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quant-ph9906129.txt |@word saturating:1 interference:3 magnetic:3 desirable:1 four:6 entropy:2 consists:9 votes:1 calculate:3 γi:3 swap:22 under:6 worth:2 conjecture:1 rise:1 p1:2 every:5 affect:1 school:1 p4:2 suffices:11 solution:5 vector:35 enhance:1 force:1 29th:2 approximation:1 elegant:2 likely:3 perfect:1 implemented:1 machines:1 even:14 errors:105 organisms:1 specification:1 sj1:1 decoding:21 above:35 designing:1 resilient:2 new:17 increasing:1 consisting:5 coefficient:2 bi:5 notions:3 equals:1 here:29 refinement:1 protection:1 represented:2 path:27 obtained:6 rigorously:1 settles:1 sjl:1 permit:1 advantages:1 fourier:25 changes:1 divide:5 tensored:1 explained:3 plenum:1 replace:7 sloane:2 stern:1 total:3 p43:1 unit:4 solovay:5 would:15 inductive:1 motivate:1 chooses:1 roychowdhury:1 m1:23 therefore:12 m2:3 care:3 type:2 until:1 preserved:2 separated:1 tolerated:1 relax:1 successful:1 oscar:1 berlin:2 reversible:2 hold:6 preserving:3 must:13 kraus:3 springer:3 word:34 pursue:1 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quant-ph9907001.txt |@word operations:2 concept:1 eigen:2 produces:1 satisfied:1 indistinguishable:2 produced:1 clones:1 bellow:2 through:2 statistical:1 foundations:1 japan:1 fidelity:1 find:2 perfect:1 write:1 derive:1 depend:1 parameters:1 density:4 interesting:1 relativity:1 written:1 new:1 ekert:1 b1:1 does:1 anirban:1 lett:3 under:1 input:7 must:2 local:1 identical:3 acta:2 them:1 relation:2 pure:2 without:1 very:1 zurek:2 possible:1 divincenzo:1 yy:5 yx:2 yz:2 kamefuchi:1 mathematics:1 using:5 rotation:2 matrices:2 condition:4 represents:1 tokyo:1 imposed:1 semi:1 presented:1 arxiv:1 isotropy:1 wooters:2 vector:5 arbitrary:2 output:6 soc:1 macchiavello:1 schumacher:1 referred:1 employing:1 txz:6 ed:1 some:1 hillery:7 maximum:1 see:5 full:1 zx:2 cloning:19 entering:1 quantum:9 our:2 operation:5 acts:1 machines:1 out:11 provided:3 shown:3 network:1 factors:1 shimony:1 shall:1 rev:3 consequence:1 3t:1 symmetric:6 state:8 indian:1 between:4 isical:2 get:2 caves:1 conditions:2 quantities:1 shows:1 ρa0:8 after:1 recently:1 reproduced:2 nature:1 qubits:4 respectively:1 each:1 here:2 ρaj:1 paper:1 ρin:2 distinguish:1 along:1 equations:1 universally:1 bz:1 cerf:2 σj:1 about:1 derivation:1 barnum:1 constraint:3 institute:1 could:1 hence:1 contradiction:1 motivation:1 σz:4 σy:4 σx:4 positive:1 mixed:1 tyx:6 qubit:8 mz:12 whole:1 bloch:4 road:1 tyy:4 mechanics:4 buˇzek:12 tyz:6 into:1 corresponds:3 negative:1 dimensional:1 will:3 xx:3 xy:3 references:1 invariant:1 txy:9 txx:4 impossible:2 unit:2 forms:1 given:2 light:1 described:2 would:2 similarly:1 a0:20 unknown:3 xz:2 copies:2 specifically:1 hilbert:1 definiteness:1 reduction:1 been:2 way:2 4t2:1 ph:1 spaces:1 universal:7 qcm:1 zy:2 obtained:2 asymmetrically:1 tzz:6 controlled:1 both:2 asymmetric:4 thus:1 smolin:1 exactly:1 