2 error:2 investigating:1 barchielli:2 taking:1 loop:1 identical:5 unitary:3 coupled:1 chaotic:4 t1:8 thus:3 often:3 coupler:7 itself:1 ready:1 seattle:1 interacts:1 currents:1 acknowledgments:1 different:1 bollinger:2 inc:1 fibers:3 journal:1 things:1 make:2 indistinguishable:1 same:5 any:4 read:1 unity:1 parts:2 quant:1 pauli:1 units:1 φi:1 proved:1 physical:4 infer:1 higher:2 development:1 independent:1 nih:1 literature:1 inadvertently:1 squaring:1 boosted:1 numerical:2 effect:30 noticing:1 constraining:1 moment:3 intended:2 changing:1 six:1 identity:1 bergquist:1 lower:1 off:1 decorrelation:1 records:1 substantially:3 variety:1 well:3 analysis:7 academic:1 without:2 components:2 consistency:4 exponentials:1 entered:1 model:1 yannoni:1 usual:3 abab:3 permissible:1 less:1 increasingly:1 observed:2 obtain:4 rest:2 reviewed:1 assigned:1 bandwidth:8 filtering:1 identify:3 atomic:2 aspect:2 summed:1 scattering:3 yet:6 tuned:1 note:6 enters:1 density:7 photons:16 z02:4 sometimes:1 conclusions:1 add:1 setting:1 instrument:1 theorem:1 eye:1 solvable:1 eigenstate:1 generalized:1 real:1 increased:1 insert:1 checking:1 evaluate:1 posed:1 possible:5 early:1 possibly:1 helicity:1 vacuum:4 press:1 world:1 bit:1 designers:1 correlated:1 loss:1 outright:1 like:4 particle:1 texts:1 follows:5 signal:1 seemingly:1 unnecessary:1 serves:1 manifest:2 specific:3 flux:6 benefit:2 mhz:1 either:2 output:1 reduced:5 lends:1 because:4 methods:5 classical:1 sequence:5 phenomena:5 under:1 competition:1 radians:2 understood:2 towards:1 µw:1 specified:2 duration:1 root:1 extended:1 lorentzian:1 scripta:1 happens:1 provided:1 uy:6 axiomatic:1 sufficiently:2 support:1 broad:2 avoid:1 measurements:6 langevin:15 extensively:1 per:2 causal:1 does:7 embodies:1 assuming:1 worthwhile:1 demonstrated:2 measuring:3 noise:30 power:4 intimate:1 seconds:1 equivalent:1 fabricated:1 stellar:1 step:1 although:1 substitution:1 concreteness:1 drawn:1 relating:1 properties:2 microsecond:1 takes:1 about:1 carried:1 algebraic:1 entailed:1 fringe:1 discussed:3 o:3 simulation:2 practical:3 carrier:1 obeys:2 done:1 mamin:1 mixed:1 eight:2 efforts:1 2x2:1 bloch:23 irreversibly:1 considerations:2 equally:1 letters:3 markovian:3 presence:2 previously:2 into:7 within:1 washington:3 nsf:1 negative:1 phase:13 appropriate:1 right:2 references:1 determine:1 substitutions:2 utility:1 variables:6 span:1 devices:2 subatomic:1 duy:1 probabilistic:1 suffice:2 initial:14 transform:2 stark:15 undetectable:1 vendors:1 detectable:2 low:4 way:1 was:2 interferometry:5 function:10 hx:2 hy:2 complete:2 form:10 energies:1 collapsed:1 regard:1 delayed:5 but:16 formalisms:1 hj:2 collected:1 illuminating:1 gain:2 atom:1 level:1 collapses:2 absent:1 portions:2 ux:6 evident:5 uz:9 whether:2 wish:1 interiors:1 up:2 us:1 foresight:1 record:7 limit:4 fluctuations:2 distribution:1 define:4 similar:1 called:1 ub:4 mechanics:1 u2y:5 ac:13 adopt:2 associated:2 fokkerplanck:1 zeno:21 computing:2 defined:3 recognize:1 abstract:1 describe:5 general:7 quantum:40 engineering:1 guessed:1 exist:1 together:1 research:3 wavelength:2 means:1 reflecting:1 formalism:2 check:2 constructed:2 compared:2 rederive:1 no:7 na:7 nb:7 when:3 detail:3 field:2 interested:1 role:2 department:2 conclude:1 area:1 generates:1 lend:1 students:6 drift:3 interferometric:21 retrospectively:1 generated:3 suppression:4 variable:9 feasible:1 building:1 rθ2:1 implies:7 longer:1 practically:1 assume:1 typically:3 required:2 resolving:2 rule:1 indirectly:1 presenting:1 time:19 push:1 introductory:2 nuclei:1 starting:4 having:3 once:1
|
quant-ph9612002.txt |@word secondly:1 positions:1 since:4 homomorphism:1 ali:2 magnetic:1 global:1 results:3 leads:4 obstruction:1 hennig:2 generalize:1 grateful:1 lll:1 partial:1 contributions:1 localized:2 compact:1 looking:1 inverse:1 tu:1 tr:2 editors:3 charge:1 behave:1 under:3 include:1 norm:3 applied:1 hibbs:1 far:1 differently:1 geometrical:1 isomorphism:2 lecture:2 matrices:1 condition:11 hamiltonian:2 irreducible:2 notes:1 nostrand:1 t1:3 admissible:2 irreducibly:2 gauge:2 linearizing:1 consistent:2 direct:1 second:4 zt:2 further:1 dynamics:8 selfadjointness:1 canonical:1 spectral:1 established:1 nonlinear:18 sub:3 brackets:1 section:8 current:1 establishes:1 international:1 method:2 clausthal:7 full:3 whose:1 respectively:2 here:1 fairly:1 objects:3 tangent:2 groups:1 represented:4 path:1 strong:1 equations:13 institute:1 leaves:1 resulting:1 poisson:3 usually:1 suitable:1 drees:1 york:9 via:2 projection:3 classification:3 extra:1 explained:1 plenum:3 summation:1 divµ:3 planck:1 use:2 trivializable:1 proceed:1 positive:2 contains:1 bundles:4 eπ:1 ψt:15 next:1 classically:1 kinematics:10 therefore:1 december:1 taken:1 associated:1 type:3 theoretical:1 more:2 flat:3 formally:1 hermitean:6 operators:10 odinger:6 curvature:2 berlin:3 basically:1 particular:2 known:1 foundations:1 hold:1 iii:4 states:17 springer:3 valued:3 defines:1 quantized:5 deformed:1 science:1 equation:8 oscillator:1 modified:1 theories:1 labeled:1 values:1 ρt:7 following:1 f1:2 f2:2 give:1 relativistic:2 lindblad:3 involve:1 vx:2 assumptions:1 arise:1 sharp:1 hhh:1 verlag:3 feynman:1 provide:1 discussion:1 utilize:1 antoine:2 positional:1 how:1 pure:10 symposium:2 parameter:2 displacements:3 classify:1 map:1 alternative:2 blocks:1 description:2 algebra:15 may:1 max:1 schro:3 xxvi:1 bks:1 representations:5 choice:2 schulte:1 realized:1 natural:6 dynamical:2 correspond:1 sniatycki:1 diffeomorphism:1 ones:1 so:3 fundamental:2 representation:9 diplomarbeit:1 order:4 restriction:2 interpretation:1 mielnik:2 developed:1 over:1 move:1 sions:1 already:1 including:2 statistical:1 mentioned:1 einer:1 its:1 sciences:1 systeme:2 group:4 symmetry:1 acknowledge:1 chosen:3 affine:1 coordinates:3 actually:1 forms:1 lu:2 fig:1 mail:1 lx:3 non:4 thereby:1 introduce:1 functional:1 gotay:1 hamilton:1 they:2 nov:1 now:1 term:1 dirac:1 university:2 classified:2 odzijewicz:1 identified:1 theory:4 l2:10 turns:1 universit:3 2i:5 characterized:1 mean:1 domain:3 differential:5 independent:1 displacement:2 equivalence:1 measure:3 quantum:25 our:1 living:1 shown:1 matrix:1 space:14 continuity:1 furthermore:1 singular:1 denotes:3 particles:2 divg:2 hill:1 formula:1 rn:4 induced:2 occurs:1 rj:1 benjamin:1 foundation:1 uber:1 linear:4 localization:4 divergence:1 standard:1 completely:1 flows:2 elsewhere:1 asi:1 r4:1 r5:1 interaction:1 r1:1 r2:2 r3:4 geometry:2 starts:2 could:1 times:1 technische:3 hence:3 generalizations:1 first:5 separable:2 xk:2 note:4 xn:1 probability:4 xc:8 gradg:8 dinger:3 restrict:1 another:1 copernicus:1 dissertation:2 angular:2 aharonov:1 illustrate:1 given:6 necessarily:1 introduction:3 leading:5 adjoint:1 system:16 relations:1 their:3 πt:3 realization:1 scheme:1 structures:2 ehrenfest:2 editor:1 convention:1 serve:1 authors:1 x2:2 x0:1 x1:3 xj:7 diffusion:1 colleagues:1 was:2 require:3 euclidean:1 classes:1 mackey:2 providing:1 symmetries:1 derivative:1 imprimitivity:2 linearizable:1 argument:1 generalization:1 eigenschaften:1 any:4 indeed:1 lie:3 depending:2 self:1 ideas:1 polarization:4 instance:2 potential:1 generalized:2 new:9 continuous:1 multiple:1 trace:3 though:1 measures:2 algebraic:3 connected:4 pair:1 class:3 commutation:1 cke:2 especially:1 nonlinearity:1 considered:1 torus:4 flow:2 ways:1 proceedings:1 points:1 χb:2 exp:1 mechanical:4 qbk:1 physics:4 sum:1 show:1 german:2 relation:6 solutions:1 analogue:2 trivial:4 find:1 finally:1 topological:1 should:2 only:7 generators:3 inherited:1 integrable:1 local:3 dn:2 mixture:1 closed:3 get:3 de:2 ϕn:1 ϕj:3 dt:6 procedures:1 gen:2 evolution:19 fields:6 arxiv:1 acknowledgments:1 2πi:1 common:2 qg:4 qf:7 woodhouse:1 riemannian:4 kernel:1 set:5 dobrev:1 achieved:2 ωg:2 see:10 geometrically:1 us:1 inequivalent:5 particle:2 αq:1 αp:1 fails:1 satisfying:3 extend:1 doebner:11 αy:2 review:2 symmetric:1 state:3 αg:1 invariant:2 geometric:8 conditions:3 counterexample:1 αt:4 terms:1 august:1 vertical:1 jt:2 confusion:1 restricting:1 combining:1 however:2 ber:1 vanishing:1 comm:2 configuration:6 topology:2 observable:1 goldin:7 similar:1 taking:1 according:1 quantization:29 connection:2 und:2 symplectic:6 context:1 contribution:1 comes:1 σt:5 unitarily:3 among:1 diffeomorphisms:1 simple:1 harmonic:1 dimensional:2 simply:1 quantizations:1 respect:1 math:5 selfadjoint:1 toru:2 described:2 publishing:2 pt:1 z0:1 px:7 py:2 due:2 been:3 describes:1 ph:1 systems:3 θj:4 nattermann:5 cotangent:3 ϑx:1 coherent:3 external:12 ϑf:1 reinhold:1 fokker:1 manifolds:3 case:1 look:2 heidelberg:3 will:7 technical:1 viii:1 unitary:3 lx2:1 lx1:1 endowed:1 metric:1 thus:3 iv:1 ii:4 reads:2 properties:2 loosing:1 wave:2 ie:1 currents:1 movements:1 different:3 φs:2 φt:2 φx:3 same:1 complex:3 quant:1 emphasize:1 mixtures:4 finite:1 subalgebra:1 evolve:1 used:3 singapore:2 i2:1 effect:1 counterparts:1 characters:1 infinite:1 changing:1 felder:1 cycle:1 schr:7 no:1 well:2 obviously:2 bohm:1 mathematische:1 sets:4 model:1 usual:1 manifold:8 struktur:1 obtain:2 homogeneity:1 identify:1 transforms:1 integer:1 polish:3 momenta:2 previous:1 nicolas:1 segal:2 preprint:1 family:2 superluminal:1 density:2 except:1 valid:1 lett:1 transformation:2 momentum:2 take:1 real:3 spinless:1 unter:1 iγ:2 possible:3 admitting:1 corresponds:1 possibly:1 press:2 using:4 displaced:1 like:1 semi:1 reduces:1 communications:1 yields:1 integrals:1 multiplicative:1 mcgraw:1 by4:1 therein:1 because:1 methods:1 classical:13 some:3 understood:1 examples:2 choosing:1 dense:1 measurements:1 does:1 proj:1 steps:1 semigroups:1 scientific:2 equivalent:1 wavefunctions:1 evolutions:4 polynomials:1 bs:2 imaginary:1 hilbert:4 discus:1 zur:1 kinematical:6 world:2 idt:1 reduced:1 compatible:1 mixed:1 germany:1 introduced:1 book:1 mathematical:3 primitive:2 final:1 into:2 integral:2 isomorphic:2 transformations:2 phase:4 square:1 operator:1 van:1 additional:2 support:2 there:7 pages:6 restricts:1 borel:15 ljk:1 way:2 sections:2 function:1 complete:2 form:5 but:1 idea:2 volume:3 construction:1 line:8 irreversible:1 longer:1 vectorfield:3 made:1 2πe:1 tpa:1 evident:1 fulfilling:4 characteristic:1 smooth:5 flip:2 differentiable:3 ψg:1 distribution:1 define:1 ωe:1 called:1 vectorfields:8 mechanics:8 constant:3 defined:4 certain:1 describe:5 influence:2 generating:1 general:9 exist:1 dθ:2 dρ:2 gruber:1 physical:1 functions:10 physikalisch:1 locality:1 corporation:2 whereas:1 generally:1 field:5 bracket:1 remarks:1 details:1 company:2 principle:1 picture:2 elements:2 varadarajan:1 respects:1 time:17 bundle:11 transported:1 commutator:1 a2:1 bounded:1 linearization:1 structure:9 building:1 implies:1 coupling:1 assume:2 requires:1 pseudo:3 together:1 notion:1 equivalently:1 mass:1 quantizable:3 observables:9 starting:1
|
quant-ph9612003.txt |@word represent:1 concept:2 consider:4 chain:4 results:2 leads:1 commute:1 computation:1 edu:1 consists:1 involved:1 contributions:1 causes:1 simon:1 alamos:1 deterministic:1 tr:9 environment:20 finally:1 monotonically:1 under:1 include:1 very:1 springer:1 wave:1 electron:2 collett:1 condition:2 paz:1 impressive:1 level:2 guo:2 solution:2 occurs:4 large:4 solved:2 small:1 approximately:1 cooperative:2 deutsch:1 sin2:1 sign:1 approximation:1 zero:2 even:3 intimately:2 nonlinear:1 plays:1 apparatus:4 near:1 expressed:7 cell:1 above:1 new:1 method:1 edited:1 evolving:1 respectively:1 jointly:1 china:3 address:1 equations:1 obtained:2 shift:8 popescu:2 larger:1 resulting:1 schumacher:3 makes:1 examining:1 useful:1 total:1 unit:1 alamitos:3 eiωt:2 use:5 feb:1 laflamme:1 hilbert:2 calculation:2 therefore:3 memory:11 taken:2 25th:1 type:2 today:2 more:4 bennett:4 started:1 operators:7 odinger:2 berlin:1 backwards:1 foundations:3 hold:1 high:3 account:1 science:7 equation:4 ρs:14 values:1 following:3 strategies:1 example:1 performed:1 compare:1 indicated:2 process:1 preserving:15 neglected:2 states:35 indicates:3 numbers:1 σlz:8 transactions:1 verlag:1 lamb:7 information:1 rather:1 s0:5 how:1 env:1 symposium:4 ordinary:2 sin:3 brassard:1 map:1 may:5 oscillators:3 after:1 deviates:1 gottesman:1 heidelberg:1 constants:1 efficiently:2 natural:1 dynamical:1 register:1 purification:1 fortunately:1 so:7 representation:2 order:3 typical:1 deco:1 afterwards:1 developed:1 pointed:1 mainly:1 satisfied:1 years:1 stability:1 course:1 thermal:1 paper:3 london:4 argued:1 fidelity:7 ieee:3 its:1 before:1 anhui:1 decay:2 interesting:2 lu:1 ηm:2 within:1 pure:1 propose:1 practice:1 steane:2 they:6 goldwasser:1 now:2 discuss:2 easily:3 always:1 university:1 evo:1 magnitude:2 mode:1 each:2 2l:4 found:4 soc:3 mean:2 subset:1 schemes:4 directly:2 ρi1:1 related:2 ρi2:1 society:4 extended:1 accumulated:1 quantum:24 eq:13 event:1 out:1 divincenzo:2 shown:3 matrix:1 factors:1 furthermore:1 since:4 rev:14 denotes:1 increase:1 eprint:1 performs:1 induced:2 ref:7 correct:4 shows:2 foundation:1 log2:2 theory:2 circumstance:1 gardiner:1 diagonal:2 free:1 vazirani:1 ρil:1 york:1 jozsa:2 inevitable:2 interaction:5 derivation:3 could:2 computers:5 feasible:1 length:1 exponentially:1 corrections:1 undergo:1 onto:1 eqs:1 first:1 major:1 there:8 probability:1 encoding:5 number:8 philosophical:1 πl:1 another:1 electronic:1 occurrence:1 temperature:5 interact:4 system:4 relations:2 unruh:2 assumption:4 scheme:7 bits:3 national:1 gives:1 collapse:1 packet:1 off:1 than:2 iωt:10 kind:1 wootters:2 modelled:1 project:1 supposed:1 amplitude:3 treated:2 behaviors:1 correction:3 ming:1 renv:1 need:4 seen:1 any:1 contents:1 efficient:4 studying:2 latter:2 ideal:1 erator:1 build:1 finding:1 i2l:2 heisenberg:4 subscripts:1 though:2 most:1 errors:3 decohered:3 phase:19 kb:4 reduces:1 clear:1 implications:3 proceedings:4 exp:15 physics:3 fact:2 nω:7 shor:4 phenomenon:3 show:1 supported:1 relation:1 lloyd:1 substituting:1 d2:3 find:2 realizing:1 based:2 just:1 parameters:1 aω:10 negligible:1 should:1 factor:5 bernstein:2 oct:2 equilibrium:1 do:1 get:1 zurek:5 overall:1 dv:1 dt:1 acm:1 evolution:2 arxiv:1 acknowledgments:1 34th:1 set:4 ser:1 undergoes:1 sensitivity:1 j1:1 j2:1 maximum:1 collectively:3 see:3 computer:11 result:3 operated:1 terms:2 satisfies:1 caldeira:1 satisfying:1 interacting:4 mentioned:1 definite:1 eigenstates:1 qubits:38 state:9 various:1 between:2 approach:1 recently:1 initially:1 however:3 hefei:1 jl:67 efficiency:2 here:1 rapidly:2 both:2 cos:2 σl:2 many:1 annual:4 space:3 fulfilled:1 hω:1 leggett:1 qubit:4 expression:1 arbitrarily:1 co:1 cn:1 point:6 simple:4 ca:3 harmonic:2 environments:4 dimensional:1 polynomial:1 considering:1 described:1 transformations:1 differs:1 basis:6 computing:2 due:1 been:11 strategy:1 yao:1 much:3 damping:13 interest:1 ph:2 unchanged:1 adopted:1 controlled:1 sufficient:1 coherence:15 photon:2 essentially:1 coherent:1 external:2 general:2 spin:6 case:6 pacs:1 expanded:1 transformation:2 will:2 dephasing:1 suppose:3 behavior:1 error:9 property:2 35th:2 mistake:1 landauer:1 unitary:1 coupled:1 von:1 thus:4 examined:1 duan:2 il:80 technology:1 different:4 suggest:2 make:3 same:10 clearly:1 quant:2 pauli:2 difficult:1 independent:6 used:3 entanglement:1 eigenvectors:1 recognized:1 schr:2 center:1 obstacles:1 remain:1 analysis:2 obviously:2 solve:2 machinery:1 model:5 dimension:1 know:2 gates:2 exploits:1 guang:1 proposed:4 obtain:2 alternative:1 yet:1 previous:1 density:13 royal:1 transformed:2 lett:3 input:7 suominen:1 remaining:1 take:2 opt:1 insensitive:1 devised:1 couple:2 possible:3 spanned:1 increases:1 entangled:2 using:2 bit:1 mod:1 follows:1 collective:11 specific:1 arbitrary:1 output:1 reduced:4 because:2 neumann:1 classical:1 people:1 some:8 back:1 choosing:1 pω:2 provided:1 describing:1 measurements:5 conservative:1 does:2 proc:3 noise:1 jl2:2 step:1 properties:1 bz:1 noisy:2 discussed:2 dependence:1 o:3 essential:1 practical:1 obeys:1 introduced:3 op:1 raised:1 offdiagonal:1 h2:1 into:6 nsc:1 attains:1 bath:5 references:1 determine:1 operator:20 proportional:2 reducing:6 r2493:1 comparing:1 assumed:1 initial:3 transform:1 fast:1 los:4 describes:1 low:1 lot:1 analyze:1 was:3 function:2 complete:1 form:5 reduce:3 smolin:2 ψm:1 calderbank:1 but:3 encode:1 hi:4 repeatedly:1 atom:2 elimination:1 role:1 made:1 whether:1 cells:2 ωt:8 decays:1 limit:1 problem:2 similar:2 called:4 storing:1 constant:2 up:1 defined:3 certain:1 abstract:1 describe:2 am:2 denote:1 single:1 exist:1 hamiltonian:6 archive:1 compared:1 no:6 ekert:2 when:1 other:2 republic:1 department:1 nice:1 picture:4 elements:1 kinds:2 superposition:1 separate:4 ustc:1 problems:1 a0:1 important:3 palma:1 lution:1 missed:2 ago:1 independently:2 correlated:1 coupling:5 dω:1 interval:1 4l:1 time:12 n1:1 decoherence:47 requires:1 original:1