but:2 sort:1 optimality:2 related:1 loss:1 known:1 cloner:1 copy:1 themselves:1 cosθ:1 applied:1 distance:2 applying:1 pacs:1 fuchs:2 was:1 equation:9 bounds:1 reproduce:1 jozsa:1 values:3 acting:1 following:2 property:2 my:12 mx:12 gisin:2 bruß:2 real:3 ac:2 unitary:2 zz:1 generality:2 process:1 tzx:6 abstract:1 aj:2 india:1 non:2 states:9 single:6 physica:2 want:1 imperfect:1 technology:1 occur:1 result:1 different:1 ρout:17 angle:1 no:8 slovaca:2 s1:16 s0:16 when:2 σk:1 same:2 machine:11 valid:1 quant:1 take:1 copying:1 mixtures:3 optimal:8 tjk:3 independent:1 used:3 generates:1 trace:1 superluminal:2 rm:1 clone:1 mechanical:2 reach:1 prepared:1 a1:26 kar:1 connected:1 jul:1 letter:1 class:1 identity:1 matrix:3 independently:1 implies:1 imposes:2 corresponding:3 expression:1 locality:1 well:1 su:1 obviously:1 sj:2 maintain:1 so:4 time:1 calcutta:1 physics:1 original:1 signaling:9
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quant-ph9907002.txt |@word represent:3 measurements:2 consider:4 csic:1 vectorial:1 magnetic:45 varying:1 dynamic:1 results:11 gy:1 correo:1 gb:2 edu:1 expressions:1 contributions:1 reynaud:1 devoted:3 whose:5 feeding:1 calculate:1 zone:1 hussein:1 concerned:2 eˆ:5 should:3 rf:3 ıa:1 quasi:1 ie2:2 those:2 elliptic:1 under:9 analogous:2 presentation:2 broaden:1 montevideo:1 applied:1 supported:1 r12:1 orthogonal:13 far:1 frequencies:4 mg:2 wave:10 sons:1 every:1 figs:3 sensitivity:1 refractive:6 mixing:4 experimentally:1 difference:1 matrices:3 condition:2 splits:1 four:5 europhys:1 incoherent:4 level:58 did:1 positions:6 guo:1 solution:4 damped:1 large:7 solved:2 leninsky:1 progress:1 small:2 enhance:1 shows:4 inspection:1 setup:2 configurations:8 governing:2 upper:5 employing:1 compensated:1 occurrence:1 prediction:1 sign:1 approximation:1 rate:8 invention:1 enhancement:13 oder:1 qualitatively:1 dynamics:3 choices:1 situated:1 theory:2 spectral:2 established:1 transverse:8 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quant-ph9907003.txt |@word yamaguchi:1 limited:2 sci:1 consider:4 chain:6 represent:2 magnetic:1 splitting:1 four:6 scalar:1 computation:1 reson:6 row:1 increase:3 leung:3 irrelevant:1 refocus:2 finally:1 monotonically:1 device:1 under:9 analogous:1 through:1 applied:8 fax:1 returned:4 advantage:1 orthogonal:2 very:1 relatively:1 results:2 every:4 figs:1 decide:1 fall:1 experimentally:1 emphasized:1 matrices:3 condition:4 illustrated:1 exponential:2 suffices:1 proposals:1 large:4 phase:5 science:1 small:1 geminal:2 application:1 expanded:1 pulse:11 sign:2 approximation:1 elegant:1 likely:1 street:1 design:1 further:4 implemented:2 even:3 appear:1 giving:2 section:1 favour:1 expressed:1 networks:1 new:3 net:1 increasing:5 method:1 satisfy:2 evolving:1 simultaneously:2 ms:3 exchange:1 never:1 water:1 varian:2 them:1 illustration:2 relaxation:1 active:7 along:1 strong:1 imperfections:2 obtained:1 convert:1 institute:1 involved:2 study:1 larger:1 experience:1 leaving:1 simultaneous:7 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quant-ph9907004.txt |@word determinate:2 consider:1 just:1 indeed:1 both:1 satisfied:1 supposition:1 course:3 relation:1 statistical:1 go:1 follow:3 decisions:1 eigenstates:2 payoff:1 define:1 certainly:1 based:2 general:1 acknowledge:1 concerned:1 written:1 tp:1 writing:1 parts:1 only:3 setting:1 specify:1 version:1 under:1 mail:1 might:2 axiom:2 arguments:1 begins:1 non:4 notation:6 get:2 rules:7 between:1 possible:2 introduce:1 me:1 game:7 cannot:1 they:2 now:4 condition:2 eigenvalue:2 like:1 follows:1 university:1 arxiv:1 sum:1 either:2 eigenvalues:2 soc:1 assume:1 mean:1 requirement:2 set:2 often:1 classical:3 deutsch:3 national:2 proc:1 see:2 jos:2 result:5 measurement:4 quantum:13 laboratory:2 happen:1 eq:36 after:1 intended:1 even:3 shown:2 reducing:1 appear:2 spectrum:1 decision:7 since:3 assumed:2 re:2 state:9 does:3 rational:1 example:3 denoted:1 values:1 suggesting:1 gov:1 ref:2 correct:3 justification:3 recently:1 theory:13 lawrence:2 deduces:1 given:9 standard:4 surely:2 references:1 berkeley:2 article:1 along:1 meaningful:1 axioms:5 interpret:2 observable:1 about:1 central:1 derivation:2 could:2 but:6 equal:7 david:1 participating:1 games:2 done:1 act:1 hospitality:1 pivotal:1 makes:1 maker:2 origin:1 probable:1 equally:1 followed:1 lond:1 probability:9 ca:1 numerically:1 outcomes:1 because:1 simply:1 operator:3 moreover:1 precisely:1 establish:1 considers:1 utility:3 use:3 guest:1 would:6 measured:2 eqs:2 claiming:1 u1:5 system:1 been:1 u2:5 however:3 way:2 taken:2 preprint:2 ph:4 was:2 consistent:1 gives:1 corresponding:2 complete:1 definition:1 offered:5 jul:1 else:1 mysterious:1 part:2 understand:1 employed:1 x2:67 attempt:1 line:1 x1:70 true:2 those:1 case:3 made:2 wish:1 equation:5 work:1 reads:3 value:5 eigenstate:2 will:2 invoking:1 while:2 assumptions:1 suppose:1 supposed:1 amplitude:2 were:5 following:2 outcome:7 specialized:1 called:1 proof:6 san:2 do:2 abstract:1 thus:1 argument:2 denote:2 states:1 examine:2 examined:1 exist:2 rule:1 want:1 our:2 need:2 hereinafter:1 lbl:1 incorrect:1 zero:1 validity:1 rather:1 write:1 when:1 same:2 any:5 note:2 how:1 other:1 quant:4 take:1 department:1 lhs:4 more:1 sufficient:1 equations:2 used:2 superposition:2 may:1 rhs:2 who:1 june:1 hand:1 meaning:1 purpose:1 nothing:1 probabilistic:6 sides:1 recent:1 implies:1 consequences:1 acknowledgement:1 considered:2 required:2 together:1 original:1 perhaps:1 without:3 so:5 allow:1 usual:1 physics:1 furthermore:2 fact:3 justify:1