|
quant-ph9612004.txt |@word consider:2 forbidden:1 particular:1 results:4 integration:1 eds:1 quadrature:1 reynaud:1 whose:1 technique:3 tr:6 finally:1 squeezing:8 under:1 analogous:1 advantage:1 very:2 rise:1 connects:1 lecture:1 experimentally:2 splitter:2 smithey:2 knight:1 notes:1 applicable:1 leave:1 discrete:1 small:1 eigenvalues:1 measuring:1 smaller:1 direct:3 cosh:2 zero:3 radon:1 substitute:1 even:2 established:1 ˆs:1 appear:1 brackets:1 sum:1 beaten:2 analogously:1 expressed:1 access:1 above:3 pioneering:1 outgoing:2 respectively:1 atoms:2 ranges:1 desired:2 nonunit:3 inversion:2 sinh:2 obtained:1 institute:1 studied:1 allows:2 stressed:1 suitable:2 named:1 locking:1 useful:2 projection:1 marginal:1 eiφ:1 scaled:1 herzog:2 summation:1 total:1 unit:1 use:5 takes:1 would:1 probabilities:1 chooses:1 call:1 raymer:1 taken:1 more:3 becomes:3 factor:2 odinger:1 aware:1 berlin:1 varying:2 known:3 high:1 account:1 ρd:6 vladimir:1 permits:3 work:3 oscillator:1 modified:1 cat:1 values:6 following:2 example:1 leonhardt:4 ρˆg:1 give:1 process:5 discussed:1 haroche:2 states:2 allowed:2 counting:3 lamb:1 needs:1 provide:1 buzek:1 means:4 write:1 how:3 instead:1 parameter:6 lai:1 singular:1 may:6 after:2 stefano:1 wallentowitz:2 representations:2 types:1 man:4 realized:1 natural:1 effective:1 element:3 rather:3 so:2 fundamental:1 representation:2 retrieval:1 holds:1 wigner:3 indeed:3 over:3 choose:1 osservatorio:1 produced:1 course:1 paper:1 through:1 during:1 mentioned:1 still:1 its:5 before:2 complicate:1 group:4 ko:4 interesting:1 scully:1 writing:1 absence:1 differently:1 easier:1 greater:2 combination:1 practice:1 walls:1 effects:1 they:1 nov:1 now:5 discuss:1 represents:2 term:2 identified:1 realistic:1 mode:2 references:1 universit:1 ports:1 weighted:1 weight:3 generation:1 reduce:1 displacement:1 related:2 frequency:1 measurement:5 tˆ:9 our:4 eq:13 es:2 large:1 shown:3 tombesi:2 matrix:11 space:1 furthermore:1 since:2 rev:21 research:1 contained:1 istituto:1 formula:1 get:4 ref:13 fisica:2 possibility:2 quite:1 davidovich:1 base:1 detecting:1 capodimonte:1 definition:1 napoli:1 could:6 length:1 hence:1 eqs:2 already:1 probability:3 kernel:3 number:13 least:1 directly:1 given:3 glauber:4 ordering:2 dipartimento:1 system:1 adopted:2 their:2 assumption:1 realization:1 scheme:5 smoothed:1 gives:1 moscow:1 stress:1 optical:3 than:6 unfortunately:1 wodkiewicz:1 tomographic:1 reconstructing:1 compensation:1 determined:2 amplitude:2 were:1 russia:1 seminal:1 beck:1 manner:1 close:1 seem:1 any:5 depending:1 able:1 mechanism:2 note:1 negligible:1 added:1 shall:4 prohibitive:1 letter:1 phase:6 measured:1 especially:1 considered:2 clear:1 detectors:4 order:2 principle:3 effect:1 physics:1 fact:3 quantity:2 lebedev:1 show:3 anyway:1 relation:2 d2:5 proposed:4 parameters:1 implementation:1 state:8 should:1 analytic:1 only:12 essence:1 local:1 reconstruction:7 di:4 dependent:1 expectation:1 beam:3 dv:1 reconstruct:2 holland:1 evolution:1 fields:1 arxiv:1 schemes:1 dodonov:1 scanning:3 reference:6 achieved:1 physically:1 detection:4 result:2 terms:3 acts:1 annihilation:1 detect:2 written:2 between:1 progress:1 approach:2 brune:3 knowing:1 recently:1 ability:1 however:4 efficiency:15 analyzed:1 problem:2 both:1 semiclass:1 last:2 kicking:1 sensitive:1 became:1 symplectic:2 passing:1 whole:1 experimental:1 otherwise:1 arbitrarily:1 relevant:1 groups:1 characterization:1 simple:1 homodyne:6 sampling:2 simply:1 respect:1 schleich:1 considering:1 particulary:1 basis:2 addition:1 create:1 due:2 much:1 ph:1 define:1 wants:1 corresponding:1 photon:10 royer:1 assert:1 coherent:3 denote:1 present:1 case:6 laser:1 pacs:1 value:4 squeezes:1 employ:1 while:2 error:1 squeezed:2 situation:2 procedure:4 della:1 remembering:1 opt:1 losses:1 vogel:4 coupled:1 vol:1 refs:2 thus:5 tomography:10 claimed:1 different:3 italy:3 make:2 radiation:4 same:1 complex:2 quant:1 wilkens:1 raimond:2 used:2 numerical:1 functions:1 hand:1 parametrized:2 lower:2 fourier:2 schr:1 modes:1 zagury:2 expression:1 well:3 coordinate:3 soviet:1 usual:1 construct:1 kiss:1 just:4 less:1 being:1 when:4 mayr:1 rotated:1 obtain:3 immediately:4 paul:3 lefevre:1 rotation:1 sampled:1 zoller:1 density:11 photons:2 realize:1 other:5 lett:6 input:1 transformation:1 kick:1 real:1 read:1 showing:2 astronomico:1 possible:3 vacuum:1 using:4 loss:1 displaced:1 like:2 signal:2 camerino:2 deleterious:1 either:2 arbitrary:1 output:1 reduced:1 mathematical:4 because:2 qed:2 classical:1 sequence:2 creation:1 springer:1 sure:1 duration:1 describing:1 cavity:9 electromagnetic:1 measurements:4 recorded:1 intracavity:2 microwave:1 eliminate:1 expressing:1 limitations:1 noise:1 eiϕ:2 power:1 nonclassical:1 qnd:1 banaszek:2 relating:1 properties:1 bz:1 simpler:2 limitation:1 pη:5 extension:1 aˆ:2 introduces:1 o:3 mixes:1 distinct:1 range:1 continous:1 mixed:1 recognizes:2 invert:1 beamsplitter:1 presence:2 into:2 square:1 ηs:4 yuen:1 operator:12 rely:1 extremely:1 there:3 transform:3 accordingly:1 low:1 way:1 was:9 assumes:1 function:12 survives:2 differences:1 but:7 construction:1 matematica:1 odkiewicz:1 injection:2 squeeze:2 count:2 paolo:1 made:1 applying:1 characteristic:2 inside:6 us:3 below:1 limit:4 distribution:4 cahill:2 similar:4 aa:1 ariano:2 ordered:2 recognize:1 abstract:1 general:1 quantum:14 examine:1 exist:1 laboratory:1 nazionale:1 distributions:1 physical:4 again:1 materia:1 no:1 generally:1 field:18 setting:1 papers:3 polar:1 elements:6 superposition:2 ηˆa:1 problems:1 faridani:1 bounded:2 allowing:3 variable:1 risken:2 ξe:1 independently:2 quasiprobability:1 interval:1 persistent:1 together:1 mancini:2 impossibility:1 hirota:1 meystre:1 indirectly:1
|
quant-ph9612005.txt |@word consider:12 sarkar:1 illustrates:2 washed:1 results:1 integration:2 leads:1 quadrature:9 spiridonov:1 consists:1 follow:1 faster:2 contributions:1 reynaud:1 whose:5 integral:2 technique:1 tr:1 γt:1 finally:3 does:3 device:1 those:2 under:4 anharmonic:1 2πm2:1 worth:1 hill:1 fly:1 advantage:1 orthogonal:1 very:4 frequencies:1 springer:1 choice:1 drever:1 figs:1 resonant:2 experimentally:1 nieto:1 difference:1 exact:2 condition:2 trm:5 immediately:3 hamiltonian:1 cause:1 developing:1 proposals:1 solution:3 damped:1 leave:1 detected:1 small:6 referred:1 optics:2 programme:1 heidmann:2 smaller:2 force:2 sin2:3 approximation:2 zero:3 further:1 ter:2 implemented:1 odd:2 leakage:1 theory:2 even:5 nonlinear:4 plays:1 appear:2 apparatus:1 brackets:2 giving:2 section:2 dephasing:2 above:9 capital:1 eie:3 technology:1 increasing:1 preserved:1 revealing:1 edited:1 simultaneously:1 gravitation:1 degree:1 respectively:2 behaviour:2 following:6 objects:1 smearing:1 free:4 relaxation:1 represented:1 path:1 november:1 strong:1 observing:1 obtained:5 remark:2 eiπ:6 institute:1 shift:1 study:2 studied:2 allows:1 approaches:1 commonly:1 resulting:1 poisson:2 formation:1 proof:1 changes:1 involves:1 plotted:5 holmes:1 named:1 useful:1 projection:1 extra:1 marginal:10 readout:1 explicitely:1 plenum:1 private:1 highly:2 scaled:2 apply:1 use:2 quasi:1 superpositions:1 would:3 prove:1 remains:2 contains:1 negative:1 jaekel:1 france:1 approach:1 m1:2 m2:2 taken:2 resonator:2 theoretical:1 more:3 sort:2 introducing:3 iu:1 operators:4 envelope:2 odinger:11 validity:1 aware:1 normalized:1 particular:4 known:2 cases:6 producing:1 analogous:1 must:3 ρa:1 high:1 account:3 ma:1 ρf:5 pout:5 equation:8 work:1 oscillator:5 cat:27 glauber:1 macroscopically:1 values:9 ρt:17 evolved:1 universe:1 growing:1 fulfill:1 example:3 address:1 performed:2 control:2 nikonov:1 figure:3 transmissivity:1 process:3 discussed:7 preserving:1 near:1 states:26 indicates:1 something:1 sense:1 sharp:1 distinguishable:1 guarantee:1 information:1 end:3 captions:1 provide:1 demolition:1 buzek:1 means:5 xˆ:2 write:2 till:1 banacloche:1 sate:1 opposite:1 holland:1 plus:1 ˆx:2 parameter:2 sin:11 intended:2 undergoing:1 algebra:2 may:6 suppose:2 after:5 movable:2 hence:2 produce:1 coming:1 requirements:1 destructive:1 heidelberg:1 man:3 short:1 natural:1 imply:1 light:4 explicit:1 thorne:1 element:1 sasaki:1 negligible:4 expression:3 fundamental:1 pay:2 representation:2 acknowledges:1 schieve:1 order:6 typical:4 restriction:1 holds:1 leggett:1 over:4 move:1 satisfied:1 meter:3 interpreted:1 course:5 thermal:10 paper:1 through:3 statistical:1 signs:1 mentioned:1 existence:3 satisfies:2 still:4 excitations:2 its:9 before:2 perfect:1 jacobs:1 derive:1 rapidly:1 malkin:1 curly:1 how:2 interesting:2 boson:2 actually:1 absence:2 distinguishing:1 degrees:1 fig:19 versus:1 non:1 good:2 affected:1 pure:6 wetenschap:1 superposed:1 processes:1 walls:4 tails:1 effects:11 haroche:2 nov:1 now:11 yt:55 wiley:1 2t:2 represents:4 term:13 several:1 vibrational:1 2s:3 always:2 delicate:2 presented:3 kerr:3 2y:3 porta:1 2e:2 magnitude:1 mode:12 each:2 2l:3 found:2 universit:1 european:1 mean:2 square:1 ei:4 vignes:1 disentanglement:1 generation:6 energy:1 reduce:1 gaussian:4 related:2 frequency:4 obtains:1 measurement:22 quantum:24 our:2 eq:30 adequately:1 out:6 try:2 shown:2 tombesi:5 matrix:1 space:4 furthermore:4 since:6 interference:9 enviroment:1 replacing:1 contained:1 daniel:1 gaussians:1 istituto:2 denoted:1 formula:2 get:2 ref:5 math:2 shows:2 benjamin:1 rewrote:1 doppler:1 linear:4 gardiner:2 fisica:3 possibility:1 nth:13 completely:1 necessarily:1 advantages:1 york:3 optomechanical:2 detecting:2 generate:1 milburn:3 definition:1 interaction:1 r0:6 created:1 could:17 times:8 motion:4 length:1 wright:1 signature:2 consequence:2 uses:1 onto:1 neglect:1 first:5 wilcox:1 initial:5 features:4 probability:3 omitted:1 variables:1 sn:2 number:18 wash:1 another:1 impossible:1 open:1 angular:1 given:4 perturbation:3 temperature:9 their:1 introduction:1 eqs:8 system:12 unruh:1 needed:3 master:3 realization:1 perfectly:1 gives:1 way:4 centered:2 moscow:1 akad:1 immediate:1 environmental:2 optical:5 signaling:1 ference:1 eliminated:1 than:7 peaked:2 kind:1 scheme:4 effective:1 cim:1 strenght:1 iteration:1 see:6 determined:2 iωc:1 ko1:1 contrasted:2 klimov:2 perturbative:3 prospect:1 function:5 rewrite:1 lines:2 correction:3 measure:1 need:1 seen:3 recover:1 any:4 ueda:1 lie:1 subsystems:4 depending:2 anharmonicity:1 latter:2 able:3 note:4 extracted:1 dyt:5 generalized:1 forces:1 so:6 hga:1 displacement:1 added:1 trace:1 shall:1 correlation:3 reach:1 αr:11 phase:10 measured:2 probable:1 kb:1 constructed:1 nonlinearity:1 considered:3 clear:2 morse:1 ko:2 physica:2 uru:2 reflecting:2 exp:7 mechanical:5 superscript:1 poissonian:1 sum:2 fact:7 quantity:1 criteria:1 think:1 lebedev:1 kg:1 show:7 supported:1 degrades:1 large:1 relation:1 solutions:2 yurke:5 longer:1 find:1 piezoelectric:1 aρ:1 naturwissenschaften:1 based:1 parameters:4 situations:2 enough:1 should:11 only:8 candidates:1 convoluted:1 factor:6 integrate:1 hamiltonians:1 achieve:1 equilibrium:1 do:1 mixture:1 dominant:1 reconstruction:1 di:4 dependent:1 simplest:1 expectation:1 degradation:1 gea:1 ones:1 closely:1 new:7 dv:1 completness:1 carmichael:1 reveal:2 evolution:6 reading:1 indicated:1 fields:2 arxiv:1 acknowledgments:1 common:2 dodonov:3 undamped:3 fixed:3 shelby:1 cole:1 enhances:1 set:1 ned:1 ser:1 reference:2 achieved:1 2πm:1 pinard:1 omitting:1 detection:4 intensity:1 stoler:1 sec:1 result:3 arg:1 discussions:1 terms:5 situation:1 closer:1 caldeira:1 phases:1 detect:2 interacting:1 phonons:2 speed:2 review:1 tend:3 boundaries:1 state:24 smallest:2 various:5 john:1 between:3 caves:2 conditions:1 law:2 brune:1 recently:1 amplitude:1 initially:1 attention:2 combining:1 however:8 gratefully:1 scully:1 come:1 distribution:18 both:5 essentially:1 braunstein:1 improved:2 2n:2 desired:3 many:1 hint:3 according:1 against:1 fulfilled:1 sensitive:1 figures:2 raimond:1 casimir:3 variance:1 feshbach:1 whole:3 comes:1 aρ0:2 among:1 relevant:1 feynmann:1 cn:2 point:2 wall:1 perot:1 dipartimento:1 harmonic:1 community:1 active:1 simply:1 exhibits:1 cs:8 moreover:1 ogawa:1 along:1 ct:2 described:2 aˆ:2 equations:1 create:2 due:16 been:4 strategy:1 defined:1 much:4 damping:8 interest:1 ph:1 ann:1 empty:2 nuovo:1 direction:1 arises:1 corresponding:1 am:2 sufficient:1 coherence:15 photon:9 cos:1 output:1 coherent:13 external:3 iπ:6 last:1 2ie:2 present:1 case:15 exponential:1 pacs:1 solid:4 truax:1 value:9 choices:1 will:12 pace:1 while:8 replaced:3 eif:17 aid:1 nonstationary:1 couplings:2 procedure:2 della:1 va:1 larger:1 satisfying:1 vogel:1 coupled:2 almost:3 ip:3 vk:1 thus:6 equal:1 obeying:1 ay:2 vs:1 insensitive:1 ib:1 ie:4 different:6 considerable:1 generic:2 media:1 radiation:15 same:10 shorter:3 villarreal:1 unity:2 imoto:1 quant:1 emphasize:1 gets:1 higher:1 used:4 peaks:2 effect:12 hand:3 effectively:1 fabre:1 moving:3 purpose:1 hospitality:1 entanglement:2 totally:1 normalization:4 recognized:1 schr:11 modes:2 zagury:1 nucleare:1 nevertheless:1 makes:1 substantially:1 modeled:1 well:5 physics:1 obviously:2 without:2 solve:2 experimental:2 model:10 proposed:2 being:1 obtain:2 rest:1 slusher:1 sources:1 human:1 integer:1 alternative:2 macroscopic:8 eigenstates:1 previous:1 density:7 photons:9 mobility:1 realize:1 quadratures:1 reasons:1 preferable:1 interested:2 lett:11 easy:3 hermite:2 input:1 mod:1 solvable:1 eigenstate:1 momentum:4 take:1 opt:4 ield:8 aspects:1 around:3 depends:3 easily:1 read:1 showing:1 injection:1 possible:3 smallness:1 increases:1 entangled:1 birth:1 destroy:4 using:9 part:1 replace:1 apart:1 loss:3 levenson:2 like:4 university:1 signal:4 performing:4 camerino:3 separately:1 hirota:1 become:2 inter:1 reduced:1 accessible:1 because:1 methods:1 classical:1 2x:11 conditional:6 phenomena:1 hacyan:1 born:2 mirror:33 oscillations:3 indirect:2 neglecting:2 merzbacher:1 provided:4 cavity:15 measurements:3 intracavity:2 schleich:2 fringes:3 tends:2 pattern:2 proc:1 hcm:1 refer:2 inserting:1 noise:1 visualize:1 power:1 2c:3 oscillating:5 bt:1 pressure:4 references:1 worthy:1 zimmermann:1 properties:2 bz:1 takes:1 works:1 mcgraw:1 freedom:2 commun:1 introduces:3 dependence:1 o:6 collett:4 financial:1 range:1 ensure:2 act:1 recognizes:1 introduced:2 slightly:1 revise:1 peak:1 soc:2 rev:30 presence:8 communication:2 into:4 within:2 disentangled:2 coefficient:1 three:1 down:2 variable:3 appropriate:2 accounts:1 operator:20 proportional:1 statistics:3 additional:1 pc:4 support:1 there:1 transform:1 long:1 width:1 cats:5 low:1 lot:1 was:3 assumes:1 questionable:1 medium:3 illuminated:1 form:6 hp:4 hq:3 but:8 hu:1 hj:1 matematica:1 quasiprobability:1 line:9 highest:2 dissipative:1 relaxes:2 partially:2 made:4 rotation:1 qualitative:1 la:1 inside:5 ponderomotive:1 up:1 us:11 crystal:1 below:1 projecting:1 ωm:8 ωc:6 cahill:1 similar:1 mechanics:3 constant:7 pin:6 ai:2 recognize:1 abstract:1 describe:1 influence:1 slowing:1 general:1 aq:6 ap:4 engineering:1 pˆ:2 nazionale:2 lifetime:1 davidovich:1 moves:1 distributions:3 check:1 interferences:1 physical:1 again:1 materia:1 compared:1 meystre:3 dotted:3 no:1 dashed:4 when:5 ne:1 field:15 other:7 role:1 becomes:6 conclusion:1 picture:1 superposition:10 separate:1 finite:1 resembles:1 reached:1 polynomials:2 generated:3 important:1 fabry:1 dissipation:6 song:1 n2:2 structure:1 sandberg:1 bch:1 coupling:4 4x:1 practically:1 assume:1 thermalization:1 dτ:5 pseudo:10 mancini:3 mimic:1 mass:3 adam:1 time:21 retardation:1 decoherence:4 starting:1 having:1
|
quant-ph9612006.txt |@word represent:2 concept:2 allowed:2 consider:21 magnetic:1 results:2 existing:1 leads:1 eds:1 scalar:8 commute:1 chiu:1 spiridonov:1 originally:1 go:2 particularly:1 4e2:1 gl:1 soc:1 whose:2 inverse:5 depend:2 calculate:4 irrelevant:1 concerned:1 radcliffe:1 passage:1 recurrence:2 charge:2 squeezing:5 preserved:1 a27:1 under:3 analogous:1 must:1 tb:1 worth:1 norm:1 applied:2 belonging:2 deforming:2 advantage:1 evolves:1 very:1 frequencies:2 rise:1 possibly:1 choice:5 quesne:1 subpoissonian:1 interpreting:1 dispersions:2 nontrivially:1 affect:2 difference:1 matrices:1 deformations:5 condition:3 identity:6 entire:1 vibrational:3 hamiltonian:43 did:1 irreducible:3 solution:4 t0:1 occurs:1 large:2 involution:1 leninsky:1 demonstrated:1 angelis:1 c00:4 eigenvalues:2 optics:8 equation:13 relative:1 application:2 too:2 version:2 oscillation:2 formfactor:1 dealing:1 coefficient:1 cosh:5 second:5 plenum:1 value:1 irreducibility:1 chaturvedi:1 further:2 dynamics:15 b138:1 theory:1 even:2 will:20 what:2 nonlinear:39 sub:4 invertible:2 brackets:3 giving:1 section:10 expressed:4 current:3 infinitesimal:1 en:3 above:10 new:34 increasing:1 cn:10 method:2 ˆn:1 body:2 led:2 notions:2 degree:3 respectively:2 here:7 diagonal:2 behaviour:6 growing:1 objects:1 free:1 groups:2 others:1 represented:2 path:1 along:4 equations:15 appears:1 change:4 obtained:8 scienze:1 generalizing:2 singapore:1 institute:1 involved:1 study:4 studied:3 allows:2 completely:2 contradiction:1 later:1 suggests:1 recently:1 periodic:1 resulting:1 poisson:12 commutators:2 usually:2 hospitality:1 changes:3 subjected:1 y12:3 matos:1 named:2 via:1 useful:1 family:2 discontinuous:1 ipk:2 prefer:2 reparametrized:5 replace:1 pf1:2 malkin:2 pf2:1 odinger:3 summation:1 apply:1 total:3 florence:1 planck:9 select:1 denominator:1 use:14 takes:2 usa:1 prove:1 recalling:2 positive:4 coupled:1 gruber:1 finally:1 next:2 comparing:1 approach:2 call:2 therefore:6 a29:1 taken:4 robertson:1 themselves:1 stage:1 type:1 start:5 more:6 zeroes:6 nauka:1 said:1 l873:1 definition:2 started:1 becomes:1 operators:38 factor:2 about:1 pfq:1 interaction:2 normalized:1 particular:12 known:3 cases:6 given:22 producing:2 kgl:1 had:1 reconstructed:1 keeping:1 valued:2 defines:2 quartic:1 permits:1 deformed:20 science:1 setup:1 created:1 oscillator:51 a22:2 theories:1 glauber:2 remain:1 fock:20 obvious:3 illustrated:1 dh:6 universe:1 following:15 making:1 projectors:1 example:13 numbers:3 beautiful:1 f1:5 compare:3 f3:1 νp:2 give:2 process:3 dβ:2 preserving:1 νx:2 ann:2 pieces:1 states:86 selfinteraction:1 performed:1 want:1 sense:1 keep:1 evidently:1 ratio:2 motion:29 counting:1 end:1 goal:1 provide:1 di:7 nondiagonal:1 σxp:3 write:9 how:4 varies:1 stemming:1 resolution:5 get:7 instead:2 ordinary:1 constraints:1 parameter:8 sin:2 ρ2n:1 exponentially:3 oscillatory:1 map:3 product:10 express:1 description:4 σf:2 algebra:2 may:19 demonstrates:1 oscillators:35 after:6 different:33 σx:5 diagram:1 applications:1 produce:1 itλ:1 ff:3 fh:12 representations:5 fk:2 data:1 concerns:1 types:3 man:13 dα:6 dynamical:8 light:1 spectra:2 lines:1 element:1 diffeomorphism:1 maintain:1 so:9 sn:2 allow:1 correlation:10 representation:7 increase:1 order:4 contrary:1 origin:1 holds:1 interpretation:6 ith:1 produces:5 september:1 developed:1 over:4 mehta:1 vary:1 choose:2 osservatorio:2 interpreted:1 twiss:2 course:5 paper:1 through:8 guadalajara:1 statistical:2 husimi:5 y1:1 existence:5 y3:1 y2:1 its:6 before:2 expansion:1 srinivasan:1 probability:1 adjoint:2 acknowledge:1 ln:5 interesting:4 fix:1 xm:1 glogower:1 stimulated:1 decreases:2 actually:4 better:1 fq:8 willing:1 degrees:4 systems:27 remarked:2 quant:1 main:1 might:3 deformation:15 texas:2 yi:6 qq:1 them:10 yj:3 motivated:1 greater:1 views:1 obtaining:3 a50:1 introduce:4 anticipated:1 they:8 symposium:1 nov:1 now:12 yu:1 realize:1 possess:1 easily:3 double:3 name:1 hω:6 invariants:1 university:1 presented:1 alternately:1 hermitian:1 birula:1 afq:1 orthonormal:1 vibrations:7 mode:17 each:8 found:3 universit:2 decreasing:2 side:3 2j:4 mean:8 kano:4 differential:3 ei:2 directly:1 weight:1 evolve:2 experiment:1 series:5 energy:10 essentially:1 idea:1 related:7 frequency:10 obtains:4 measure:1 quantum:40 our:6 nonlinearities:3 special:2 out:4 respects:1 shown:9 matrix:13 factors:1 restricted:1 furthermore:1 since:11 rev:13 denotes:2 looking:2 acting:1 vector:8 istituto:1 denoted:1 formula:10 rn:1 induced:1 evaluation:1 integrated:1 math:3 common:1 benjamin:1 earlier:3 turning:2 linear:15 contain:1 fisica:1 possibility:5 standard:5 admits:1 clarify:1 reason:2 carried:1 reparametrizations:1 york:2 nα:21 put:1 region:1 anyhow:1 generate:1 capodimonte:2 temperature:6 r4:3 degeneracies:1 r6:2 fixed:1 language:2 napoli:5 could:3 honest:1 counterpart:4 turn:2 int:2 abuse:1 isotropic:5 consequence:3 uses:1 austin:1 eqs:2 first:10 xj:8 xk:4 intuition:1 initial:7 xn:2 features:1 symmetry:2 laguerre:2 xb:3 variables:11 xa:4 synonymous:1 number:13 clear:4 done:1 construct:4 another:10 fi:4 polychronakos:1 illustrate:2 differ:1 necessarily:2 bracket:10 rewritten:1 hyperbolic:1 introduction:2 test:1 dipartimento:1 system:27 relations:17 parallel:1 their:13 quadratic:1 master:1 constants:5 statement:1 realization:1 rates:1 structures:3 recovered:1 gives:6 a79:1 way:2 trapped:1 ch:1 moscow:2 moiariello:1 serve:1 foliation:1 required:1 jordan:1 much:2 bagrov:1 x2:9 x3:1 x0:9 x1:2 representing:2 than:4 coefficients:2 modes:11 e3:1 wide:1 kind:5 was:16 approximations:1 namely:2 submitted:1 limiting:1 annihilation:13 minimize:1 classes:1 iωa:4 n4:1 amplitude:3 were:8 ber:1 russia:1 a49:1 exhibit:1 symmetries:6 generality:2 fluctuation:1 dynamically:1 turned:1 generalization:5 already:3 say:3 manner:1 emission:1 conjugate:4 seen:7 any:13 influences:1 lie:1 quadrature:7 natural:1 zero:2 depending:5 identification:2 studying:1 latter:1 polyatomic:1 recourse:1 aa:4 contour:1 note:2 instance:4 high:3 f2:6 take:5 analogy:2 xi:11 ˆi:1 coincide:2 canonical:1 modulus:2 tensor:1 heisenberg:5 blue:2 continuous:4 fundamental:1 twodimensional:1 harmonious:8 satisfy:9 phases:1 extending:1 satisfying:1 connected:1 formulae:1 phase:9 comparison:1 inserted:1 class:6 eigenfunctions:2 observation:1 consequences:4 considered:11 calculated:2 partition:7 ko:13 µp:2 physica:1 face:1 countable:1 proceedings:1 hi:3 βen:1 principle:1 exp:8 kt:9 boson:3 physics:5 notion:7 fact:7 reparametrize:4 lebedev:1 phenomenon:2 intensity:1 show:4 detection:1 charles:1 converge:1 attempts:1 multiplicities:1 relation:14 solutions:4 daskaloyannis:1 upper:1 wigner:7 analogue:2 find:5 occupation:2 partners:1 electromagnetic:4 based:1 just:1 parameters:1 situations:3 written:3 should:6 analytic:3 only:5 explicitly:3 black:2 molecules:1 indeed:2 fq2:1 integrable:2 hamiltonians:2 hopf:1 checked:1 equilibrium:1 dn:5 ωy:1 goes:1 viewpoint:2 means:10 dependent:6 simplest:1 satisfied:1 ones:8 legitimate:1 dx:2 dy:2 unaltered:2 applying:1 dt:3 distortion:1 procedures:1 αk:13 closure:1 evolution:9 de:3 λb:1 tot:1 fields:2 arxiv:1 acknowledgments:1 qa:1 influenced:1 experiments:1 noncanonical:7 dodonov:2 qf:1 qi:2 y32:3 qk:2 αn:4 discussing:1 view:2 preserve:2 set:4 computed:2 exists:5 plane:1 physically:2 problem:1 frame:1 correlations:1 respect:3 packet:2 lnm:1 differs:3 depends:6 descriptions:5 biedenharn:1 y0:5 cyclotron:1 portrait:3 dµ:1 satisfies:2 2n2:3 acquires:1 appear:2 hilbert:10 still:1 fisiche:1 commutation:16 mentioned:1 matter:1 marmo:7 label:1 state:35 belov:1 various:1 chosen:2 between:8 αi:2 invariant:6 geometric:1 αj:1 x21:3 deforms:2 x23:3 x22:3 available:1 wf:1 notice:2 terms:7 statistically:1 do:3 initially:1 yi2:1 analogues:1 however:7 moyal:3 kerr:1 creates:1 wq:1 analyzed:1 bose:3 multivariable:1 wh:1 relying:1 suggested:2 both:13 cos:2 ωb:1 last:2 2n:33 brown:2 many:4 taking:2 uncertainty:4 equal:3 against:1 etc:1 connection:2 eta:1 symplectic:1 filho:1 σp:5 expression:1 experimental:3 otherwise:1 among:4 lm:3 a2:5 sinh:55 point:5 simple:3 poissonian:7 cn1:3 c200:1 presumed:1 harmonic:25 dimensional:9 maintained:1 coordinates:14 consideration:1 polynomial:2 constant:7 november:1 speak:1 pr:1 forms:1 jetp:1 described:6 transformations:4 basis:8 trajectory:2 trifonov:1 radiative:1 three:3 been:11 ai:7 cosine:1 pf:5 treat:1 interest:2 tino:2 ph:1 algebras:1 unchanged:1 important:1 differently:1 generating:3 corresponding:8 easy:3 natale:1 mind:1 photon:19 remark:4 modelling:1 coherent:78 derivative:1 x2i:1 2n1:3 denote:3 spin:1 present:1 case:29 p1:1 macfarlane:1 japan:1 defining:2 akad:1 iyk:2 choices:3 aim:2 technical:1 while:7 p2:8 replaced:3 aij:5 situation:5 property:5 leaves:1 procedure:3 iy:2 identical:2 notation:2 unitary:1 a24:1 a25:1 a4:1 played:1 vol:1 ip:3 von:3 tω:4 thus:9 according:1 ii:1 reads:3 ij:1 properties:2 wave:4 ia:4 return:1 c0:5 shift:3 bargmann:1 underlining:2 eigenfunction:1 containing:3 italy:2 akj:2 klauder:3 distributions:3 make:5 belong:1 radiation:2 admit:1 same:31 check:1 unity:1 complex:18 pad:1 emphasize:2 widely:1 constructed:5 breaks:1 difficult:1 mostra:1 independent:4 used:5 infinity:1 see:3 trivially:1 susskind:1 trajectories:1 sudarshan:7 effect:3 counterparts:1 hand:4 ion:1 moment:2 moving:1 analyticity:2 federico:1 publishers:1 normalization:5 subspaces:1 a52:2 estimation:1 shortly:1 center:2 nucleare:1 nevertheless:2 makes:1 variety:1 well:9 without:2 peculiarities:1 contact:1 components:6 bjk:1 coordinate:3 fk2:1 usual:21 world:1 proposed:1 less:4 being:4 generally:1 guided:1 obtain:12 vanishes:1 torus:1 λa:3 relevant:1 transforms:1 qh:1 facts:1 λj:3 alternative:4 eigenstates:11 previous:2 gluons:1 integer:1 vibration:4 photons:3 conclude:2 character:1 parametrization:1 density:2 discuss:2 quadratures:6 belongs:1 lett:12 versa:1 theorem:4 extend:1 grow:1 mod:3 transformation:6 momentum:2 generalized:4 real:6 iθ:2 exhibited:1 bij:3 reparametrization:4 iα:2 iγ:2 astronomico:2 possible:14 admitting:1 corresponds:2 early:1 δnm:3 vibrates:1 vacuum:1 press:1 using:11 unique:1 hermite:2 wiss:1 ni:1 loss:2 theor:1 necessary:2 like:8 particle:6 meucci:1 follows:1 reduces:1 velocities:2 dρ:1 specific:6 continue:1 yields:1 either:1 sezione:1 always:1 become:3 stationary:2 reduced:1 replacement:1 because:2 old:3 neumann:3 classical:22 undistinguishable:1 creation:6 some:10 remarking:3 algebraically:1 repeat:1 examples:6 choosing:1 pervading:1 oscillations:1 small:3 extended:1 nonnegative:1 happens:1 provided:3 describing:1 lead:1 eiθ:4 measurements:1 schr:3 subclass:3 does:4 decomposition:1 expressing:1 ensemble:1 y22:3 proc:1 minimal:1 refer:1 inserting:1 considering:2 measures:1 integrals:3 zα:3 bm:1 arbitrary:1 continuing:1 nonlinearization:1 bj:1 bk:1 mexico:1 eiφ:2 eiψ:2 super:2 permitted:1 guaranteed:1 integers:1 stone:3 would:3 vogel:1 algebraic:5 freedom:7 electrostatics:1 discussed:8 dependence:5 o:1 2i:1 compatible:2 mutually:1 hanbury:2 carrier:2 extensions:2 zaccaria:6 introduced:6 slightly:1 contours:2 hence:3 vi:1 considerations:1 primitive:1 contains:2 presence:2 h2:4 into:5 h1:2 integral:9 functional:2 bji:1 due:4 down:1 multiply:1 appropriate:1 right:3 references:1 sov:1 operator:21 couplings:1 λn:7 statistics:5 deal:2 few:1 assumed:2 strictly:1 there:16 transform:2 fast:1 noticed:1 dispersion:7 width:1 cauchy:2 quanta:1 low:1 lot:1 ed:1 bialynicka:1 scientific:1 analyze:1 sections:5 far:2 naturally:2 function:57 medium:1 arise:1 complete:5 form:10 offer:1 phenomena:1 becoming:1 denoting:1 but:7 gaussian:1 heat:3 construction:6 hn:2 repeatedly:1 larger:1 convergence:1 line:2 hf:4 vectorfield:4 ωx:1 made:4 compute:1 nonlinearity:34 2πi:1 wish:1 up:1 us:6 below:1 decays:1 limit:4 planes:1 reviewed:1 distribution:22 define:5 similar:1 called:2 vectorfields:2 mechanics:9 µx:2 ab:1 associated:10 defined:6 abstract:1 describe:2 influence:3 correction:2 general:7 globally:1 single:2 exist:4 dθ:3 formulation:2 nazionale:1 formalism:2 commuting:3 eigenstate:2 august:1 physical:15 nh:1 again:2 functions:12 nk:8 completeness:4 no:9 eq:7 when:8 detail:1 nf:16 schwinger:1 field:17 other:8 role:2 quantities:2 department:1 nq:1 gagliardi:1 pi:2 acceptable:2 conclusion:1 picture:3 elements:2 kinds:1 superposition:2 calculating:1 models:1 gas:1 setting:3 problems:2 polynomials:2 stay:1 a1:1 commutator:3 ξk:6 a5:1 log:1 n1:29 variable:2 qψ:1 finding:1 nuclei:1 structure:4 multimode:1 subspace:4 bases:1 correlated:2 coupling:2 dψ:1 vice:1 dφ:1 values:2 space:31 orbit:3 original:5 a8:2 aspects:1 nelson:1 time:6 n0:14 observables:1 n2:38 n3:2 starting:3 having:9 once:1
|
quant-ph9612007.txt |@word represent:1 homomorphism:2 consider:11 particular:1 results:2 eds:2 scalar:11 computation:1 go:1 spaced:1 gl:1 alk:1 compact:1 whose:1 preserves:1 inverse:2 noncompact:1 recurrence:1 uniqueness:1 giordano:1 preserved:5 under:1 decomposition:2 analogous:1 presentation:1 mehta:1 case:2 rise:4 wave:5 isomorphism:1 every:1 stays:3 matrices:14 dubrovin:1 cmj:1 immediately:1 hamiltonian:13 notes:1 ryan:1 large:1 discrete:2 convenience:1 vector:19 science:1 indices:1 eigenvalues:1 findings:1 direct:2 approximation:2 likely:1 eλk:33 further:1 dynamics:7 odd:4 theory:1 even:7 what:5 appear:1 invertible:1 brackets:11 giving:2 sum:1 expressed:1 3t:1 version:1 obvious:1 construction:1 equivalent:4 ˆn:3 satisfy:1 dψk:2 degree:1 respectively:2 fock:1 nena:1 here:4 understanding:1 behaviour:1 sinh:4 others:1 along:2 quite:1 equations:14 change:4 obtained:4 scienze:1 institute:1 involved:2 inspired:1 studied:2 allows:1 experience:1 example:2 products:8 poisson:21 akl:1 action:2 hospitality:1 uniquely:1 examining:2 via:2 family:3 plenum:1 addressed:1 stern:1 summation:1 should:5 planck:2 bra:1 seligman:1 use:4 would:3 positive:6 stated:1 finally:1 hilbert:14 anticommutation:1 nucl:1 call:1 therefore:3 ψl:5 ψm:2 scope:1 associated:19 until:1 more:2 zeroes:1 introducing:1 hermitean:12 thus:5 operators:12 quant:1 odinger:8 carrying:2 fija:1 known:5 iii:2 potential:1 must:2 springer:1 valued:2 defines:4 recall:3 equation:10 work:3 oscillator:5 infinitesimal:2 values:5 following:6 reexamined:1 give:3 introduces:1 preserving:2 states:11 dxj:1 dxi:1 nonnegative:1 counterpart:1 provide:2 discussion:1 means:2 write:4 how:2 pure:1 answer:2 instead:3 parameter:1 map:1 product:28 de:1 description:3 algebra:8 may:11 bkm:1 oscillators:1 lengthy:1 fa:23 fb:22 fc:1 coming:1 fh:10 verified:1 summarize:1 choice:1 compatibility:2 man:4 stress:1 natural:1 dynamical:7 imply:1 sp:2 explicit:1 element:4 cannot:1 green:2 allow:1 correlation:1 representation:1 wigner:9 subsections:1 indeed:2 over:1 mainly:1 satisfied:1 osservatorio:2 course:1 paper:6 vito:1 guadalajara:1 iachello:1 still:2 excitations:1 suffix:1 clm:2 derive:4 group:3 maps:1 interesting:1 solving:1 coordinates:1 actually:1 complex:9 degrees:1 systems:10 jacobi:3 derivative:2 defining:2 deformation:2 texas:2 correspondence:1 eventually:1 them:5 fourth:1 questions:1 practice:1 federico:1 vecchio:1 mention:1 kamefuchi:1 they:4 symposium:1 nov:1 now:15 2t:1 represents:2 several:3 dirac:1 2s:6 university:1 level:4 identified:2 2f:1 vibrations:1 mode:1 found:4 universit:2 side:1 associative:5 differential:1 another:1 arbitrariness:1 simplicity:1 hadronic:1 energy:3 related:4 inhomogeneous:1 frequency:2 measurement:1 quantum:29 our:18 beyond:2 leave:1 shown:2 matrix:14 space:39 restricted:1 since:2 rev:4 research:1 acting:1 strocchi:1 wolf:1 blk:1 istituto:1 denoted:1 lecture:1 get:3 induced:1 math:4 shows:1 foundation:1 linear:9 associate:7 fisica:1 standard:5 admits:3 completely:3 cari:1 put:1 generate:3 capodimonte:2 1t:1 definition:1 derivation:2 language:1 napoli:4 geometry:1 could:3 times:1 motion:20 produce:1 derivations:1 austin:1 dipartimento:1 first:1 xj:18 xh:3 xi:23 parastatistics:1 symmetry:6 variables:5 xa:5 symbolic:1 number:6 amenable:1 done:2 construct:7 directly:1 distributive:1 cassinelli:1 genova:1 illustrate:1 given:10 fk:8 rewritten:1 introduction:1 eqs:1 system:15 relations:18 physically:1 ion:1 assumption:2 a2n:1 statement:2 realization:1 variational:1 structures:11 ehrenfest:5 gives:5 moscow:1 moiariello:1 immediate:1 part:1 x2:1 july:1 representing:1 sˆ:2 intrinsically:1 reflection:1 kind:2 determines:2 cyclic:1 dfa:1 see:1 annihilation:2 matter:1 determined:2 amplitude:1 were:1 powers:4 russia:1 result:1 rewrite:1 respecting:2 modern:3 measure:1 few:1 endomorphism:1 say:5 manner:1 need:2 st:2 any:12 lie:17 zero:2 lin:1 instance:3 without:1 take:1 δnm:2 so:3 heisenberg:8 bilinear:8 play:1 shall:3 magri:2 okubo:1 satisfying:1 but:3 preliminary:2 pair:4 acknowledgements:1 jx1:1 constructed:1 consequences:2 considered:4 clear:5 ibort:1 ko:4 kl:2 proceedings:1 bracket:13 exp:1 mechanical:1 physics:3 fact:1 ambiguities:3 saying:1 lebedev:1 show:7 spaces:3 relation:9 interpretation:2 find:12 based:1 knowledge:1 state:3 than:1 only:2 going:2 molecules:1 cirelli:1 identification:1 equally:1 hamiltonians:2 local:1 hope:1 do:4 his:2 notation:3 di:7 between:4 expectation:3 ones:1 integrable:2 dx:2 new:15 dt:8 takahashi:1 a83:1 evolution:6 approach:1 arxiv:1 investigate:1 dodonov:1 fixed:1 valid:1 available:1 set:4 constructing:1 exists:1 δji:1 lett:3 ωt:1 λk:1 namely:3 descriptions:21 jx:3 paul:1 acquires:1 project:1 said:2 fisiche:1 commutation:15 pictures:7 definite:6 marmo:9 symmetric:7 written:1 various:6 simplest:1 invariant:2 conditions:1 preserve:1 terms:8 sections:1 jt:3 confusion:1 attention:1 however:2 extent:2 analyzed:1 ket:1 tensors:2 observer:1 both:5 last:1 uncertainty:1 equal:1 jt2:1 admit:2 symplectic:6 context:1 lo:1 finds:1 cj:1 relevant:1 cn:1 characterization:1 simple:2 lagrangians:1 harmonic:4 dimensional:8 simply:1 interrelations:1 