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quant-ph9907005.txt |@word consider:3 switched:1 results:2 leads:2 p01:1 p00:1 entropy:1 expressions:2 causes:1 devoted:1 subjected:2 deterministic:1 nonlocal:1 petersburg:1 stochastic:1 analogous:2 include:1 case:3 wave:3 lyapunov:1 formula:1 exact:1 condition:1 ωin:11 hamiltonian:1 turns:1 t2:2 solution:5 t1:3 large:1 vector:1 small:1 force:2 zi:1 zero:1 expressed:1 d3:5 goes:1 lifshitz:1 new:4 increasing:1 body:1 bifurcation:1 behaviour:3 objects:3 others:1 directions:1 consideration:1 equations:3 z1:7 change:1 z3:9 box:1 institute:1 allows:1 leaving:1 minsk:2 suggestion:1 published:1 action:1 resonance:1 f0:6 followed:1 total:1 asymptotic:1 probabilities:9 process:2 call:1 therefore:1 more:2 nauka:2 eiδ2:1 eiδ1:1 initial:3 berlin:1 bogdanov:3 known:2 eγ:1 high:1 springer:1 te:10 tokyo:1 equation:6 averaged:8 oscillator:4 values:2 following:7 control:1 f1:7 f2:7 give:1 predict:1 states:5 weighting:1 verlag:1 information:1 provide:1 csa:2 write:1 trieste:1 parameter:1 sin:5 δij:1 may:5 earlier:1 fi:2 fj:1 data:1 plank:1 constants:1 natural:2 description:2 st:5 emphasise:1 allow:1 representation:2 order:1 typical:1 developed:1 over:2 zel:1 paper:2 through:1 looks:1 mentioned:1 existence:1 satisfies:1 chemical:1 supplemented:1 chosen:1 solving:1 systems:6 lp:1 main:1 setting:1 them:2 belarus:2 ya:1 evolution:2 p10:1 framework:1 they:2 now:1 several:1 2p:3 2r:1 νe:1 2z3:1 found:2 2n:1 mean:1 homogeneous:1 reactions:2 differential:1 formulate:1 z12:2 energy:1 reduce:1 gaussian:1 frequency:2 quantum:11 our:2 witness:1 out:2 ru:2 shown:2 space:1 rep:1 dewitt:1 chaos:5 research:1 re:1 investigation:2 denoted:1 got:1 cause:1 ωout:4 theory:1 gardiner:1 formation:1 york:1 definition:1 derivation:1 transition:7 correctness:1 nonnegative:1 motion:2 turn:1 φout:3 first:1 already:1 features:1 representations:2 impossible:1 introduction:2 system:4 1d:2 exponents:1 gives:1 way:2 moscow:2 pnm:2 x2:2 specify:1 stc:1 see:1 final:2 determined:1 russia:3 randomly:2 constructions:1 convenient:2 k3:1 k2:1 k1:1 internal:1 forces:2 k4:1 performance:1 switching:2 formulas:1 vnm:2 z2:9 regular:4 but:1 z32:2 considered:1 ki:1 ks:1 proceedings:3 exp:2 physics:1 fact:1 walking:2 random:11 solutions:2 d6:2 d4:6 d5:2 d2:6 find:1 d1:5 multichannel:1 parameters:1 state:2 should:1 only:1 bases:1 coefficients:2 parabolic:1 local:1 do:1 above:1 get:1 ones:1 dz:1 international:2 dt:2 processes:5 arxiv:1 baz:1 dovich:1 analytical:1 requirement:1 correlations:1 namely:2 recently:1 subsequent:1 functionals:3 written:1 limit:6 approach:1 terms:1 matveev:1 come:1 distribution:5 cos:5 hψ:1 designations:1 expression:2 trajectories:1 point:1 simple:3 harmonic:3 dimensional:2 z4:2 conference:1 described:3 basis:1 trajectory:1 three:1 been:1 int:1 workshop:2 treat:1 interest:1 ph:1 pi:2 z42:1 obtained:3 generating:2 corresponding:2 external:2 func:1 qst:1 c2:4 c1:4 present:1 bifurcations:1 p2:3 p1:4 ǫi:1 value:1 while:5 suppose:2 procedure:2 chaotic:2 averaging:3 tions:1 non:1 im:1 fn:2 pastur:1 φin:6 different:1 italy:1 complex:2 quant:1 finite:3 φm:1 φn:1 independent:1 calculation:1 used:3 numerical:1 hand:1 moment:1 levels:1 task:1 off:1 p11:1 