respect:8 ct:1 considering:4 described:2 transformations:7 kinematic:1 basis:3 skew:1 been:3 int:1 basic:1 ph:1 algebras:3 partial:1 define:9 aj:1 corresponding:1 deeper:1 concerning:1 subspace:1 remark:2 observers:2 coherent:1 coherently:1 present:4 p2:1 talking:1 might:1 will:12 while:1 associates:1 lx:3 aij:3 investigating:1 skewsymmetric:1 property:6 study:1 unitary:3 mexico:1 endowed:2 δfa:8 ii:2 ij:1 im:1 reports:2 ready:1 simoni:1 zaccaria:3 different:9 italy:2 generic:1 make:3 formulations:1 hψ:1 same:8 clearly:2 unity:2 parts:4 pad:1 finite:9 difficult:1 mostra:1 used:2 akm:1 numerical:1 sudarshan:4 hand:1 usually:2 levels:1 lxa:1 infinite:3 δf1:2 identity:4 lxh:2 schr:8 center:1 nucleare:1 onedimensional:1 no:4 well:3 analysis:1 thought:2 contact:2 solve:3 easily:3 position:2 dimension:3 usual:2 among:2 obtain:1 properties:1 thanks:1 aspect:2 integer:1 facts:1 alternative:31 previous:8 preprint:1 generator:1 conclusions:1 thinking:1 had:1 quadratures:1 other:2 treatment:1 versa:3 transformation:5 momentum:2 generalized:1 real:13 aspects:1 isomorphisms:1 quasidistribution:1 astronomico:2 possible:8 know:1 vacuum:3 press:1 using:8 intersection:1 decomposes:1 domains:1 mod:1 like:5 particle:1 follows:1 collective:1 adiabatic:1 δn:2 benefit:1 sezione:1 amd:1 parity:1 because:2 classical:7 creation:2 some:7 back:2 examples:3 b2:3 atakishiyev:1 describing:1 dimensions:1 avoid:1 investigations:1 does:1 connecting:2 provides:1 closely:1 trap:1 ba:1 bn:1 morandi:2 imaginary:6 2n:6 integers:2 about:1 rubano:3 usa:1 world:1 commutator:1 freedom:1 discussed:2 meaning:1 o:2 compatible:9 mukunda:1 carrier:4 plus:1 restate:1 ferrario:1 raised:1 h2:2 into:2 h1:2 bound:1 appropriate:1 square:4 references:1 determine:2 a8:1 operator:11 additional:1 elastic:1 ψk:27 assumed:1 support:1 there:4 question:4 long:1 noticed:1 start:5 quadratic:13 low:1 way:2 scientific:1 was:5 function:21 form:4 converse:1 ht:1 repeated:1 properly:1 link:1 russian:1 hc:1 true:1 he:2 vectorfield:18 made:1 applying:1 nonlinearity:2 cij:6 up:2 us:2 below:1 jω:1 problem:7 similar:1 called:4 vectorfields:1 b1:3 mechanics:5 ab:1 constant:5 choosing:1 ag:1 af:2 defined:9 implications:1 abstract:1 describe:1 denote:1 examine:1 arises:1 right:1 nazionale:1 exist:1 formalism:1 gruber:1 physical:6 again:2 functions:16 variety:1 when:4 vanishes:1 field:1 setting:6 role:1 becomes:3 department:1 ohnuki:1 picture:13 briefly:1 models:1 problems:2 precision:1 a1:1 a0:1 generated:2 important:2 a5:1 vectors:1 sharma:1 structure:25 longer:2 vice:3 assume:1 requires:2 d22:1 original:1 equivalently:1 mass:1 remarked:1 n0:3 observables:3 starting:6 having:1
|
quant-ph9612008.txt |@word represent:1 partial:1 consider:4 rev:20 results:1 leads:1 eds:1 quadrature:10 generalize:1 spiridonov:1 follow:1 expressions:8 λik:1 inverse:1 depend:4 calculate:12 recurrence:1 squeezing:52 under:1 breach:1 analogous:6 include:1 dramatically:1 norm:8 applied:1 fax:2 r12:14 advantage:1 r11:14 very:4 seemingly:1 choice:2 figs:2 dispersions:2 husimi:2 associated:6 difference:2 matrices:4 identity:3 24y:2 mc:1 presented:1 turns:1 scalar:26 large:4 discrete:6 leninsky:1 demonstrated:1 science:1 small:1 optics:1 equation:1 upper:10 strongly:1 mn:2 tel:2 prudnikov:1 det:2 direct:3 pulse:2 sign:2 approximation:1 second:5 plj:2 evaluated:4 recalculate:1 cat:1 odd:8 amplified:1 canonical:5 even:8 aim:1 3y:1 nonlinear:3 appear:2 section:11 axes:3 expressed:13 symmetric:3 annals:1 above:2 utkenhaus:1 new:10 bateman:1 bird:3 notions:1 degree:2 respectively:5 never:1 component:1 equals:1 here:5 behaviour:4 cancelled:1 asymmetry:1 amplification:1 china:1 appears:1 change:1 obtained:10 institute:3 specialized:1 studied:3 products:11 usually:1 hospitality:1 demonstrates:1 changes:1 involves:1 uniquely:2 being:2 useful:1 convolution:2 family:1 nikonov:1 hermite:38 summations:1 substitution:10 highly:1 coinciding:1 gordon:1 apply:1 total:1 planck:2 linearly:1 plot:2 conventional:1 takes:2 working:1 prove:2 positive:1 contains:1 negative:2 frog:2 next:3 calculation:7 nucl:1 m1:2 therefore:4 characteristics:1 taken:5 means:5 bialynicka:1 type:4 minor:1 more:6 zeroes:1 introducing:1 transcendental:1 integers:1 becomes:4 operators:13 odinger:3 berlin:4 appendix:8 normalized:8 particular:3 known:6 central:1 cases:12 given:20 maryland:2 negativity:1 must:5 account:2 vladimir:1 recall:1 der:1 work:3 mi:1 worth:1 erd:1 fock:23 values:17 following:24 root:5 example:6 proof:2 f0:1 f1:1 f2:1 f4:1 f5:1 figure:2 give:2 process:2 numerator:3 organized:1 purposes:2 chiu:1 states:133 numbers:11 xmin:2 r22:14 axis:3 2r12:1 2r11:1 six:4 orthogonality:3 regions:1 how:1 pure:3 opt:3 shortens:1 parameter:37 displacements:1 derivations:1 oscillatory:5 ζa:1 product:22 express:3 blocks:2 may:3 max:3 after:4 derived:2 hence:1 produce:1 demonstrating:1 multiplication:1 representations:1 law:1 parallel:6 constants:2 man:11 transposed:2 realized:1 µmn:13 sectors:1 invariants:1 light:11 explicit:9 extremal:1 perform:2 cannot:2 sm:2 correlation:2 representation:26 integrand:2 order:2 wigner:17 produces:1 over:3 mainly:1 paper:5 through:1 statistical:2 experimentally:1 differs:1 japan:1 y2:15 excitations:28 its:2 before:1 2λd:1 write:1 group:1 chosen:5 interesting:3 lm:1 boson:1 forms:1 strange:1 fig:13 jacobi:23 mail:2 main:3 might:1 easier:1 maximal:5 them:1 fourth:1 villarreal:1 rotations:1 introduce:2 primary:1 walls:2 they:5 nov:1 now:4 yu:1 discuss:2 possess:1 easily:3 term:2 finite:3 2r:1 2s:1 nfn:5 kerr:1 2z:3 sin:1 possibilities:1 inequality:1 mode:1 radial:1 2l:17 found:3 2n:21 2h:4 side:1 2j:23 2k:34 homogeneous:1 kano:2 square:5 weight:1 series:13 barnett:1 reduce:2 gaussian:6 related:1 society:1 npn:1 obtains:18 measure:2 quantum:4 our:2 2λm:1 graw:1 eq:50 special:23 out:3 shown:2 matrix:9 resonators:1 space:1 restricted:1 furthermore:2 since:4 squared:1 denotes:4 fta:1 method:1 orthonormalized:1 vector:4 hill:1 denoted:2 formula:15 squares:1 induction:3 correct:1 math:8 shows:3 dodonov:9 frank:1 diagonal:1 possibility:2 indices:10 reason:4 8y:1 complicated:4 york:5 members:2 publication:2 definition:3 pairs:1 derivation:1 r2:4 geometry:8 could:2 transition:7 plane:3 place:1 βa:1 consequence:2 onto:4 βi:2 first:10 origin:1 xk:1 major:1 there:5 features:2 malkin:2 laguerre:3 pn0:1 variables:4 number:18 reaches:1 restrict:1 multiplying:1 another:4 changing:1 brychkov:1 reached:2 angular:1 constructing:1 differ:1 rewritten:1 glauber:4 introduction:4 leading:1 eqs:10 system:2 relations:13 their:6 intermediate:1 types:1 alfred:1 final:1 gives:3 calculations:1 moscow:3 proving:1 larger:1 part:2 nieto:1 authors:1 yurke:1 coefficients:3 distance:2 kind:4 determines:1 effective:1 ara:2 double:2 depends:2 limiting:4 annihilation:3 elementary:1 future:1 contrary:1 amplitude:2 were:2 powers:5 russia:1 klimov:3 perspective:5 symmetries:1 nuovo:1 ann:1 turned:2 argument:6 already:2 manner:1 close:1 seen:1 occupied:1 ty1:1 symmetrized:2 trifonov:1 angle:1 zero:4 depending:1 convenient:1 buˇzek:3 oliveira:1 z1:5 generalized:4 interior:2 modulus:3 begin:1 trace:1 index:1 denominator:3 reach:1 systems:1 germany:1 gauss:2 definitions:1 phase:7 inserted:1 class:3 chap:2 unequal:1 considered:7 arising:1 calculated:5 ko:11 physica:1 kr:1 proceedings:2 pnj:1 exp:48 ky:1 normally:1 sum:15 play:1 lebedev:3 phenomenon:1 show:3 2r22:1 relation:15 substituting:1 find:3 occupation:3 partners:1 parameters:12 written:2 should:1 analytic:2 only:14 explicitly:4 rotation:1 factor:5 mechanics:1 hamiltonians:1 visual:1 do:5 legendre:12 cooperation:1 notation:1 get:3 dependent:2 mx2:2 de:2 expectation:8 ones:1 dz:1 dx:6 despite:1 dv:1 during:1 gen:1 dq:2 λc:3 evolution:2 arxiv:1 preliminarily:1 reorganized:1 xmax:2 qi:1 including:1 fixed:2 wrote:1 view:2 n12:1 reveals:1 set:3 gegenbauer:10 exists:3 ary:2 signs:3 relative:1 y1:14 see:14 computer:2 result:8 captions:1 inequivalent:1 uncorrelated:1 nonstandard:3 seems:2 closer:1 evaluation:2 exponent:1 mentioned:2 pictures:2 review:1 definite:1 yet:1 αa:2 state:35 determined:1 closed:6 between:3 invariant:3 geometric:1 approach:5 αl:1 multiplied:1 terms:23 di:1 nature:1 however:7 vanishing:7 concentrate:1 manko:1 bibliography:1 multivariable:10 suggested:1 both:8 essentially:5 last:2 leipzig:1 taking:2 uncertainty:11 equal:11 ln:1 connection:2 σx:1 figures:5 casimir:1 hπ:6 mean:1 expression:3 finds:13 experimental:1 otherwise:1 aa:1 relevant:1 cn:1 cm:2 point:3 simple:6 poissonian:3 each:1 corresponds:1 height:1 dimensional:5 cx:4 simply:1 16y:2 xi:1 polynomial:8 constant:6 schleich:3 speak:2 conference:3 pq:2 described:4 transformations:2 px:1 three:2 been:4 quickly:1 ai:2 workshop:1 z2:8 transformed:3 ph:1 pn:37 ak:4 pl:1 define:1 direction:2 corresponding:8 scalars:1 am:1 sufficient:1 wheeler:1 photon:42 cos:2 gap:1 seperated:1 coherent:40 hmi:1 c2:2 denote:1 present:4 case:24 greenbelt:2 look:1 exponential:2 pacs:1 truax:1 cnλ:1 value:10 will:5 evaluating:1 squeezed:41 nonstationary:2 property:1 region:1 stoler:1 klauder:1 real:6 unitary:8 vogel:1 vol:3 ip:5 thus:7 yk:1 according:8 rik:2 elsevier:1 fn:2 mod:2 bargmann:1 nonunitary:3 agarwal:1 different:7 marichev:1 lengths:1 identities:2 make:4 formulations:1 same:9 nasa:2 unity:1 complex:6 quant:3 arguments:4 pauli:1 proved:5 gets:1 higher:1 independent:2 used:3 complemented:1 sudarshan:2 effect:2 hand:1 action:1 4m:2 moving:1 purpose:1 kim:1 frequently:1 landau:1 contribution:1 normalization:15 schr:3 acknowledgement:1 nevertheless:1 min:1 well:8 obviously:1 without:1 components:1 sets:1 coordinate:5 position:3 parametric:1 comprise:1 usual:10 background:1 λt:2 moments:4 generally:1 λx:3 rotated:1 obtain:4 reviewed:1 abbreviation:2 ultraspherical:1 shape:2 ch:1 thanks:1 summed:1 progress:1 eigenstates:1 λm:6 knight:2 5y:1 integer:2 density:1 characterization:2 character:1 parametrization:1 realize:1 quadratures:3 setting:5 combine:1 lett:8 easy:2 diagonalization:1 n02:1 transformation:1 momentum:3 take:2 identical:3 explained:1 aspects:1 conclude:1 sums:4 possible:13 cf:1 increases:2 appendices:2 vacuum:6 average:1 using:17 ni:1 cahill:1 displaced:14 necessary:2 like:6 differentiations:1 prospekt:1 follows:6 qualitative:1 δn:1 δm:3 steps:1 either:2 integrals:3 arbitrary:8 become:3 weiner:1 detr:2 reduced:2 parity:5 because:4 methods:2 classical:9 creation:3 some:10 back:1 hacyan:1 expansions:1 respect:2 oscillations:2 gave:1 nonzero:2 2d:3 multidimensional:1 electromagnetic:1 integration:2 conditionally:1 strahlung:2 decomposition:3 yields:1 understandings:1 proc:1 lifshitz:1 minimal:3 obey:1 indicated:1 derivatives:1 problems:1 equivalent:2 chaussee:1 perpendicular:8 step:3 binomial:6 2m:20 plots:3 imaginary:3 properties:10 asymptotic:1 comparison:2 about:3 cautious:1 cn2:2 discussed:6 dependence:2 o:1 essential:1 nonvanishing:1 mutually:1 range:10 a2:10 wolf:2 act:1 introduced:3 elyi:1 gamma:3 soc:1 22l:2 press:1 pergamon:1 into:5 formulae:1 integral:9 due:2 down:1 appropriate:1 right:1 promise:1 determine:1 operator:14 amsterdam:1 substitutions:3 ellipse:1 statistics:27 additional:1 springerverlag:1 initial:2 nova:1 dispersion:1 cats:2 low:4 way:17 ed:1 was:13 combined:1 function:27 complete:5 form:29 forming:2 m2:1 analyse:1 but:12 displacement:22 hj:3 hi:1 hn:19 hm:10 4z:1 nonclassicality:2 true:2 doubling:3 infn:1 made:2 applying:9 annihilate:1 instructive:1 up:2 us:4 international:2 below:1 limit:1 demonstrate:3 distribution:20 pm:2 called:1 vourdas:1 detailed:1 gesellschaft:1 ordered:5 ad:2 nauka:1 defined:7 certain:1 abstract:1 describe:2 influence:4 generating:2 general:13 engineering:1 formulation:2 diversity:1 recalculated:1 distributions:4 proceeds:1 physical:4 again:1 functions:8 completeness:4 cim:1 nn:9 no:1 na:1 whereas:2 when:2 wuensche:1 field:1 other:4 role:1 neighbourhood:1 brings:1 np:1 arithmetic:1 conclusion:1 deviation:1 elements:2 superposition:4 excitation:11 symbol:1 remarked:1 nonclassical:8 polynomials:80 stay:1 a1:2 meaning:1 important:2 additionally:1 vectors:3 variable:7 birula:1 nn2:4 structure:2 multimode:1 correlated:3 quasiprobability:23 auxiliary:1 4y:2 hni:1 physics:1 factors:1 appl:1 hmn:13 together:1 hnn:1 superpositions:2 correspondingly:2 adam:2 taiyuan:1 time:1 n0:1 n1:1 n2:1 starting:2 original:1
|
quant-ph9612009.txt |@word represent:1 consider:2 magnetic:1 results:2 four:2 scalar:1 lewenstein:2 edu:1 expressions:1 contributions:1 nonlocal:1 quasi:6 present:1 th:1 under:1 applied:2 wave:4 electron:1 refractive:1 mixing:1 exact:1 condition:3 hamiltonian:15 did:2 welsch:2 guo:1 vector:2 optics:4 smaller:1 concise:1 consistent:1 hillery:4 approximation:2 zero:2 rigorous:1 further:1 canonical:11 subscripts:1 index:1 nonlinear:36 section:2 expressed:12 above:2 sup:1 new:2 method:10 satisfy:4 justification:1 exchange:1 respectively:2 component:1 here:6 china:3 expansion:7 making:1 quasisteady:1 equations:23 obtained:2 involved:1 inspired:1 vectors:1 approaches:2 aki:1 makes:1 klyshko:1 composed:1 orthonormality:1 followed:1 modifying:1 analyzing:1 apply:1 unit:2 standing:1 use:2 feb:1 comparing:1 linear:13 approach:5 until:1 more:1 introducing:1 becomes:2 operators:13 mismatch:1 holo:1 jmn:1 varying:1 known:2 kumar:1 quantized:2 science:2 equation:2 mn:8 reproduce:1 following:3 meet:1 example:2 abram:3 numbers:1 indicated:1 give:3 process:5 carroll:1 performed:1 arise:1 simple:1 axis:1 rather:1 holds:1 arrangement:1 rubin:1 parameter:1 may:3 after:1 derived:1 treatments:1 plane:2 choice:1 effective:1 hasty:1 light:1 explicit:3 sk:1 so:4 order:10 approx:1 eigen:1 pointed:1 mainly:1 satisfied:1 paper:2 london:2 statistical:1 innovative:1 satisfies:1 its:3 derive:4 chosen:3 lm:1 forms:3 lu:1 choose:1 mail:1 nienhuis:1 them:1 propose:1 polarizations:1 material:2 now:2 dielectric:2 term:1 electro:1 fully:1 university:1 presented:1 quantizing:1 mode:2 found:1 characterized:1 ei:2 ej:1 energy:3 barnett:2 principles:1 inhomogeneous:10 used:6 quantum:8 eq:8 out:2 ru:1 jackson:1 acknowledgment:1 space:4 furthermore:2 rev:17 re:1 dxdy:1 ref:7 correct:1 independence:1 benjamin:1 foundation:2 wiley:2 theory:1 free:4 difficulty:1 completely:3 complicated:1 york:2 put:1 8v:1 interaction:2 derivation:8 length:1 place:1 derivations:1 δij:2 first:3 already:1 symmetry:1 sev:1 variables:1 huttner:2 simplified:3 approximately:1 dispersive:5 given:5 rempe:1 similarly:1 introduction:1 relations:6 their:1 returns:3 kµ:49 2ωi:1 john:2 loudon:5 gives:1 transverse:3 optical:9 than:2 coefficients:2 wide:1 determines:1 third:5 second:5 annihilation:5 matter:1 determined:4 amplitude:1 were:1 iωi:6 dielectrics:2 electrodynamics:1 cohen:2 kennedy:1 ming:1 medium:6 conjugate:2 glauber:2 viewed:2 relatively:1 polarization:1 k2:2 k1:1 potential:3 take:3 negligible:1 δnj:2 heisenberg:6 play:1 towards:2 though:1 who:1 most:1 phase:2 gruner:1 tensor:3 volume:1 nonlinearity:2 kj:2 ki:8 later:1 steady:5 kn:2 physica:1 kl:2 physics:1 fact:1 incorporate:1 ωci:1 show:3 absorbing:1 supported:1 rotating:1 attempts:1 gauge:2 inconsistent:1 substituting:3 αk1:1 d3:9 based:2 commutators:2 only:1 explicitly:1 factor:1 thompson:1 hamiltonians:6 iee:1 shepherd:1 dj:1 goes:2 get:5 dd:1 between:4 db:1 watson:1 cannot:1 du:1 processes:3 fields:11 arxiv:1 expansions:7 europhys:2 transversality:3 monochromatic:3 coefficient:1 set:2 ser:1 phenomenologically:1 national:1 hδ:1 achieves:1 sec:3 result:1 terms:3 incorporating:1 collinear:1 commutation:3 nondegenerate:1 functionals:2 state:6 µi:4 µj:1 conditions:2 recently:1 extend:2 nature:1 εij:1 however:3 hefei:1 ji:2 news:1 iki:1 jauch:1 taking:1 reasonableness:1 quantization:37 propagation:1 expression:1 erators:1 cn:1 point:2 appeared:1 baumberg:1 dimensional:2 called:1 16v:1 cavities:1 source:1 addition:1 three:1 been:6 ai:2 much:2 slowly:1 interest:1 ph:1 empty:1 lett:4 field:38 direction:1 corresponding:1 sergienko:1 photon:1 imation:1 developments:1 those:1 case:3 pacs:1 expanded:3 while:1 suppose:2 di:6 procedure:14 orientation:1 vogel:1 tions:1 quantize:1 ij:6 duan:1 dual:2 technology:1 fki:1 santos:2 media:29 make:2 radiation:1 same:3 clearly:1 quant:1 several:1 independent:2 extended:1 spectively:1 infinite:1 center:1 obviously:1 coordinate:1 parametric:3 guang:1 proposed:5 when:4 obtain:1 slusher:1 infeld:2 alternative:2 blow:1 k3:2 density:1 had:2 bloembergen:1 bnj:1 treatment:1 ski:1 momentum:3 gave:1 opt:2 louisell:1 decomposed:1 early:4 know:1 using:1 mod:1 sk1:1 sk2:1 follows:3 δt:2 susceptibilities:2 arbitrary:1 δb:1 essential:1 often:2 deal:1 shen:3 creation:5 phenomena:1 born:2 growth:1 δbn:1 matching:2 electromagnetic:16 integration:1 ωia:1 prog:1 proc:3 pose:1 bi:2 bj:1 properties:3 simpler:1 central:1 khosravi:1 discussed:1 a2:1 introduced:2 op:1 soc:3 presence:1 maxwell:10 into:8 nsc:1 functional:5 hermitian:1 references:1 determine:1 operator:1 classical:1 there:1 long:1 dispersion:1 noting:1 way:1 rela:1 analyze:1 was:3 function:6 project:1 successfully:1 complete:2 form:3 oll:1 drummond:2 hj:1 ho:1 hc:4 inside:1 ωi:8 frequency:3 similar:2 clear:1 shih:1 constant:2 defined:3 abstract:1 am:1 general:2 isochronous:3 kimble:1 formulation:2 ing:1 ni:1 functions:6 completeness:2 no:1 generally:1 detail:1 application:1 other:1 role:1 spatial:2 department:1 mertens:1 phoenix:1 ustc:1 a1:1 commutator:4 important:1 generalized:5 time:1 n2:15 starting:3
|
quant-ph9612010.txt |@word outcomes:1 they:1 just:1 basel:1 satisfied:1 quotes:1 cambridge:2 letters:1 trivial:1 its:2 steward:1 shorter:1 preserves:1 simon:1 kluwer:1 auser:1 guaranteed:1 enough:1 actually:1 only:2 experiment:3 ℜa:2 inconsistencies:1 mail:1 hidden:4 bernstein:2 might:1 variables:3 happened:1 real:2 shadows:1 non:2 his:1 sense:1 pauli:1 straightforward:1 pages:1 decomposed:3 expectation:1 number:1 cannot:1 every:2 entangled:1 words:1 half:2 press:3 world:1 interrogated:1 difference:1 matrices:1 combined:2 contextual:1 groups:1 wojciech:1 february:1 measures:1 necessary:1 particle:4 podolsky:1 did:1 follows:2 university:4 arxiv:1 yield:3 asher:1 discrete:5 theory:2 van:1 roger:2 arbitrary:4 kochen:2 equation:1 mean:1 closed:1 www:1 because:1 dordrecht:1 methods:1 exists:1 reck:2 wheeler:1 publishers:1 measurable:3 tex:1 surrounding:1 second:1 extended:1 considered:1 measure:2 quantum:9 disturbing:1 happen:1 theories:1 scientific:1 even:1 shown:1 specker:3 matrix:3 space:2 broad:1 review:2 since:2 counterfactual:5 reasoning:1 particles:1 consistently:2 state:4 hauptstraße:1 decomposition:3 proviso:1 between:1 drawn:1 rotation:1 conditions:1 spartan:1 shows:1 gives:1 performing:1 defined:1 excludes:1 unspeakable:1 journal:2 component:1 given:1 here:2 merwe:1 surely:1 term:1 although:1 imagine:2 additive:1 imaginary:2 singlet:1 equations:1 svozil:4 science:1 suggested:1 observable:4 σi:1 actual:1 extension:1 always:1 debate:1 involved:1 could:8 theorems:1 equal:1 tuwien:3 called:1 archibald:1 due:1 ernst:2 der:1 experimental:2 first:1 jammer:2 twodimensional:1 spatially:1 murnaghan:1 probability:1 bell:6 search:1 into:5 washington:1 corresponds:1 contributions:1 system:3 dimensional:2 austria:1 references:1 selecta:1 hubert:1 einstein:2 operator:6 impossible:1 missing:1 along:2 readily:1 selfadjoint:1 pp:4 necessarily:1 institut:1 reference:1 would:2 adjoint:7 there:1 theoretische:1 been:1 hilbert:2 their:1 assumption:1 axis:2 therefore:1 way:1 realization:2 expected:1 ph:1 john:5 type:3 vienna:2 separated:1 obtained:1 modern:3 corresponding:2 complete:1 definition:2 naive:1 theorem:2 albert:1 andrew:1 but:1 speakable:1 zeilinger:2 editors:1 part:1 zurek:1 foundations:2 denote:1 spin:5 oxford:2 quantummechanical:1 case:1 states:1 made:1 nathan:1 birkh:1 penrose:2 whether:1 wiedner:1 setup:3 see:1 value:1 ur:1 reviews:2 assume:1 books:1 values:1 princeton:2 concepts:1 following:1 irrespective:1 problem:2 dec:1 certainty:1 decompose:1 ia2:2 mechanics:8 boris:1 ac:3 unitary:2 associated:3 figure:2 predict:1 explicit:1 abstract:1 measurement:5 thus:1 argument:3 general:1 ℑa:2 peres:1 minds:1 file:1 iσ2:1 counterfactuals:2 element:4 technology:1 any:6 physical:11 verified:1 thereby:1 mermin:1 no:1 things:1 self:7 rosen:2 vanishes:1 reality:7 note:1 instance:1 unity:1 complex:1 quant:1 generalized:1 pure:1 significance:1 performance:1 finite:2 parameter:1 operators:1 difficult:1 gleason:2 elements:2 http:2 description:1 trace:1 singapore:1 max:2 according:1 representable:1 publ:1 a1:12 commutator:1 rise:1 a2:10 allowing:1 physik:1 measured:1 class:1 bertani:2 subspaces:1 selleri:1 nevertheless:2 epr:6 tph:3 thought:1 academic:1 mathematics:2 without:1 verlag:1 involves:1 components:1 anton:1 observables:1 quantity:2 physics:3 make:1 reprinted:3 usual:1
|
quant-ph9612011.txt |@word consider:2 rev:14 global:1 results:2 illustrated:1 quadrature:15 consists:1 transmittances:1 contributions:1 localized:1 devoted:1 whose:2 feeding:1 calculate:3 worth:1 supported:1 finally:1 efficiencies:1 squeezing:2 tk:2 excluded:1 under:2 tr1:2 cm2:7 p2:2 random:1 straightforward:1 song:1 very:4 2re:1 rise:3 conditions:1 readout:1 electron:1 figs:1 husimi:10 nieto:1 difference:2 condition:1 splitter:11 presented:1 knight:1 tanh:1 proposals:2 scalar:2 t1:8 large:3 convenience:1 coincidences:3 2xz:1 science:1 small:2 optics:2 noted:1 h2n:1 upper:1 zk:1 approximation:1 second:3 chopping:1 zy:1 further:4 odd:4 port:3 quite:2 even:5 will:4 what:1 nonlinear:1 sub:1 section:1 current:1 ˆb:1 above:1 new:2 ˆk:4 connected:1 preserved:1 advantageously:2 vitali:2 full:1 respectively:5 component:15 here:1 analysed:1 separation:1 concluding:1 ratio:1 november:1 strong:2 equations:1 change:1 obtained:6 arrive:1 study:1 studied:5 commonly:1 evading:3 resulting:2 action:3 plotted:1 transmittance:2 appropriately:1 buˇzek:1 useful:1 hermite:3 summations:1 highly:6 decrease:1 summation:2 apply:1 rarely:1 kobayashi:1 derivatives:1 use:1 superpositions:5 distinct:1 contains:1 negative:1 classically:1 live:1 noting:1 therefore:2 m2:33 type:3 until:1 reflects:1 more:6 separated:3 transcendental:1 operators:5 apparent:1 line:2 odinger:21 needed:1 appendix:3 particular:9 known:3 producing:1 must:1 πnm:3 smears:1 indicates:1 ml:4 equation:3 work:1 oscillator:1 cat:21 macroscopically:4 fock:2 values:8 modifies:1 dec:1 numbers:11 figure:7 give:2 calculation:2 expanding:1 organized:1 states:60 effectively:1 dm:2 performed:3 coincident:7 standard:2 counting:2 distinguishable:5 verlag:1 photodiode:1 switches:1 get:1 xˆ:1 arrangement:1 write:2 instead:1 ordinary:1 parameter:4 sin:3 oscillatory:2 product:2 algebra:1 may:6 max:1 oscillators:1 after:3 derived:2 hence:1 produce:2 forschungsgemeinschaft:1 deutsche:1 su:1 so:3 representation:2 order:3 typical:5 six:1 wigner:15 amplifying:1 balanced:2 produced:1 experiments:2 statistical:3 mentioned:1 still:2 perfect:1 derive:2 manuscript:1 la:1 chosen:4 exhibits:2 better:1 wineland:1 detected:11 microscopic:1 systems:1 derivative:1 photodiodes:3 eventually:2 them:1 good:1 walls:1 they:4 erdelyi:1 rotation:1 now:2 realize:1 restrict:1 always:1 identified:1 2z:1 porta:1 realistic:10 mccall:1 vibrations:1 mode:14 each:2 found:4 universit:1 ports:2 2j:1 2k:10 subsystem:2 lectures:1 schemes:1 another:1 mesoscopic:1 hypergeometric:2 principles:1 jena:2 frequency:1 measurement:5 quantum:11 our:1 eq:19 aˆ1:6 special:1 out:3 shown:5 tombesi:2 matrix:2 driving:1 space:3 since:5 interference:9 denotes:1 increase:1 hill:1 π2m:1 formula:1 ref:3 shows:1 aˆm:1 written:1 possibility:1 effect:4 ban:2 orm:1 bayes:1 approach:2 akademie:1 pairs:1 prepare:1 omit:1 lossless:1 ψm2:6 nonnegative:1 bears:1 place:2 assumed:2 consequence:2 βn:1 lth:1 jex:1 first:5 already:2 features:3 probability:10 omitted:1 number:28 channels:7 done:1 directly:1 precisely:1 illustrate:1 xxxiv:1 given:18 similarly:1 introduction:1 eqs:15 notational:1 amsterdam:1 system:2 relations:7 their:4 expand:1 calculations:3 realization:1 dt2:2 dt1:3 scheme:8 gives:1 trapped:1 mehler:1 larger:4 part:2 injected:2 yurke:5 coefficients:1 observed:4 kind:1 unfortunately:1 zero:1 recording:3 contrary:1 vinogradov:1 zx:1 enables:1 exhibit:2 generality:1 rewrite:1 unchanged:1 measure:2 close:3 seen:3 avalanche:2 clearly:2 strength:1 min:1 homodyne:1 latter:1 ryzhik:1 note:6 emphasis:1 channel:10 heisenberg:1 subscripts:1 opposite:3 unused:4 most:2 germany:1 gradshteyn:1 remarks:1 measured:11 appear:1 considered:2 calculated:5 detectors:1 kn:1 tpi:1 optical:3 quasicoherent:1 exp:11 typically:1 sum:2 fact:1 quantity:1 precise:1 phenomenon:1 show:4 hm:4 x2:4 relation:3 king:1 substituting:2 trivial:1 find:3 multichannel:2 eiϕ0:1 resemblance:2 parameters:2 series:1 freyberger:1 homodyning:1 should:1 only:1 molecules:1 factor:2 parabolic:2 probabilities:1 mixture:2 dj:1 means:3 ϕt:2 de:1 2nm:3 bear:1 ϕr:3 beam:11 preparing:2 dx:1 dy:2 opatrn:1 platz:1 holland:1 reveal:1 increasing:4 fields:2 arxiv:1 summary:1 paper:2 photodetectors:1 analytical:2 qo:1 reveals:2 observes:1 detection:8 see:10 sec:4 result:1 terms:2 project:1 phases:4 einϕ:1 pattern:3 naturwissenschaften:1 state:34 various:8 jth:2 between:7 physikalisches:1 caves:1 αm:4 available:1 recently:4 2m:2 attention:1 however:1 efficiency:1 york:2 distinguish:3 2αm:2 problem:1 improve:1 suggested:1 both:3 cos:4 2n:8 taking:2 according:3 filho:1 mean:4 com:1 regarded:3 experimental:1 otherwise:1 cn:1 cm:6 simple:3 poissonian:3 harmonic:2 represented:1 simply:4 decreases:1 polynomial:1 constant:2 schleich:2 described:1 basis:4 wien:1 been:11 t2:8 z2:4 basic:2 expected:2 ph:1 n1m:1 pn:4 ak:3 xz:1 fig:5 generating:2 photon:22 coherent:12 2n1:2 former:1 present:6 case:5 theoretisch:1 appearance:1 aim:1 near:1 behavior:6 squeezed:14 property:1 stoler:1 opt:3 cylinder:2 unitary:1 vogel:4 vol:1 ip:3 thus:2 walmsley:1 reads:4 im:8 limit:1 monroe:1 different:1 prior:2 media:1 radiation:1 lett:9 same:1 any:1 complex:1 quant:1 mixtures:1 modification:1 products:1 several:1 events:6 higher:1 used:4 peaks:5 schiller:1 kis:1 numerical:2 functions:5 hand:1 parametrized:1 purpose:2 normalization:3 destruction:2 eigenvectors:1 schr:21 modes:2 well:4 obviously:1 efficient:4 without:2 ˆout:4 left:1 teich:1 kiss:1 proposed:4 matos:1 being:11 λy:1 λx:1 obtain:6 photonic:1 slusher:1 abbreviation:1 shape:1 klauder:1 paul:1 macroscopic:1 eigenstates:1 tables:1 λx2:1 density:7 photons:30 iϕ:1 discuss:2 friedrich:1 transformed:1 derivation:1 versa:1 input:14 mod:2 transformation:5 real:1 easily:2 rules:2 multiport:1 possible:1 corresponds:5 increases:2 campos:1 entangled:1 vacuum:9 using:17 like:18 loss:1 modifications:1 photonnumber:4 lost:1 follows:3 signal:3 harmonically:2 yields:2 δk:1 integrals:1 ˆbk:3 output:21 reduces:2 therein:2 parity:1 nm2:3 classical:1 formulas:1 conditional:27 oll:1 back:3 dead:1 examples:4 respect:1 oscillations:1 ˆin:3 absent:1 pronounced:1 progress:1 sufficiently:2 measurements:3 recorded:2 overlap:1 magnitude:1 herent:1 welsch:3 l3:2 measuring:1 destroys:1 process:1 eiϕ:1 indicated:1 fed:1 expansion:1 broken:1 although:1 become:2 losing:1 plots:2 super:1 properties:8 raymer:1 asymptotic:1 comparison:1 mcgraw:1 aˆ:1 discussed:2 dependence:3 recalling:4 wolf:1 mixed:2 eight:1 introduced:1 h2:1 into:2 photodetection:2 integral:8 bound:2 phase:7 references:2 operator:8 proportional:1 statistics:5 institut:1 log:2 vˆ:6 vac:2 there:1 accordingly:1 mandel:3 way:2 ed:1 was:4 function:26 academic:1 creation:3 north:1 some:5 ψm:30 analyse:1 but:2 gaussian:4 hj:1 hk:9 properly:1 hn:2 hl:1 atom:3 technologies:1 collapses:1 reflectances:1 made:3 applying:3 us:4 theoretical:1 those:2 demonstrate:2 distribution:13 similar:5 distance:1 detailed:1 smeared:1 successfully:1 defined:2 abstract:1 combining:2 general:3 single:6 rule:2 saleh:1 crystals:1 distributions:6 interferences:3 regime:1 again:2 mutual:1 nk:1 nm:17 no:3 whereas:3 when:8 detail:1 meekhof:1 event:2 field:3 other:9 proposal:1 conclusion:1 deviation:3 picture:2 elements:1 superposition:8 calculating:1 symbol:1 nonclassical:1 in1:1 polynomials:2 prepared:6 generated:2 peak:3 sides:2 structure:5 acknowledgment:1 gedankenexperiment:1 correlated:2 implies:2 vice:1 assume:2 berlin:1 together:1 4n:1 equivalently:1 walker:2 n1:26 n2:6
|
quant-ph9612012.txt |@word code:1 sci:2 particular:1 grateful:1 research:1 localized:1 relationships:1 amplification:1 const:1 send:1 passage:1 device:1 those:1 stable:1 te:2 tb:11 sent:3 ta:8 supported:1 provides:1 frequencies:5 assuming:1 wave:2 every:1 experimentally:1 severely:1 δt:2 cable:1 did:4 applicable:1 occurs:1 large:3 small:2 optics:2 employing:1 estimates:1 pulse:7 zero:3 pass:2 implemented:1 hamper:1 spectral:4 employ:2 nonlinear:1 sum:1 selected:1 intelligencer:1 above:1 new:1 public:2 satisfy:1 morgan:1 exchange:1 respectively:1 equals:1 experimentalist:1 separation:4 imperfections:1 sending:1 luther:1 institute:1 leaves:1 studied:1 experience:1 fond:1 narrow:10 changes:1 odinger:2 unit:2 use:1 takes:1 would:5 remains:2 chooses:1 definiteness:1 therefore:4 taken:4 simpler:1 type:4 more:2 linewidth:1 nauka:1 pavlov:1 preserving:1 formally:1 becomes:1 under:1 emission:3 correspondingly:1 announce:1 known:3 central:2 must:1 involve:2 account:4 ma:1 grant:1 equation:3 work:1 fock:3 transparency:1 following:3 dec:1 scatter:4 numbers:1 renormalization:1 bennett:4 high:2 performed:3 allowed:2 guarantee:1 information:3 end:2 rather:4 describes:1 purpose:3 delay:4 located:1 instead:1 absolute:1 brassard:2 after:1 derived:1 law:1 constants:1 man:2 realized:1 short:7 attempt:3 remember:1 effective:3 negligibly:1 register:4 element:1 complexity:1 so:4 allow:4 worst:1 hellman:1 discussion:1 typical:1 restriction:1 indeed:1 interpreted:1 course:1 paper:3 pulses:2 eavesdropping:4 affect:1 still:5 its:4 chosen:1 cryptology:1 actually:4 better:1 window:1 parts:2 choses:1 differed:1 main:1 affected:1 orthodox:1 band:11 effects:2 they:2 now:3 inequality:6 each:2 found:1 mean:1 generation:4 series:1 energy:8 einstein:1 reduce:1 gaussian:1 used:8 interferometer:2 frequency:17 measurement:8 quantum:10 wavelength:1 extract:1 shannon:1 out:3 shown:1 announces:1 since:5 rev:6 adhere:1 semiconductor:1 re:2 rare:1 receiving:2 correct:1 math:1 disclose:1 fiber:5 possibility:1 standard:1 detecting:1 molotkov:2 retained:1 widths:1 could:4 impose:1 messages:1 times:5 length:11 fian:1 first:3 major:1 probability:1 xb:3 coding:1 xe:1 channels:1 smaller:1 fast:1 wavevector:1 carry:3 message:1 open:3 privacy:1 system:3 least:1 their:1 zeros:2 realization:1 postulate:1 scheme:4 townsend:2 jovanovich:1 fraction:2 centered:2 completed:1 tapster:1 optical:2 x2:7 than:10 wide:4 see:1 rarity:1 preparation:1 a47:1 states:9 a45:1 were:3 russia:1 iωt:2 exhibit:1 hz:2 spectra:2 epr:1 spectrum:5 randomly:1 krylov:2 close:1 any:6 relatively:1 conversion:1 mermin:1 able:2 ideal:1 k0:1 take:3 brace:1 smolin:1 channel:23 accuracy:4 even:2 fundamental:7 shall:1 price:1 systems:1 phase:1 measured:2 reduces:2 salvail:1 calculated:1 ko:2 km:4 principle:2 exp:5 physics:1 laws:2 random:4 contemporary:2 attempts:1 relation:8 carefully:1 2dω:4 find:3 photodetector:11 based:5 parameters:2 should:10 only:3 factor:1 employed:2 alde:1 do:1 cryptography:2 means:2 syst:1 cannot:5 legitimate:2 shared:1 during:3 dt:3 procedures:1 evolution:1 podolsky:1 arxiv:1 yield:1 dodonov:2 photodetectors:3 through:5 view:3 coefficient:3 ser:1 reference:1 generally:2 violated:1 packet:2 up:1 detection:3 intensity:1 enhanced:1 discussions:1 terms:1 arm:2 detect:2 αx:2 review:1 tend:1 µm:1 state:3 various:1 between:5 limit:1 conditions:1 publishers:1 recently:1 nature:2 wm:1 emitted:1 weak:1 however:2 efficiency:1 key:14 distinguish:2 article:1 amer:1 observable:1 x2e:2 uncertainty:9 according:1 distinguished:1 somewhere:1 experimental:1 otherwise:2 arbitrarily:3 among:2 relevant:1 point:8 cryptosystem:12 corresponds:2 wider:1 proved:1 fruitful:1 broadening:2 described:3 second:1 addition:1 three:1 been:3 secret:4 much:3 basic:1 expected:4 ph:1 choose:1 corresponding:2 restrictions:1 fire:3 sufficient:1 photon:20 zhetf:3 systematic:2 mandelstam:3 present:1 case:3 hughes:1 laser:1 unlike:1 pacs:1 solid:1 will:2 while:2 error:1 situation:2 study:1 procedure:5 detailed:1 larger:2 vol:1 thus:3 increased:3 different:1 author:1 make:1 lett:5 same:2 shorter:3 complex:1 quant:1 units:2 several:1 attenuation:10 numerical:1 effect:4 hand:1 moment:1 uses:1 user:23 lower:1 task:2 schr:2 variety:1 well:5 bohr:5 academic:1 simmons:1 parametric:1 proposed:4 less:3 moments:1 when:2 observed:1 bandwidth:1 ch:1 ps2:1 moscow:1 photons:1 bell:1 guaranteed:1 signals:2 potential:1 location:1 trudy:1 input:3 remaining:1 real:4 around:2 possible:1 chernogolovka:1 secrecy:12 press:1 biphoton:3 particle:3 systematically:1 signal:8 discarded:2 franson:1 imposes:1 either:1 security:1 essential:1 because:1 sequence:2 sends:3 some:2 acad:1 jeffers:1 respect:1 duration:3 shutter:4 describing:1 broad:1 absolutely:1 measurements:12 does:6 t12:3 unavoidably:2 minimal:1 run:1 scientific:1 ps:1 expansion:1 βim:4 although:3 imaginary:2 properties:1 bz:1 stage:1 about:1 actual:2 eaves:1 eavesdropper:9 discussed:1 practical:2 ensure:3 act:3 presence:2 communication:13 into:6 within:1 obtaining:1 down:1 nothing:1 ussr:1 references:1 determine:1 registration:4 reducing:2 statistics:1 prepare:2 tamm:3 there:1 long:3 dispersion:11 width:7 quadratic:4 way:1 was:3 uncontrollable:1 function:1 barnett:1 form:1 registered:1 but:5 russian:1 line:3 true:1 he:4 absent:1 made:1 bandwidths:1 dω:1 maximum:2 us:4 simplifying:1 ωa:2 distribution:4 ωb:2 similar:1 average:2 cryptosystems:2 mechanics:1 required:1 associated:1 defined:3 abstract:1 describe:1 substantially:1 single:6 governed:1 our:1 pis:1 inc:1 2dt:1 no:2 ekert:2 rosen:1 field:1 other:1 role:1 papers:1 techn:1 deviation:2 users:5 phoenix:1 prepared:1 palma:1 independently:1 implies:1 faster:1 practically:1 assume:2 interval:2 rule:1 carrying:1 time:21 dyer:1 harcourt:1 once:1