peculiarities:1 without:1 lim:3 model:1 chemistry:1 arising:1 moments:1 obtain:1 morette:1 scattering:4 previous:1 sciences:1 nonrelativistic:1 other:1 treatment:1 guarantees:1 realisations:1 designate:1 iβ:1 formal:3 loss:1 necessary:2 follows:1 specific:1 arbitrary:2 rearrangement:2 works:2 stationary:8 replacement:2 because:1 methods:3 classical:5 conditional:1 some:1 trends:2 describing:1 integration:1 cnm:5 elworthy:1 noise:1 power:2 qnm:9 after:2 o:1 act:1 introduced:1 perelomov:1 dξ1:1 dξ3:1 dξ2:1 functional:3 down:1 hermitian:1 operator:1 reducing:1 realisation:1 there:3 approximate:1 quadratic:1 handbook:1 lot:1 was:2 function:8 creation:1 form:4 enough:1 jul:1 wnm:8 construction:1 hn:2 true:1 grigoryan:1 d21:2 decays:1 exploration:1 demonstrate:1 problem:6 mechanics:1 constant:1 computing:1 defined:5 h00:1 denote:1 exist:1 constructed:1 functions:9 nm:6 interested:1 special:1 briefly:1 symbol:1 polynomials:1 variable:2 2d1:1 2d3:1 assume:1 d23:2 d22:2 hnm:1 d24:2 gredeskul:1 time:5 n3:1 having:2
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quant-ph9907006.txt |@word limited:3 equiprobable:1 1mhz:2 illustrated:1 zappa:1 avalanche:1 entropy:3 computation:1 consider:1 simon:1 deterministic:1 quasi:1 under:1 case:1 supported:1 very:2 frequencies:1 springer:3 choice:2 affect:1 difference:1 randomness:3 did:1 notes:2 standards:1 large:1 coincidences:1 small:6 seminumerical:1 glued:1 pulse:4 approximation:1 rate:3 masson:1 further:1 port:1 even:1 annals:1 goes:1 acknowledgments:1 counters:2 quenched:1 led:4 path:2 strong:1 box:1 100khz:1 olivier:1 changes:1 involves:1 technique:1 explained:2 decrease:1 counts:1 quenching:1 apd:1 confidence:1 usb:1 would:1 monomode:3 few:1 therefore:1 criteria:1 type:1 today:1 andr:1 separated:1 introducing:1 sharing:1 outputs:3 tested:1 particular:2 account:1 room:1 mm:2 science:2 work:2 example:2 point:1 bureau:1 figure:3 process:6 numbers:6 serial:1 counting:1 verlag:2 requirements:1 goal:1 fortunately:2 hugo:1 delay:2 adjacent:4 brassard:1 after:7 diagram:1 xilinx:1 fits:1 minimizes:1 realized:1 short:1 third:1 counter:3 rather:1 si:1 so:1 decreasing:1 order:3 pulsed:1 qrng:1 correlation:7 indeed:1 meter:1 stability:1 thermal:4 paper:1 pulses:3 statistical:3 owens:1 its:2 before:1 perfect:3 group:1 wallace:1 cryptology:2 window:2 offers:1 systems:4 quant:1 umontreal:1 photodiodes:1 maximal:1 good:1 greater:2 they:3 discuss:1 february:1 university:1 crypto:2 labeling:1 inequality:1 mode:2 found:1 mean:3 generation:3 series:1 eg:1 hard:1 frequency:1 geiger:1 quantum:8 our:3 operation:1 prototypes:1 since:2 rev:1 issue:1 fiber:2 maurer:2 theory:1 base:1 detecting:1 generate:2 applications:1 optics:2 computers:1 programming:1 times:2 caption:1 circuit:1 hence:2 first:1 jennewein:1 major:1 xi:2 features:1 probability:3 xc:1 variables:2 number:13 reaches:1 long:2 impossible:1 size:1 given:1 temperature:2 behaves:1 