|
quant-ph9612013.txt |@word consider:3 chain:1 results:3 grateful:1 consists:2 adjustment:1 whose:1 violate:2 send:1 stochastic:1 γa:7 tb:5 ta:6 supported:1 worse:1 far:1 frequencies:8 2γa:1 2γb:1 electron:6 every:1 affect:1 emphasized:2 difference:6 disturb:2 hamiltonian:1 did:1 leave:1 small:1 optics:2 noted:1 employing:2 zh:2 luther:1 pulse:1 second:1 qualitatively:1 implemented:2 even:1 will:3 nonlinear:1 complexities:1 sum:1 new:4 increasing:1 public:1 simultaneously:1 morgan:1 fiz:3 respectively:1 here:2 atoms:1 slow:1 separation:1 remark:1 spite:1 institute:2 allows:2 example:1 narrow:10 klyshko:3 york:2 logical:2 achievable:1 select:1 use:2 would:3 positive:1 therefore:4 taken:1 linewidth:1 pavlov:1 formally:2 knows:1 ugge:1 emission:2 validity:3 berlin:1 particular:2 known:3 high:1 springer:1 quantized:1 tunnel:1 safko:1 work:1 fock:2 obvious:1 transparency:1 following:6 dec:1 scatter:1 history:1 process:4 states:5 performed:1 employs:3 allowed:1 quasistationary:1 occur:1 verlag:1 information:3 rather:2 holds:1 feature:1 delay:6 very:2 brassard:1 after:3 long:3 announce:1 law:1 fl:1 fian:1 types:1 man:1 short:3 natural:2 effective:1 light:1 register:1 so:3 fundamental:4 correlation:1 playing:1 interpretation:1 indeed:1 over:3 paper:1 through:2 eavesdropping:6 satisfies:1 still:1 its:2 before:2 decay:1 energies:3 actually:2 better:1 detected:2 choose:1 defining:1 violating:2 photodetection:5 orthodox:1 landau:1 band:21 they:5 now:1 realize:1 easily:1 always:1 level:7 sufficiently:1 inequality:3 breach:1 each:3 schemes:1 fired:1 generation:4 series:1 energy:11 barnett:1 iordanskii:1 used:7 interferometer:1 frequency:8 measurement:13 quantum:13 wavelength:1 eq:10 event:1 special:1 large:1 network:1 since:4 rev:7 bennet:2 research:1 increase:1 ra:2 ref:2 inevitably:1 fiber:2 theory:1 circumstance:1 possibility:1 base:1 advantages:1 intruder:1 inevitable:1 molotkov:2 r5:1 pairs:1 could:1 transition:1 times:2 length:3 place:1 gordon:1 hence:1 teor:2 first:1 already:1 features:1 probability:2 variables:1 least:1 carry:1 impossible:3 precisely:2 aharonov:2 size:1 necessarily:1 iω0:1 system:5 relations:1 their:1 zeros:1 too:1 statement:1 realization:3 scheme:3 speaking:1 fraction:1 centered:1 academy:2 completed:1 took:1 tapster:1 optical:2 attempt:1 than:2 specify:1 relative:2 kind:1 perfectly:2 require:1 zero:2 rarity:1 determined:3 contrary:1 townsend:2 russia:1 a48:2 peierls:1 ann:1 spectrum:1 randomly:1 krylov:1 seen:1 any:4 viewed:1 absorber:1 mermin:1 a128:1 able:1 instance:1 absorbed:2 take:1 detector:11 channel:1 accuracy:3 shall:2 reach:1 regular:1 pair:1 measured:3 considered:1 average:1 adopt:1 detectors:7 km:1 order:3 exp:3 mechanical:2 velocity:1 oscillates:1 physics:1 fact:1 quantity:1 currently:1 lebedev:2 random:3 contemporary:2 registers:1 relation:8 ground:1 photodetector:5 based:6 t0b:1 t0a:2 situations:1 state:4 should:6 only:5 explicitly:1 employed:8 alde:1 hamiltonians:3 do:3 cryptography:2 get:1 dependent:1 zurek:1 ko:1 joint:2 cannot:4 during:1 arxiv:1 yield:1 nauk:1 dodonov:1 photodetectors:10 fixed:2 view:2 ser:1 observes:1 physically:1 detection:2 depends:1 result:3 discussions:1 close:3 electrode:4 detect:3 attempting:1 review:1 complementary:1 µm:1 written:2 γb:5 between:12 wide:12 available:1 nature:3 however:3 key:9 distinguish:2 article:1 jetp:3 originates:1 both:5 realizable:1 uncertainty:6 according:2 chosen:1 context:1 regarded:3 arbitrarily:5 eksp:2 ch:1 point:2 simple:1 wootters:1 cryptosystem:7 sequences:2 fruitful:1 hω1:1 hω2:1 described:3 window:1 been:1 ph:1 systems:1 dots:1 corresponding:2 fire:3 quantities:1 transferring:1 photon:23 coincides:1 fund:1 understand:1 systematic:1 mandelstam:1 spin:1 present:3 case:4 hughes:1 solid:1 value:2 heidelberg:1 employ:1 technical:1 while:2 suppose:1 situation:3 tunneling:1 procedure:3 coupled:1 refs:1 thus:1 equal:1 ii:1 different:3 grant:1 perform:1 radiation:2 same:2 shorter:1 unity:1 quant:1 units:1 constructed:1 literature:1 see:2 hand:2 moment:1 levels:2 user:9 obviously:1 bohm:1 without:2 components:1 coordinate:1 distances:1 construct:1 protocol:2 proposed:3 less:1 moments:5 generally:1 distribute:1 obtain:1 sources:1 bandwidth:4 distant:1 atomic:1 macroscopic:1 rapid:1 signal:1 sciences:2 absorption:1 photons:8 conclude:1 seems:1 source:1 lett:7 versa:1 trudy:1 formal:1 excited:3 momentum:1 absence:1 possible:2 chernogolovka:1 picosecond:1 biphoton:7 occurring:1 follows:1 reduces:2 discarded:1 steps:1 either:1 security:1 reduced:4 mathematical:1 because:2 classical:1 some:1 examples:1 choosing:1 duration:2 specific:1 measurements:10 exceeding:1 does:1 infinitely:1 equivalent:1 illustration:1 step:1 although:1 interferometric:1 stage:1 gained:1 about:2 central:2 eavesdropper:7 discussed:1 practical:1 introduced:1 izvestiya:1 statements:1 into:2 within:3 appropriate:1 ussr:1 references:1 determine:1 registration:7 tamm:1 assumed:1 strictly:1 there:2 fast:3 width:3 way:3 analyze:1 was:2 function:3 medium:1 form:1 but:1 tartakovsky:1 atom:1 russian:7 line:3 he:1 made:2 bandwidths:1 dω:1 ur:1 limit:1 ωa:4 problem:3 ωb:3 similar:2 distance:1 mechanics:3 separated:1 uspekhi:1 defined:1 certain:2 abstract:1 measure:4 single:4 lifetime:3 physical:5 no:4 ekert:2 wavefunction:1 when:3 field:5 narrowband:1 other:6 role:1 deviation:1 users:19 phoenix:3 prepared:2 important:2 palma:1 independently:1 correlated:6 vice:1 assume:2 interval:4 impossibility:1 time:17 dyer:1 having:1
|
quant-ph9612014.txt |@word exponentiation:1 magnetic:5 reversibility:1 idealised:3 four:5 entropy:1 consists:2 oldest:1 equiprobable:2 looking:1 calculate:1 γs:1 γi:2 under:4 hermann:1 worth:1 digit:5 every:2 experimentally:1 believed:2 school:1 solution:1 10l:1 deutsch:10 miller:1 direct:1 pulse:3 approximation:1 second:20 rigorous:2 estimated:1 machines:2 shining:1 even:9 errors:4 negates:1 above:8 toll:1 new:10 increasing:2 ever:2 consisting:2 coefficient:1 evolving:1 simultaneously:2 notions:1 never:1 abstractly:1 here:7 atoms:3 asymmetry:2 plenio:1 represented:2 path:1 digits:6 luther:1 study:2 approaches:1 fourier:9 york:1 divide:4 classification:1 explained:1 highly:1 remnant:1 turchette:1 stern:6 total:4 formalised:1 plot:2 would:10 call:1 therefore:7 type:2 until:5 composite:1 reversible:5 hold:1 must:1 me:11 setup:1 work:2 concepts:1 my:1 example:16 give:1 preserving:1 reach:1 involve:3 want:2 end:4 provide:2 machine:1 how:21 answer:3 gate:24 ψin:1 description:1 turing:4 after:11 diagram:1 parallel:1 types:1 attempt:1 effective:1 neglect:1 complexity:10 maintain:1 algorithms:10 enter:4 order:4 operations:27 deco:1 over:6 satisfied:1 london:7 thesis:1 affect:5 before:5 personal:1 writing:1 differently:1 potentially:1 schmidt:1 overcome:2 eventually:3 them:4 affected:2 steane:1 effects:5 they:14 goldwasser:1 represents:2 each:20 side:1 successively:1 taught:1 combining:2 laboratory:2 extract:1 divincenzo:4 network:11 crucial:1 particles:2 laid:1 rb:1 reader:1 washes:1 numerical:2 log2:4 linear:2 little:1 estimate:2 enormous:1 silicon:1 sigact:1 already:4 features:3 coding:1 adopted:1 another:5 hood:1 illustrate:3 toy:1 likely:1 similarly:1 top:1 needed:4 too:2 hypothetical:3 wootters:1 ranging:3 tool:1 took:1 distance:2 target:1 showed:2 enabled:1 rate:1 preparation:2 matter:2 classes:3 enables:5 seminal:1 fashion:2 rewrite:1 mind:1 seen:2 unaffected:2 tells:3 strength:2 convenient:1 responsible:1 isolated:1 thorough:1 absorbed:1 transmit:1 decoheres:1 exactly:5 shall:1 regular:1 retaining:1 acknowledgements:1 calculated:1 detectors:1 bracket:1 principle:4 left:3 notion:3 dot:1 signatures:1 random:1 gerlach:6 subtle:1 just:5 implementation:4 coefficients:3 alde:1 falsely:1 do:1 mixture:1 cryptography:3 despite:1 report:2 reconstruct:2 beads:1 textbooks:1 fields:1 method:8 testing:1 margolus:2 detection:1 depends:8 result:12 fail:1 disturbing:1 news:1 best:6 subject:3 said:2 yet:2 simplest:1 caves:1 approach:1 preserve:1 terms:5 nature:2 weak:1 however:10 equals:1 extent:2 bose:1 essentially:1 raimond:1 logic:4 exceeds:1 distinction:1 qubit:24 argue:1 asked:1 timescale:1 polynomial:12 loaded:1 conference:1 broadening:1 asks:1 basis:9 three:6 been:12 much:8 interest:2 basic:5 dots:2 quantities:1 concerning:1 coherent:4 catch:1 spin:21 transformation:5 employ:1 euclidean:1 suppose:2 property:1 35th:1 elaborate:1 procedure:1 interacts:1 containing:1 perform:10 make:2 complex:7 quant:1 split:1 big:1 plates:1 several:7 grows:7 inventors:1 independent:2 emphasise:1 peaks:5 welsh:1 trajectories:1 hand:3 potentials:1 pioneers:1 mentioning:1 suitable:2 academic:1 greatest:3 paradigm:1 maxima:1 assembling:1 alluded:1 transforms:1 facts:1 eigenstates:4 previous:5 candidate:2 regarded:2 wright:1 spread:3 transformed:1 easy:2 technological:3 realisations:2 lcs:1 possible:28 destroy:1 apart:2 performing:10 specific:4 steps:1 arbitrary:1 invaluable:1 security:2 right:6 deal:1 successfully:1 somehow:1 cooper:1 bottom:1 electromagnetic:1 normal:1 comments:1 exposition:1 shamir:2 illustration:2 translated:2 post:9 normalisation:1 properties:1 takes:3 excitons:1 ensure:1 islands:2 slightly:2 nerve:1 soc:6 22l:15 obtaining:1 bound:1 down:7 lies:2 reducing:3 support:1 initial:3 transform:8 fight:1 way:8 was:9 form:12 encodes:2 encoded:3 true:1 maximum:1 devices:3 benchmarks:1 proved:1 computing:7 abstract:4 hypothetically:1 evidence:1 peres:2 exist:2 simulations:1 check:2 constructed:1 radically:2 oversimplification:1 dotted:1 no:17 na:1 whereas:1 generally:3 successful:4 interested:3 digital:1 np:1 picture:5 superposition:13 phoenix:1 journey:1 palma:1 dense:1 longer:3 together:4 time:34 remarkable:1 varying:1 focus:2 leads:1 computation:47 devoted:2 depend:2 summarises:1 zone:2 technique:2 environment:11 answered:1 finally:2 division:4 orthogonal:4 frequencies:3 choice:1 maali:1 coprime:4 presented:4 did:1 magnet:1 solved:4 diu:1 stands:1 international:2 morgan:1 lange:1 dissipates:1 understanding:1 alone:1 along:2 appears:2 superconductor:2 shift:1 rethink:1 trial:2 usually:3 decouple:1 plotted:1 useful:4 logical:1 bangalore:1 alamitos:1 handled:2 positive:1 live:1 memory:2 encode:1 theoretical:4 today:1 introducing:1 bennett:7 ua:19 appendix:3 cases:2 insights:1 fly:2 ibm:3 labeled:2 values:20 following:7 detached:1 trans:1 heart:1 figure:14 performed:5 allowed:1 redundancy:1 monitoring:2 fortunately:3 s2:4 s1:4 write:1 pure:1 divides:6 inputs:2 product:1 may:10 respective:3 produce:2 designed:1 lenstra:2 data:2 grow:3 natural:1 outline:1 nussenzveig:1 τdec:10 fraction:1 so:10 progressively:1 definitions:1 typical:1 indeed:5 pointed:2 fredkin:1 years:2 course:3 statistical:1 cuts:1 still:4 ieee:5 thank:1 acknowledge:1 interesting:1 decreases:6 forms:2 main:1 decades:1 non:4 impulses:1 processes:2 introduce:3 symposium:2 now:11 discuss:1 developments:1 execute:1 january:1 realistic:1 brassard:2 eǫt:1 individually:1 weighted:3 retrieve:2 begun:1 year:1 wavelength:1 eq:9 shown:6 resonators:1 factors:9 furthermore:1 interference:2 increase:3 correct:4 shows:3 earlier:1 theory:11 possibility:3 quite:5 orm:1 complicated:2 remainder:3 language:1 transition:2 programming:1 inverts:1 pollard:1 φout:4 think:2 first:23 intuition:1 flying:1 striking:2 blink:1 xy:2 simplified:2 long:8 directly:2 carry:1 impossible:1 tame:1 open:2 size:19 given:10 checked:1 unitarity:1 unruh:1 indicate:1 1b:1 convention:1 bits:8 gives:7 inefficient:3 continuous:1 eliminates:1 representing:1 than:11 specify:1 connections:1 unfortunately:3 wiesner:2 require:1 computes:1 superfluid:1 future:1 were:6 outcome:18 decompose:1 published:1 correction:2 say:3 weinfurter:2 any:27 subsystems:1 efficient:18 isolate:1 ideas:1 note:3 potential:1 take:8 performance:2 switching:3 multiple:4 opposite:1 track:1 informatsii:1 keeps:1 importantly:2 successive:3 multiply:1 considered:2 average:2 later:3 nuclear:1 mabuchi:1 laws:3 shor:10 drastically:2 show:3 contemporary:2 merit:2 faster:5 ground:1 ratio:2 title:1 written:5 only:30 explicitly:1 implemented:4 amplifying:1 probabilities:1 get:3 simplistic:1 cannot:5 prime:3 synapse:1 outperform:1 yield:2 bounds:1 relative:2 namely:1 actively:1 college:1 violates:1 fails:1 ways:5 subsequent:3 review:1 outside:1 john:1 between:7 prentice:2 reading:1 notice:1 vertical:1 qubits:24 jr:4 gratefully:1 article:1 tractable:1 reinterpreted:1 many:9 according:3 flipped:1 expression:1 comes:1 among:1 betweeen:1 period:19 poly:3 exploit:1 moreover:2 considers:1 considering:1 invert:1 odel:1 fig:20 direction:1 enable:1 photon:1 observe:1 coherently:1 careful:3 irrelevant:1 those:2 case:21 hughes:1 promising:2 situation:13 orientation:1 coupled:1 characteristics:1 superconducting:1 technology:2 binary:1 different:23 approximatively:1 inquire:1 same:10 shifts:1 k2l:2 knuth:1 physical:11 wires:4 closest:3 trivially:1 running:1 delicate:1 invariance:1 cr:1 eventual:2 without:7 solve:1 components:2 very:15 model:1 otherwise:1 ekert:8 gates:16 being:2 when:24 adjusted:1 valuable:1 speed:2 multiples:2 zoller:1 thinking:1 except:2 setting:1 lett:10 versa:2 suominen:3 eigenstate:1 real:2 easily:5 read:2 sums:1 early:2 test:1 world:2 21l:1 correcting:3 mod:6 englewood:1 particle:2 reduces:1 either:6 multiplicative:1 output:10 reduced:1 conditional:3 specified:1 duration:1 provided:1 confirm:1 recorded:1 legal:1 critical:1 adleman:2 provides:4 refer:2 measuring:11 power:3 retains:1 equivalent:3 ratios:1 found:4 repeating:4 central:3 discussed:1 meaning:1 acm:1 practical:1 obeys:1 act:3 mixed:1 referred:1 road:1 communication:1 references:1 einstein:1 operator:5 technically:1 log:7 prepare:3 assumed:1 strictly:1 there:9 vedral:1 los:1 lot:1 complete:5 enough:4 fundamentals:1 smolin:2 technologies:4 irreversible:1 divisors:1 amplify:1 applying:4 improved:1 ωi:1 define:2 agree:1 multiplications:2 cirac:1 certain:3 ak:2 describe:2 am:1 deep:1 general:8 kimble:1 ar:5 au:1 formulation:1 ax:3 again:5 unwelcome:1 storage:1 field:9 valid:1 includes:2 a1:4 a0:5 a3:4 a2:2 nucleus:1 peak:1 tackle:1 controlled:3 curve:2 mimic:1 parallelism:5 dyer:1 decoherence:30 external:1 epeau:1 consider:11 splitting:2 follow:1 research:2 tr:1 asterisks:1 returning:1 far:7 supercomputer:1 induce:1 sons:1 worst:1 decide:1 randomness:1 hamiltonian:4 issue:1 large:10 small:3 employing:1 periodicity:6 fragility:1 zero:4 pass:2 what:4 sub:1 section:11 brief:1 version:1 scientists:1 microchip:1 public:3 contrast:1 edited:2 full:1 behaviour:3 modular:1 selective:1 divisor:3 amount:3 periodic:9 schumacher:1 via:2 followed:2 backed:1 establish:2 select:2 readily:1 gaas:1 eye:1 proceed:1 distinct:4 contains:1 comparing:1 automata:1 taken:2 ψf:1 wipes:1 more:25 operators:2 emission:2 particular:9 known:4 foundations:3 producing:1 evolves:5 keeping:1 science:3 dev:2 sent:1 evolved:1 learn:1 abandon:1 dec:1 spontaneous:1 scramble:1 ions:2 f7:1 suggestions:1 states:25 minimum:1 numbers:13 sense:1 sharp:1 axis:3 information:12 needs:4 rather:4 acts:5 eigenenergies:1 maps:2 wiley:1 mapping:1 fa:12 randomised:4 register:63 sect:6 fundamental:5 dream:1 help:1 hierarchy:1 developed:1 soon:4 thermal:1 paper:1 through:4 suffer:1 its:15 rapidly:1 energies:1 solving:1 actually:3 detected:1 microscopic:1 systems:7 alter:1 good:3 return:2 number:26 oxford:5 abacus:2 instructions:1 growing:2 finite:1 subtler:1 always:3 decimal:1 level:3 2x:1 ttot:4 2l:28 2m:12 2n:8 polynomially:5 2i:1 2j:1 2k:2 mental:1 energy:3 reduce:2 idea:3 used:11 extended:1 expect:2 measurement:42 quantum:147 organised:1 operation:17 bxi:1 discrete:7 since:8 induces:3 denotes:1 acting:3 evaluation:4 occurs:3 difficulty:2 reason:2 imagine:3 ask:1 beginning:1 generate:1 pairs:1 3pu:1 computers:28 exponentially:11 reversing:1 probability:27 encoding:1 reflected:1 done:3 construct:2 story:1 perturbation:1 introduction:1 dft:21 interact:4 least:6 assumption:2 calculations:1 scheme:1 store:1 shifted:1 trapped:1 part:3 differentiate:1 translation:1 traps:1 peaked:1 albeit:1 kind:1 hundred:1 horizons:1 determined:1 supposed:1 comput:1 7a:1 randomly:3 7x:1 paths:1 built:3 depending:6 self:1 onset:1 build:1 finding:9 play:1 towards:1 programmers:1 effecting:5 most:9 extremely:1 appear:3 tη:1 clear:4 optical:2 electrons:5 exp:10 physics:12 phenomenon:2 registers:14 carefully:2 fine:1 find:4 completion:3 ox1:1 kaler:1 factor:19 intractable:3 his:1 notation:3 zurek:2 preparing:2 during:2 arxiv:1 fuchs:1 common:5 set:9 art:1 achieved:1 undergoes:1 unpublished:1 see:17 individual:1 close:8 factorisation:17 various:3 probably:1 conditions:2 knowing:2 recently:4 creating:1 initially:4 complement:1 attention:2 selectively:1 alters:1 both:9 prospects:1 paradigms:1 last:5 annual:1 ramsey:1 experimental:7 arbitrarily:2 point:6 simple:7 cryptosystem:1 corresponds:1 whatever:1 dimensional:1 simply:3 church:1 consuming:3 described:2 quantisation:1 due:3 describes:4 ph:2 pi:2 addison:2 fund:1 understand:2 look:5 exponential:11 ǫk:1 reliable:1 evaluated:1 while:7 superposed:1 reliably:1 error:7 landauer:1 kingdom:1 unitary:17 calculator:1 probabilistically:1 reads:1 itself:1 rid:1 monroe:1 anymore:2 belong:2 rules:2 higher:1 calculation:3 literature:1 uses:1 purpose:2 recent:1 lower:1 task:4 finesse:1 try:3 subexponential:1 analysis:4 obviously:1 concrete:1 speculative:1 calderbank:1 atomic:1 questions:3 using:9 regardless:1 loading:1 kluwer:1 conclusions:1 signals:1 relevance:1 input:26 excited:1 evaluate:1 showing:1 matters:1 game:1 entangled:1 sanpera:1 integer:2 bit:28 imposed:1 follows:3 signal:1 yields:1 popular:1 spins:17 mathematical:4 methods:1 some:11 understood:1 experienced:1 b0:2 b1:2 b2:1 b3:1 scale:1 describing:1 affects:1 measurements:1 per:1 behave:4 eliminate:1 tends:1 proc:7 run:3 bc:1 ufa:1 bn:1 processing:3 bi:2 step:5 plots:2 cnot:4 superpositions:3 integers:5 computational:6 into:15 within:1 phase:5 appropriate:3 coppersmith:1 realisation:2 r2493:1 few:3 measured:2 question:3 fast:3 brun:1 sections:3 φjk:2 properly:1 line:2 2πi:5 characteristic:5 implementing:2 probabilistic:2 up:14 us:13 fluctuations:1 uf:5 similar:2 called:2 ub:12 constant:2 defined:5 globally:1 single:10 formalise:1 defines:1 codes:2 dashed:1 application:1 outputs:1 nice:1 dictating:1 explaining:1 elements:7 clean:1 problemy:1 problems:14 prepared:3 generated:1 ago:1 algorithm:36 vice:2 age:1 required:4 equivalently:1 requires:9 having:2 once:1 illustrates:2 results:6 existing:1 illustrated:3 amplified:1 compact:1 concerned:3 factoring:7 include:1 dramatically:1 resources:1 ingredient:1 labels:1 electron:2 manipulated:1 putting:1 cellular:1 resonant:4 continued:1 wipe:1 lalo:1 knight:3 deals:1 seminumerical:1 optics:1 smaller:1 dynamics:1 click:4 peredachi:1 apparatus:5 giving:2 analogously:1 networks:8 consistently:1 experiment:1 3b:2 3a:1 led:1 degree:1 exchange:1 respectively:5 teleportation:1 desired:1 objects:1 others:1 great:1 wesley:2 technical:1 involved:1 larger:3 leaving:1 resulting:4 implement:9 makes:2 involves:2 composed:1 named:1 scales:1 eiφ:2 private:1 outcomes:8 scaled:1 hardy:1 decrease:1 condensates:1 apply:1 tools:2 use:1 asymptotic:2 remains:4 pedagogical:1 next:2 classically:1 doubt:1 themselves:1 gyromagnetic:2 becomes:4 haroche:1 carrying:1 account:1 ρf:1 challenge:1 obvious:1 control:4 plate:1 process:7 purposes:1 pieces:1 high:3 something:1 rods:1 united:1 gcd:6 varies:1 instead:1 collection:1 multiplication:5 efficiently:8 discusses:1 22nd:1 computations:3 correspond:2 lβ:1 lα:4 produces:1 move:1 mathematicians:3 looks:1 decay:5 chosen:3 li:1 previously:1 choose:1 defining:1 ly:1 violating:1 greater:1 runs:9 dirac:1 university:2 sufficiently:3 magnitude:1 l2:1 truth:2 accompanied:1 macchiavello:1 modo:1 grosso:1 barnett:1 related:7 inverted:1 elementary:9 frequency:5 measure:2 our:3 transitions:1 out:11 matrix:5 res:2 rev:21 holevo:1 performs:4 retrieved:1 diagonal:7 completely:3 ρin:2 factored:2 ρij:2 jozsa:3 could:14 times:9 counterpart:2 4th:1 hence:5 retain:2 manuscript:1 precisely:1 behaves:2 system:13 relations:1 their:7 siam:1 perfectly:1 final:4 townsend:1 completed:1 transistor:1 rsa:1 rivest:2 environmental:1 observed:1 submitted:4 amplitude:2 india:1 providing:1 exhibit:1 cohen:1 curves:2 unlikely:1 dictate:1 clearly:2 mappings:1 inform:1 able:3 davies:1 parks:1 instance:23 detector:4 techniques:3 mit:3 unless:2 connected:1 representation:1 device:8 class:4 stronger:1 repeated:1 graphs:1 proceedings:2 mechanical:1 normally:1 fact:2 underpins:1 supported:1 purely:3 lloyd:1 trivial:4 decade:3 principal:1 q1:3 q2:3 based:2 knowledge:1 should:6 employed:1 local:1 achieve:1 equilibrium:1 insight:1 handle:1 means:4 familiar:1 diagnosing:1 joint:1 ones:2 ossbauer:1 δxx:1 qp:1 evolution:4 calling:1 contain:1 fixed:4 view:3 available:1 requirement:2 multiplying:2 computed:2 exists:1 edition:1 intensity:3 computer:40 phases:1 interacting:3 pattern:1 nightmare:1 tend:1 state:81 closed:1 progress:2 neither:3 brune:1 barenco:7 ability:1 opening:1 efficiency:3 key:3 sleator:2 ket:3 problem:19 adriano:1 limits:2 taking:1 equal:4 etc:3 hω:1 passing:2 estimation:1 kets:1 ck:2 ci:1 relevant:1 conclude:2 ca:1 cf:8 cy:11 cx:8 deflected:1 table:8 occured:1 cavities:1 addition:1 trajectory:1 copies:1 immense:1 isolating:2 aj:2 corresponding:4 sufficient:3 scrutiny:1 inflected:1 c3:2 c2:1 c1:5 c0:5 present:6 divisions:2 contexts:2 plain:1 value:9 will:36 wilf:1 devoret:1 almost:1 neuron:1 thus:12 hardware:1 optimistic:1 φin:2 capture:1 cross:1 unity:1 parts:1 schematic:1 largest:3 gets:1 infer:1 difficult:2 upon:2 effect:8 nonorthogonal:1 ion:1 infinite:1 off:4 nevertheless:3 thought:2 firstly:1 latest:1 obtain:7 underlying:1 distant:2 voltage:1 macroscopic:3 preprint:3 density:7 hall:2 reasons:1 caltech:1 nor:4 unprecedented:1 term:1 increases:2 five:1 know:4 press:3 lincoln:1 necessary:2 like:3 success:6 setups:1 become:3 works:1 accessible:3 indications:1 because:4 classical:38 sequence:4 γst:1 phenomena:1 choosing:2 proofs:1 lead:1 does:11 dipoles:1 assuming:1 limitations:1 noise:2 obey:2 slight:1 selecting:1 journal:2 expansion:1 clarendon:2 although:2 offset:9 stage:1 gained:1 about:13 cliffs:1 actual:1 carried:1 extension:2 getting:1 universe:1 certainty:1 important:1 bounded:1 introduced:1 equally:3 own:1 h2:2 h1:2 included:1 square:1 additions:1 forget:1 mere:4 utility:1 additional:4 transfer:2 tannoudji:1 recognised:1 interferometry:1 function:16 but:23 volume:1 ucnot:4 construction:1 gain:4 he:1 made:6 compute:5 evident:1 society:1 whether:3 wish:1 record:4 limit:2 distribution:2 piece:1 display:1 cryptosystems:2 mechanics:10 int:1 universal:2 contribute:1 periods:2 effected:3 functions:6 other:15 theor:1 clicks:2 conclusion:1 repeat:2 ultimately:1 coupling:15 inset:1 cleve:1 determination:1
|
quant-ph9612015.txt |@word code:24 consider:9 equalities:1 results:4 existing:1 leads:1 generalize:3 c2:8 follow:3 research:3 equivalences:1 depend:1 knill:1 technique:1 tr:73 finally:6 under:5 suffered:1 case:2 conjecture:4 orthogonal:3 corollary:4 formula:1 matrices:1 condition:3 identity:1 dim:27 did:2 irreducible:1 vector:3 erasures:6 indices:1 eigenvalues:1 trs:48 inspection:1 trt:2 upper:1 abbreviated:1 tex:1 second:2 qeccs:1 linear:8 even:1 3y:3 errors:7 giving:1 section:5 decoding:1 henceforth:1 above:1 new:16 consisting:1 satisfy:1 error:7 ranges:5 desired:2 address:1 alone:1 november:1 equations:1 remark:2 clarify:2 vectors:4 allows:1 suggests:1 permutation:1 action:1 suitable:1 makes:1 involves:1 equivalence:3 useful:1 projection:13 replace:1 sloane:2 tools:1 unit:7 readily:2 use:6 would:2 codewords:1 remains:4 positive:4 uniqueness:1 m1:69 therefore:1 criteria:2 associated:9 more:3 duality:6 becomes:1 operators:14 em2:3 corrected:1 reversible:1 particular:5 known:1 producing:1 must:2 room:1 recall:2 reviews:1 mt:4 obvious:2 ms:26 mr:1 following:10 dec:1 proof:27 claim:1 computers:1 give:6 bennett:1 implementations:1 states:3 minimum:17 something:1 degenerate:1 sense:1 conversely:1 occur:1 information:1 rather:1 verify:2 discussion:1 hom:2 att:1 maps:1 occasionally:1 pure:5 ordinary:1 obius:1 map:3 product:1 ovv:1 blocks:6 date:1 qecc:2 proceeds:1 whenever:1 consequently:5 summing:1 st:2 so:5 definitions:2 kbi:8 interpretation:1 help:1 22n:1 indeed:1 over:10 kbd:6 enumerators:48 paper:1 including:2 kbs:6 its:2 before:1 group:1 thank:2 how:2 chosen:1 mail:1 easier:1 eus:11 them:1 good:1 greater:3 combination:4 introduce:3 motivates:1 they:4 now:9 easily:3 inversion:1 equality:2 invariants:3 2y:3 orthonormal:3 each:5 2n:3 subset:5 another:1 weight:13 ee:1 related:3 quantum:39 relates:1 ev:5 matrix:1 space:2 since:2 crucial:1 denotes:1 hill:1 print:3 nontrivially:1 suffices:2 correct:2 shows:1 theory:6 contain:2 given:2 quite:1 manifestly:3 complicated:1 york:1 e1:13 e2:11 definition:8 could:1 omit:1 programming:3 nonnegative:1 turn:1 impure:1 place:1 onto:1 first:7 xn:4 encoding:5 powerful:1 number:2 rank:3 restrict:1 construct:2 directly:2 carry:1 precisely:2 size:11 1s:10 necessarily:1 1t:2 similarly:7 introduction:2 least:7 their:2 assumption:1 normalization:1 statement:1 final:1 speaking:1 gives:2 relationship:2 somewhat:1 alphabets:1 than:6 coefficients:1 clarifying:1 distance:17 holland:1 namely:1 ranging:3 correction:1 randomly:1 talking:1 need:4 cumbersome:1 element:1 clearly:9 mountain:1 constructions:2 convenient:1 note:5 instance:2 k1:2 absorbed:2 indexed:1 unless:2 extending:1 connected:2 encodes:1 pair:1 tensor:1 observation:1 typeset:1 nondegenerate:1 occasion:1 fact:6 quantity:1 shor:15 show:3 random:3 spaces:2 analogue:1 d2:15 fifth:1 d1:9 based:1 writes:1 distributed:1 state:2 lemma:2 only:14 explicitly:1 em1:2 factor:1 erasure:2 dk:4 notation:1 di:4 between:5 expectation:1 murray:1 closely:1 dy:5 combinations:1 applying:1 arxiv:1 acknowledgments:1 mapped:1 through:2 fixed:1 set:3 exists:2 bounds:2 writable:1 see:5 result:6 discussions:1 inequalities:1 ways:1 definite:1 written:1 hopefully:1 invariant:4 conditions:1 terms:4 extend:3 nature:2 qubits:7 complement:1 attention:1 wi:3 wt:5 outer:1 holds:2 both:2 σi:3 σn:1 many:1 equal:2 σz:1 σy:1 σx:1 variance:1 qubit:4 com:1 otherwise:2 point:1 simple:2 dimensional:2 simply:1 polynomial:1 moreover:3 throughout:1 erased:2 transformations:1 basis:3 equivalent:2 been:2 defined:5 much:3 combined:2 basic:3 ph:4 define:8 corresponding:1 quantities:2 concerning:1 subspace:2 essentially:1 observe:2 quick:1 c1:7 denote:1 those:1 applied:2 semidefinite:1 will:12 while:2 suppose:3 applies:1 unitary:13 laflamme:15 vi:5 thus:8 concatenation:2 vn:3 vs:15 vt:5 vv:13 ave:1 binary:3 macwilliams:6 same:2 any:18 quant:4 proved:1 physical:1 used:2 v1:5 v2:1 uses:1 expand:1 recent:1 no:1 well:3 machinery:1 dimension:7 just:2 less:1 being:1 generally:1 using:4 facts:1 yet:1 alternate:1 character:1 extends:1 inner:2 easy:1 theorem:31 remaining:1 enumerator:9 depends:1 lanl:3 confined:1 immediately:3 ams:1 correcting:10 like:2 semi:1 lost:1 sizes:1 follows:9 specific:1 benefit:1 arbitrary:1 terminology:1 old:1 classical:2 some:5 strongest:1 specified:3 curious:1 happens:1 2d:1 fourth:1 everything:2 does:2 refer:1 bd:5 shadow:4 problems:1 bn:2 bi:6 bt:3 bu:1 bs:29 hilbert:3 simpler:6 about:4 usa:1 extension:1 most:2 freedom:2 assertion:2 o:4 distinct:1 carries:1 act:1 introduced:1 slightly:1 block:9 op:7 em:1 into:2 bound:3 hermitian:2 references:1 operator:5 additional:1 strictly:1 there:5 transform:3 decode:3 low:1 way:1 analyze:1 was:1 north:1 form:2 concatenated:3 m2:68 but:5 construction:1 larger:1 encoded:1 compute:1 supp:8 wish:1 up:2 us:27 below:3 ui:5 ud:3 problem:2 called:1 ab:1 constant:2 ad:10 ai:11 certain:1 abstract:1 general:2 eu:4 examine:1 proves:2 au:2 identities:3 eric:8 defines:1 again:1 nj:1 codes:30 nonetheless:1 rains:10 when:8 other:1 nr:1 ns:7 nt:3 conclusion:1 elements:1 photon:2 uniformly:3 polynomials:3 helpful:2 helping:1 allowing:1 implies:2 algorithm:5 assume:3 rs:2 n1:2 n2:2
|
quant-ph9612016.txt |@word lagrangian:11 entropy:87 whose:2 calculate:13 under:2 rise:1 p0:1 affect:1 bringing:1 school:3 solution:4 unrelated:1 approximation:1 second:2 rigorous:2 implemented:1 even:2 revolves:2 above:3 new:10 increasing:2 coefficient:3 κm:1 evolving:2 evaluating:1 κe:2 equals:2 here:10 asymmetry:2 represented:1 path:5 κs:1 obtained:10 study:3 completely:1 subdynamics:1 adopting:2 stipulated:1 spacetime:4 attractor:1 elaborated:1 plenum:2 highly:2 hindsight:1 total:3 propagators:2 unit:3 plot:2 would:1 negative:1 call:1 therefore:3 m2:6 type:1 until:3 brings:1 curvature:1 tying:1 hole:4 must:3 me:1 md:1 ma:1 work:18 temperatures:4 concepts:2 example:9 impose:1 indicated:1 give:9 caution:1 want:1 hoc:6 provide:1 feature:1 recovers:1 how:8 answer:1 sato:1 description:2 thermodynamic:1 oscillators:10 earlier:8 lay:1 constants:4 bekenstein:4 effective:3 davies:2 decreasing:1 acknowledges:1 order:10 grabert:3 vanderlinde:1 zeh:3 zel:1 xi:16 london:1 thesis:3 satisfies:1 integrands:1 before:2 fiz:2 highlights:1 fix:2 writing:4 hakim:1 differently:1 easier:1 versus:3 eventually:1 them:2 effects:2 they:9 represents:1 reasonably:1 each:2 d40:1 d45:1 mean:2 financial:1 evolve:2 series:2 displacement:1 extract:1 dewitt:1 particles:5 re:3 independence:1 foundation:3 linear:4 grangian:1 little:1 free:6 standard:3 lnew:2 recovering:1 created:2 starts:1 ds2:1 decohering:1 isn:1 δij:1 ise:1 primary:1 another:1 similarly:2 approximately:1 needed:1 master:2 too:1 eqn:3 leggett:3 discussion:5 keldysh:2 roles:2 approximations:1 rate:1 preparation:1 matter:1 e2iφ:1 enables:1 rewrite:1 boston:1 mind:1 quantising:1 seen:3 giovanni:2 strength:2 subscripts:1 2εn:1 shall:3 object:1 viscosity:1 simplify:3 jept:1 steinhardt:1 phase:9 don:2 calculated:11 principle:1 sum:11 probe:1 solutions:4 substituting:2 enjoyed:1 coefficients:16 integrate:1 borrowed:1 do:4 dk:1 de:14 foremost:1 dx:11 despite:1 dt:2 du:3 ds:14 dq:9 ˆk:3 fields:9 habib:2 depends:4 result:19 fail:1 incorporating:1 clarifies:1 pavon:3 simplest:3 conceptual:1 d52:1 d53:2 approach:7 terms:14 nature:4 weak:3 however:7 vernon:4 harvard:1 suggested:3 cos:52 cot:2 uncertainty:20 variance:1 contribution:4 confronted:1 inflaton:2 minimises:1 minimised:2 κt:2 conference:1 basis:6 minisuperspace:1 three:2 been:11 quickly:2 much:1 frw:1 interest:2 basic:1 expected:7 deeper:2 quantities:7 iµ:1 coherent:11 applied:2 tanh:5 remaining:1 aim:1 suppose:10 aij:13 leaves:1 procedure:1 a21:1 a22:27 iz:4 im:80 interacts:2 hong:2 things:2 make:4 quant:3 split:1 dimensionless:2 grows:1 independent:8 numerical:2 monotonic:1 hand:2 supposing:1 joos:3 changes:1 academic:1 just:8 thanks:1 previous:9 adding:1 hao:1 had:2 prokopec:3 weiss:1 spread:1 board:1 iθ:2 iκ:3 bakshi:1 possible:1 possibly:1 background:2 replace:1 appearing:1 workshop:1 specific:2 steps:1 arbitrary:6 mahanthappa:1 ferreira:1 fourth:2 normal:1 umd:1 asking:2 kandrup:4 slin:14 super:2 properties:3 dˆ:8 o:27 plus:1 primitive:1 markovian:2 obtaining:2 bath:23 down:1 koul:2 sov:1 methods:1 vafa:1 support:2 initial:17 approximate:1 class:2 width:5 anderson:1 way:7 was:19 irreversibility:1 form:11 becoming:2 differences:1 encodes:1 true:3 absent:1 inside:1 maximum:1 tell:1 lindenberg:1 b1:11 proved:1 moore:1 lowering:1 abstract:1 exist:4 dζ:59 perez:1 adelaide:4 no:8 wavefunction:1 generally:2 ne:1 schwinger:2 ny:2 setting:2 role:1 papers:1 picture:1 a11:30 a12:20 models:5 ξr:2 ξi:3 invested:1 dissipation:16 regime:4 dω:4 assume:2 together:4 time:40 observables:2 concept:1 stressed:1 particular:7 brownian:6 leads:3 certainly:1 depend:2 april:1 environment:33 finally:3 sorkin:2 division:2 advantage:1 zhang:9 frequencies:2 choice:2 exact:2 swapping:1 level:1 turns:4 leave:6 solved:1 upper:1 mn:1 findings:1 spectral:5 axes:3 realizing:1 shares:1 international:1 sidorov:2 annalen:1 prescriptions:2 climbs:2 understanding:1 groups:1 address:3 along:1 change:6 noticeable:1 studied:2 usually:2 hospitality:1 noticeably:1 studies:1 useful:5 f2:5 positive:1 explicitly:3 renormalisation:1 pont:1 australian:1 theoretical:4 today:1 introducing:1 apparent:2 ruffini:1 appendix:4 cases:6 originally:1 oscillator:31 χxi:1 fock:2 values:4 novikov:1 following:12 making:2 claim:1 figure:6 zaldarriaga:2 confused:1 dxi:5 counting:1 conversely:1 s2:3 s1:3 write:17 pure:4 parameter:11 may:1 max:8 applications:1 natural:3 sectors:1 ss:1 explicit:2 su:3 cosmology:8 sh:20 so:40 representation:7 sa:1 se:4 ρred:2 noteworthy:1 indeed:1 pointed:2 raised:1 years:1 stability:1 course:2 statistical:13 argued:1 group:1 interesting:1 2zi:1 forms:1 mail:3 main:1 non:3 matches:1 evolution:6 introduce:1 nov:1 now:23 term:15 realistic:1 individually:1 square:1 significantly:1 kang:2 gaussian:7 owing:1 