approximately:2 their:1 cooling:1 perturbations:2 scheme:2 bits:11 testing:1 lot:1 geneva:2 took:1 tapster:1 optical:5 eliminated:2 than:3 intrinsically:1 achieves:1 unige:1 unfortunately:1 zero:1 rarity:1 project:1 individual:1 impinge:1 troublesome:1 sac:1 fluctuation:1 modern:1 raw:2 weinfurter:1 any:2 paths:2 mostly:1 thoroughly:1 able:1 complexity:1 note:1 ideal:2 take:1 algorithms:1 detector:9 lectures:2 play:1 though:1 measures:1 most:1 but:4 significant:1 successive:2 device:1 intrinsic:1 laurent:1 windows:1 detectors:1 points:1 principle:1 agnew:1 physics:2 fact:1 bell:1 selection:1 phenomenon:2 violation:1 random:34 cheap:2 rejecting:1 impact:1 fibre:2 based:5 distributed:2 state:1 should:1 only:6 generators:4 employed:2 achieve:1 do:1 above:1 cryptography:2 get:1 between:8 truly:1 recombining:1 procedures:2 reveal:2 processes:1 arxiv:1 switzerland:1 vincent:1 voltage:2 art:1 ecuyer:2 physically:1 national:1 correlations:2 detection:6 edition:1 computer:4 procedings:1 techniques:1 detect:3 away:1 µs:1 outside:1 various:1 simplest:1 conditions:1 arrival:3 wo:1 weak:1 however:2 efficiency:6 key:1 interface:1 both:1 sensitive:1 connection:1 contribution:1 disappears:1 esprit:1 supply:1 simple:2 effective:1 ca:1 coincidence:1 pct:1 cancel:1 fibres:1 described:2 second:1 due:2 montecarlo:1 much:2 interest:1 basic:1 ph:1 prototype:2 hardly:1 universal:1 digits:1 corresponding:3 hildebrandt:1 sufficient:1 photon:12 zeilinger:1 understand:1 external:2 present:2 applied:5 engineering:1 value:2 will:1 behavior:1 irrespective:1 procedure:3 variabilities:1 coupled:2 vol:7 von:2 thus:1 bias:2 iro:1 around:1 binary:1 different:1 fibers:1 patent:1 indistinguishable:1 same:4 potentially:2 schematic:1 knuth:1 events:2 breakdown:1 used:2 keys:1 numerical:3 effect:2 makes:1 locality:1 well:2 without:1 sets:1 bellow:1 less:1 being:1 when:1 obtain:2 sources:1 ch:1 thanks:1 immediately:2 speed:1 electronically:1 nicolas:1 generator:17 photons:3 passively:1 source:2 lett:1 easy:2 apart:2 build:1 tests:2 increased:1 coron:1 advances:1 increases:1 using:2 bit:3 mod:1 necessary:1 like:3 detections:2 output:5 security:1 reduced:2 mathematical:1 www:2 because:2 neumann:2 sequence:4 some:2 dead:3 proper:1 gradually:1 affects:1 avoid:1 extensively:1 per:2 critical:2 demonstrated:1 noise:3 run:1 power:1 journal:3 use:4 wesley:1 although:1 plug:1 beamsplitter:3 into:2 three:1 appropriate:1 references:1 determine:1 einstein:1 rely:1 statistics:3 stefanov:1 support:1 there:1 fast:2 strict:1 low:1 way:2 analyze:1 was:1 fpga:1 enough:1 jul:1 weihs:1 volume:1 gain:1 true:3 applying:1 circuits:1 variations:1 below:2 autocorrelation:1 distribution:2 more:3 gisin:1 mechanics:1 fulfills:1 addison:1 defined:1 abstract:1 measure:1 influence:2 proven:1 peres:2 ripple:1 single:5 simulations:2 partly:1 check:2 physical:4 nm:1 no:10 generally:2 other:2 detected:1 test:3 mathematics:1 ns:5 conclusion:1 deviation:1 distance:1 multimode:3 cryptographic:2 zbinden:1 afterpulses:1 coupling:1 normally:1 pseudo:2 together:1 time:9 original:1