ew:1 er:1 shown:7 space:7 squared:1 cancels:1 increase:7 investigation:1 blh:2 dominate:2 shows:4 after:1 theory:10 divergence:1 quite:2 matacz:10 complicated:1 chen:1 e1:1 derivation:3 language:5 transition:1 motion:12 turn:4 place:1 view:1 first:13 origin:6 simplifies:1 variables:4 xx:3 simplified:1 directly:3 open:15 angular:1 given:6 necessarily:3 1z:1 unruh:2 1d:1 white:7 structures:1 gives:10 eliminates:1 x2:10 x0:9 x1:6 than:4 disequilibrium:1 third:1 require:1 ambegaokar:1 were:1 generality:1 ann:2 argument:1 say:1 any:3 subsystems:3 ξxi:1 note:9 take:3 formulas:1 begin:1 altered:1 trace:1 investigations:1 gunzig:1 clearer:1 analytically:1 inserted:1 considered:4 average:1 later:8 feynman:5 quantity:2 show:6 notations:1 frolov:1 tend:4 ground:3 aφ:1 state:40 analytic:2 only:12 going:1 black:4 over:7 viewpoint:1 get:3 simplistic:1 cannot:1 reveal:1 summary:2 predicted:1 discussing:1 ignored:1 physically:1 relative:2 college:1 uncorrelated:1 caldeira:4 kˆ:3 ways:1 subsequent:1 review:4 functionals:2 enough:1 between:5 justified:1 betwen:1 jr:6 jetp:1 come:1 σi:2 many:2 expression:3 σu:3 among:1 grants:1 constant:16 considering:2 west:1 computing:1 arxiv:1 damping:3 fig:2 6c:1 formed:1 andrew:1 bmp:2 case:22 eis:1 variances:1 squeezed:29 conformal:1 strominger:1 coupled:10 metric:1 couples:1 technology:1 different:4 develop:1 etc:2 paz:11 same:11 ya:1 inquiry:1 constructed:2 singapore:3 modes:1 without:1 solve:3 comes:1 components:3 model:1 ck:6 being:10 when:9 rest:1 ch:13 aspect:1 speed:1 blow:1 photons:1 conclude:2 interested:2 treatment:1 eigenstate:1 real:3 b59:1 easily:3 decomposed:1 early:5 inflation:3 vacuum:13 using:29 mod:2 brandenberger:2 particle:15 agreement:1 121a:1 either:2 integrals:7 reduced:17 qn2:1 competition:1 2ξi:1 nonzero:1 provided:2 eiε:1 confirm:2 critical:1 expressing:1 bessel:1 refer:2 scientific:3 power:1 problems:3 equivalent:6 refers:2 tanh2:3 comparison:1 central:1 discussed:4 practical:1 oz:1 act:1 mixed:1 2k:4 cambridge:2 numerically:4 variable:2 references:1 determine:1 elementary:1 lastly:1 theoretically:1 schramm:2 area:1 assumed:4 strictly:2 there:9 start:4 cosine:2 low:4 combined:1 regard:1 bombelli:2 sophisticated:1 dissipative:2 applying:2 quantitatively:1 ωn:1 agree:2 regimes:1 strongly:2 ad:6 certain:2 describe:2 am:1 general:10 au:3 κc2:2 graining:16 again:6 completeness:1 graduate:1 field:41 valid:2 mathematics:2 massless:2 briefly:1 separate:1 bilinearly:2 deriving:1 a2:7 recognise:1 serious:1 a9:1 a8:1 d24:1 d26:1 mass:7 adam:1 decoherence:6 2mω:1 starting:1 original:1 consider:11 groundwork:1 scalar:7 follow:3 expressions:8 content:1 albrecht:2 tr:3 kη:1 spain:1 th:1 ti:35 stochastic:3 subtleties:1 b180:1 amplitudes:1 hibbs:1 returning:1 very:5 morais:1 difference:7 condition:3 treating:1 illustrated:2 hamiltonian:3 list:1 large:11 small:9 b24:2 b23:1 b22:6 zero:15 design:1 further:5 calzetta:4 bilinear:2 what:6 nonlinear:1 brackets:2 section:6 brief:2 method:1 full:1 behaviour:2 relaxation:2 strong:1 equations:7 allows:2 amount:1 extremes:1 action:4 via:2 followed:1 maths:1 commonalities:1 establish:1 readily:1 conventional:1 proceed:2 contains:2 comparing:1 nucl:1 sitter:14 taken:3 more:15 flat:1 knows:1 operators:1 varying:1 known:2 evolves:4 science:2 equation:11 remain:1 dec:1 spontaneous:2 history:2 f1:4 compare:4 cosmological:2 cosmic:1 states:11 minimum:1 numbers:1 sense:1 information:8 needs:1 rather:2 csc:1 oye:1 explains:1 simplicity:1 inflationary:4 derived:4 short:2 developed:1 indistinguishable:1 thermal:9 paper:7 through:2 committee:1 existence:1 avenue:1 its:22 rapidly:1 solving:6 scully:1 fruitful:1 late:12 absence:2 systems:14 might:2 yi:1 good:1 motivated:1 transcribing:1 framework:2 oxford:2 yu:3 2t:13 2u:1 2v:1 2r:6 always:6 2z:17 2d:1 2e:4 inequality:2 2a:3 2c:17 found:7 2i:4 characterized:2 referred:1 generation:6 energy:1 reduce:1 expect:3 quantum:42 really:1 dominates:2 ωmax:4 since:17 research:1 acting:1 hill:1 denoted:1 issue:2 difficulty:1 reason:2 ask:1 asi:1 beginning:1 generate:1 definition:3 pairs:1 conformally:1 exponentially:3 consequence:1 probability:1 relate:1 number:5 done:7 construct:1 differ:2 perturbation:1 temperature:24 srednicki:1 introduction:2 leading:6 least:3 assumption:1 calculations:4 dt2:1 smoothed:1 anastopoulos:1 park:1 part:1 jordan:1 focusing:1 translation:1 peaked:1 2f2:1 2f1:2 determines:1 gotten:1 determined:4 toward:5 ijmpa:1 paths:1 kˆ2:5 depending:1 internal:1 generalized:1 finding:1 added:1 measures:5 most:3 plan:1 nothing:1 measured:3 kb:1 clear:2 unreasonable:1 physica:1 exp:23 grishchuk:2 physics:8 sector:1 relation:5 carefully:1 find:7 m50:1 parameters:2 nonlocally:1 iem:1 factor:1 dominant:1 notation:5 dependent:7 zurek:8 generalizable:1 nonequilibrium:2 closely:1 combinations:3 during:1 coth:14 continuum:1 ohmic:7 investigate:4 dovich:1 common:3 approaching:1 set:7 plausible:1 see:14 sec:6 descriptions:1 close:2 gravitation:1 fang:1 smallest:1 various:5 eksp:2 conditions:13 recently:2 initially:7 ρsys:3 diminution:1 both:10 last:8 improves:1 context:2 arbitrarily:1 point:5 simple:4 lagrangians:1 semiclassical:1 raval:1 ensures:1 pq:1 described:7 damp:1 due:2 a212:3 dropping:2 coarse:16 collected:1 ph:4 lett:16 mercader:1 modelling:1 neumann:3 σcl:4 understand:1 ctp:2 2ie:1 2ib:1 p2:2 attractors:1 intriguing:1 look:1 solid:1 reliable:1 while:10 replaced:1 behavior:1 couplings:2 unitary:1 von:3 itself:3 lengths:2 i22:4 ωn2:1 stimulated:2 higher:2 used:10 comprehensive:1 purpose:2 recent:3 lower:1 task:1 analysis:2 2a11:1 belgium:1 questions:1 world:3 spatially:1 readers:1 carat:2 chou:1 sydney:2 solvable:3 transformation:2 australia:2 evaluate:2 appendices:1 emergence:1 formal:1 rotate:2 follows:6 yields:1 mcgraw:1 mathematical:1 often:1 spring:1 creation:10 some:21 b4:13 examples:4 b2:9 b3:5 scale:3 describing:1 though:2 integration:5 per:1 eliminate:3 tends:1 prog:1 proc:1 minimal:1 redoing:1 s12:2 bi:5 step:1 plots:1 relating:1 dictated:1 hilbert:1 tracing:1 2iφ:2 cutoff:4 into:12 within:1 integral:11 proportional:1 ellipse:3 nsw:1 uncertainties:1 statistics:2 u1:10 u2:12 bosons:2 sections:1 propagator:6 kunstatter:1 elsewhere:1 governs:1 registered:2 delta:5 characteristic:1 up:4 us:6 fluctuations:11 similar:3 called:4 entropies:2 associated:1 defined:11 decreases:1 influence:16 doesn:1 single:1 formalism:7 defines:1 paradox:2 amounts:1 application:2 priori:1 department:3 draw:1 elements:1 calculating:8 nonclassical:1 meaning:2 kz:2 sides:1 structure:1 vice:1 i11:4 i12:5 equivalently:1 implied:1 requires:1 having:1 once:1 gr:2 results:18 existing:1 gg:2 eds:3 houches:1 edu:2 go:1 contributions:1 issues:4 anglin:3 squeezing:12 excluded:1 maryland:3 include:1 random:3 g2:2 g1:2 implicitly:2 wave:1 matrices:3 entire:2 knight:1 hartle:2 optics:1 noted:1 smaller:1 zh:2 zi:61 sin2:3 l2u:2 l2v:2 dynamics:4 index:1 vakkuri:2 expressed:5 justification:1 led:1 lee:2 degree:1 ihβ:1 respectively:4 sint:4 ihα:1 les:1 others:3 consideration:2 sine:1 z2:1 deduced:1 giovannini:1 1f1:1 suggests:1 resulting:1 rdm:2 climb:1 makes:1 composed:2 examining:1 danger:1 integrations:1 addressed:1 decrease:1 apply:2 standing:1 use:13 asymptotic:2 usa:1 next:3 process:1 depicted:1 formally:1 started:1 becomes:7 4ac:2 high:22 account:1 ρe:4 integrating:5 ρr:4 obvious:1 calculation:4 depiction:1 something:1 triangle:1 zeldovich:1 commutable:1 holds:1 varies:1 frontiers:1 sin:31 greatly:1 physical:8 xqn:1 correspond:1 gravitons:1 allow:2 ingold:2 divided:2 wigner:4 produced:2 including:2 deducing:1 bunch:1 la:1 ln:19 primordial:1 choose:2 derivative:1 a97:1 a90:1 greater:1 material:2 rotation:3 verifying:1 university:9 l2:3 mode:9 disregard:1 accompanied:1 homogeneous:1 gasperini:3 related:3 inverted:9 operator:4 decays:1 static:15 measure:6 our:24 special:2 out:13 matrix:31 borderline:1 vch:1 rep:3 rev:46 math:2 christensen:1 approached:1 diagonal:4 approaches:6 york:3 kobes:1 hubble:1 interaction:3 could:5 times:16 length:3 derivations:1 hence:6 teor:2 facilitate:1 intuitively:1 precisely:1 πh:1 behaves:1 system:62 relations:3 their:7 fermions:1 final:2 vigorous:1 exactly:2 mukhanov:3 penrose:1 submitted:1 halliwell:5 fluctuation:2 unchanged:2 discussions:2 thorne:1 need:8 apparently:1 minimally:2 zf2:2 able:2 gravity:3 decomposing:1 ωeff:1 detector:3 subject:1 linde:1 lectures:1 unless:1 centre:1 rearrange:1 propagate:1 definitions:3 intrinsic:2 why:2 talk:1 veneziano:1 fact:5 parker:3 rotating:1 99b:1 trivial:1 agrees:2 sh2:5 based:3 should:5 bases:1 isham:1 local:3 equilibrium:4 means:4 familiar:1 overall:1 bear:1 ones:1 words:1 kong:1 qq:3 qp:1 processes:2 qu:2 densities:1 qv:1 differential:1 grav:2 qc:2 hydrodynamic:1 contain:1 qi:25 qk:1 qn:2 predictive:1 national:1 correlations:1 hη:1 closer:1 interacting:3 diverge:1 written:4 identification:1 closed:5 boundary:4 comparable:1 importance:2 emitted:1 key:1 limits:4 taking:4 equal:5 chosen:2 otherwise:1 unitarily:1 relevant:3 cl:4 cc:1 harmonic:7 coordinates:4 ct:9 romero:1 treat:1 hawking:2 define:3 arises:1 corresponding:1 route:1 coherence:10 essentially:2 angles:2 c2:22 present:3 c4:2 harder:1 value:5 choices:2 will:23 rename:1 vi:1 vj:1 thus:5 surface:2 nardone:1 vs:1 generic:1 radiation:2 cross:8 parts:2 finite:7 4ct:1 upon:1 effect:3 v1:5 v2:10 4ck:4 expand:1 off:3 acknowledgement:1 modeled:4 well:2 mathematische:1 english:1 firstly:1 position:5 usual:5 less:1 obtain:7 bogoliubov:11 preprint:1 adp:1 density:39 smith:1 guth:1 add:1 nato:1 dqi:10 checking:1 keski:2 increases:2 five:1 know:3 press:5 loss:3 displaced:1 necessary:2 lost:3 alternatively:1 become:2 works:2 page:1 classical:10 growth:1 choosing:2 neglecting:2 happens:1 lead:3 does:3 demonstrated:1 locate:1 noise:16 clarendon:1 although:5 imaginary:1 includes:1 simpler:1 about:6 2ct:3 universe:8 eqns:1 dependence:7 surge:1 important:4 2ck:1 introduced:3 own:1 h2:1 pergamon:1 functional:13 en:1 joyce:1 phy94:1 smoothing:1 inner:1 ed:4 function:25 but:13 hu:31 squeeze:9 made:1 whether:2 wish:4 smooth:1 frequency:17 limit:11 demonstrate:2 problem:1 mechanics:9 kruczenski:2 int:1 denote:2 interchanged:1 pis:1 functions:8 compared:2 variety:2 other:4 details:6 theor:1 conclusion:1 zhou:1 coupling:17 factors:2 persistent:1 4d:1
|
quant-ph9612017.txt |@word monte:1 partial:1 consider:6 reversibility:1 results:2 four:3 montr:4 computation:5 denotes:2 whose:2 simon:5 deterministic:2 editors:1 factoring:1 finally:2 helps:1 bqp:6 under:4 applied:1 random:3 string:6 advantage:1 orthogonal:8 very:2 reader:1 corollary:2 vegas:2 worst:4 difference:2 exact:7 høyer:1 randomness:1 hamiltonian:1 did:1 notes:1 having:1 solution:3 occurs:4 large:1 solved:7 pspace:1 small:1 optics:1 programme:1 upper:2 smaller:3 says:1 occurrence:1 deutsch:3 sign:4 jump:1 zero:4 preimages:1 valiant:1 7th:1 ruled:1 carlo:1 machines:4 belief:1 even:1 index:1 what:2 appear:4 giving:1 section:1 uniform:1 access:1 version:2 above:2 new:1 ever:1 bn:1 satisfy:1 notions:1 respectively:1 gilles:1 following:4 separation:2 address:1 concluding:1 strong:1 observing:1 z1:5 z2:5 obtained:1 divisor:1 shift:4 study:1 allows:2 odense:3 accomplished:1 pick:1 fourier:1 makes:2 merely:2 logical:1 apply:3 establish:1 use:1 would:5 prove:2 distinct:7 stated:1 therefore:4 centre:1 25th:1 today:1 more:4 tolerated:1 bennett:2 occurred:3 refrain:1 reversible:1 particular:2 known:5 foundations:2 cardinality:4 producing:4 springer:1 ibm:1 science:6 challenge:1 obvious:1 believed:1 making:1 dec:1 example:2 proof:5 claim:2 give:2 process:2 december:1 allowed:1 states:1 walsh:3 numbers:1 sense:3 made:1 occur:3 g2:10 information:2 g1:11 rather:1 holds:2 unlucky:1 how:1 answer:10 optimal:1 verlag:1 priori:1 brassard:6 inputs:2 product:1 rise:1 turing:4 after:6 mapping:1 produce:1 designed:1 data:7 compatibility:1 las:2 changes:1 natural:1 third:1 w2n:6 lemmas:1 register:13 yielding:2 element:4 provide:1 complexity:7 algorithms:6 order:5 exclusive:1 selman:1 interpretation:3 produces:1 over:1 paper:3 london:1 thesis:1 y1:3 existence:1 still:3 ieee:3 its:5 before:2 machine:1 group:5 zn2:4 personal:1 interesting:2 solving:1 better:4 ours:1 into:3 versus:1 queried:1 yk:2 yj:2 return:4 they:1 symposium:3 transversal:1 now:1 smoothness:1 structural:1 ebec:2 term:1 name:1 certainty:1 university:2 each:14 found:1 universit:3 mean:2 subset:1 weighted:2 significantly:2 challenged:1 related:1 society:1 extended:1 measure:3 quantum:40 our:8 event:7 out:2 canada:2 leave:1 shown:2 discrete:2 since:9 crucial:1 research:3 reformulate:1 seriously:1 conjectured:1 lecture:1 evaluation:1 correct:11 weaknesses:1 theory:7 little:1 vazirani:2 members:1 initialize:1 jozsa:3 perform:2 benioff:1 determining:1 could:2 computers:5 keep:1 turn:1 exponentially:1 eqp:1 hence:1 first:7 xj:3 xk:2 major:1 xi:8 probability:15 ville:1 bijection:1 number:1 oracles:2 done:1 directly:1 impossible:1 open:5 given:10 likely:2 needed:1 introduction:1 unknown:6 berthiaume:3 system:3 least:2 their:1 returns:4 bijections:1 efficiently:1 bits:2 final:3 store:1 gives:2 contains:1 exactly:5 proving:1 immediate:1 part:2 authors:1 x2:2 x1:2 than:14 specify:1 royal:1 unfortunately:1 require:1 second:8 project:1 classes:4 amplitude:2 outcome:1 result:2 fcar:1 logarithms:2 generality:1 modern:2 turned:1 bitwise:1 say:3 unlikely:1 need:1 any:16 complete:1 able:1 phase:1 note:5 instance:1 concerns:2 useless:1 so:4 strengths:1 gill:1 unless:1 though:1 probed:2 simplify:1 significant:2 reducible:1 coin:1 probabilistic:9 probes:1 sometimes:2 hg2:4 hg1:4 proceedings:5 mechanical:1 subgroup:12 physics:1 notion:3 dot:1 shor:4 supported:2 12n:3 discovered:1 find:3 knowledge:1 title:1 sˆ:16 jan:1 lemma:9 only:14 factor:1 bernstein:2 do:1 dk:2 notation:2 familiar:1 de:3 overall:1 cannot:2 applying:3 prime:2 qp:15 qu:2 denmark:1 arxiv:1 factorization:3 investigate:1 queries:2 through:1 fixed:2 view:1 guessing:1 requirement:2 set:4 computed:2 exists:5 physically:1 relativized:3 mentioned:1 computer:11 w2:2 y0:1 close:1 theoretic:2 concern:1 y2:2 probable:1 siam:4 please:1 state:3 iro:2 email:2 available:9 fˆ:5 nature:1 initially:1 confusion:1 however:4 here:2 times:2 distribution:1 essentially:1 annual:4 according:2 nserc:1 0n:1 finds:3 comes:1 otherwise:1 arbitrarily:2 among:1 co:1 groups:1 point:1 simple:1 hemaspaandra:1 ca:1 leeuwen:1 corresponds:3 simply:1 church:1 polynomial:26 moreover:1 conference:1 pp:10 abelian:2 basis:1 zpp:3 due:1 been:2 strategy:1 defined:1 secret:1 basic:1 expected:5 ph:1 define:3 imada:1 corresponding:1 retrospective:1 sufficient:1 campusvej:1 epartement:1 those:2 case:7 exponential:3 value:3 choices:1 will:4 while:1 suppose:1 error:6 evaluates:1 35th:2 inspired:1 h3c:1 vol:6 thus:1 3j7:1 ii:1 disjoint:1 different:1 verified:1 author:1 perhaps:1 make:1 clearly:2 member:7 quant:1 emphasize:1 finite:1 development:1 used:3 yi:6 again:2 counterparts:1 running:2 uses:1 subgroups:1 lower:1 cardinalities:1 try:1 well:3 subexponential:1 without:1 solve:5 weakest:1 answers:2 just:1 less:3 being:1 obtain:2 transforms:1 integer:5 facts:1 yet:1 captured:1 rapid:1 application:1 esprit:1 guaranteed:6 counted:1 belongs:1 cosets:1 theorem:7 input:1 occurring:1 take:1 easily:2 evaluate:1 possible:5 np:4 know:2 similarly:1 using:1 bit:8 projects:1 mod:1 loss:1 necessary:1 success:2 follows:8 bpp:13 steps:1 either:2 arbitrary:5 conclusion:1 because:4 classical:16 sequence:1 conditional:5 some:5 strongest:1 b1:1 peter:2 nonzero:18 provided:4 decision:8 shall:2 does:3 provides:1 prob:2 run:2 power:4 performed:1 equivalent:1 bi:1 step:7 references:1 hadamard:3 2n:26 bz:7 about:4 actual:1 carried:1 anything:2 most:1 completing:1 acm:1 compatible:13 ou:1 2k:1 other:1 equally:4 computational:2 communication:1 umontreal:1 bound:2 device:1 appropriate:1 promise:3 van:1 log:1 springerverlag:1 there:17 question:7 transform:8 long:2 editor:1 way:3 was:4 function:11 eal:4 form:1 but:4 hg:2 reset:2 coset:5 compute:5 calls:2 versions:1 whether:2 smooth:2 up:1 devices:1 below:2 tosses:1 demonstrate:2 problem:27 z42:1 partition:1 constant:4 computing:9 ai:1 recognize:1 abstract:2 measurement:1 proven:1 denote:8 eu:1 exist:1 journal:7 az:3 ni:1 functions:4 compared:1 no:8 whereas:1 when:4 field:1 setting:1 remarks:1 department:1 mathematics:1 you:1 realisable:1 nice:1 maximizes:1 elements:5 superposition:9 separate:2 models:1 sided:1 problems:5 a1:1 bounded:5 included:1 generalized:1 structure:1 factorized:1 algorithm:35 assume:6 values:6 statistical:1 required:2 zqp:6 original:1 parallelism:1 image:1 time:34 oracle:14 requires:1 avoid:1 once:1
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.