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quant-ph9907007.txt |@word represent:1 logarithms:1 concept:1 customary:1 consider:15 remarkable:1 switched:6 rev:3 desirable:1 results:3 existing:1 roy:3 commute:1 overlap:1 computation:46 foundations:2 consists:1 particularly:1 contributions:1 issues:1 row:4 whose:2 certainly:3 simon:2 ceases:2 unblocked:1 vs:4 ts:5 factoring:2 finally:4 those:3 th:2 under:21 arranged:1 include:5 tc:2 apparatus:3 merchant:1 applied:1 conjecture:1 string:2 returning:1 very:3 desired:1 continues:2 idealised:1 suggesting:1 novel:1 every:2 condition:4 abandoned:1 generalised:4 entire:2 perceived:1 gov:3 did:3 turns:1 list:2 solution:1 large:7 discrete:1 vector:6 subscript:1 small:11 proof:4 configurations:2 measuring:2 abbreviated:1 des:1 decompositions:1 deutsch:4 det:1 consistent:5 sin2:1 past:1 imply:4 design:1 insertion:9 pass:1 further:5 implemented:1 columns:1 goes:1 even:5 will:23 what:5 richard:1 28th:1 giving:3 sum:9 selected:2 while:3 expressed:1 henceforth:1 allowing:2 version:1 subspaces:14 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quant-ph9907013.txt |@word barone:1 interference:5 magnetic:2 leads:1 eds:2 amplification:1 depend:1 present:4 include:2 advantage:2 orthogonal:1 very:8 frequencies:3 wave:11 affect:1 difference:7 treating:1 splitter:3 large:1 small:3 optics:3 milano:1 pulse:1 approximation:1 second:4 insertion:1 substituting:1 index:1 arfken:1 optoelectronics:1 current:2 above:1 new:4 method:7 nakamura:1 respectively:1 component:1 here:4 iωτ:2 kilometers:2 path:8 strong:2 observing:1 obtained:1 photomultiplier:1 shift:2 changed:2 vibrating:2 periodic:9 narrow:1 spacetime:1 winkler:1 via:1 extra:1 modulated:1 schilling:1 conventional:1 would:1 arms:9 few:1 bender:1 robertson:1 israel:2 operators:1 ruffini:1 normalized:2 known:1 ward:1 amaldi:1 effectively:1 averaged:1 values:1 following:1 mirrors:1 calculation:1 discussed:1 high:1 indicates:1 times:2 pinto:1 photodiode:1 american:1 sin:2 may:1 produce:1 waves:12 effective:1 light:12 thorne:2 correlation:4 order:5 ohanian:1 over:2 years:1 stability:1 thermal:2 lasers:1 converting:1 lg:3 d38:1 destroyed:1 detected:1 recombined:1 main:2 easier:1 maximal:1 freeman:1 zucker:2 introduce:1 number:2 half:1 hall:1 term:3 university:2 vibrations:1 each:2 cliffs:1 d47:1 side:1 suspended:1 misner:1 idea:1 related:1 interferometer:17 frequency:3 measurement:6 quantum:2 wavelength:1 eq:7 special:1 er:1 radicati:1 restricted:1 hils:1 since:6 rev:6 denotes:1 modulation:4 electronics:1 induced:2 math:1 ghatak:1 quite:1 difficulty:1 york:3 detecting:2 feasible:1 length:2 first:4 mcmillan:1 evans:1 reflected:1 huttner:2 another:1 michelson:5 given:1 ordering:1 eqs:1 indicate:1 norton:1 hundred:1 mandel:1 optical:6 july:1 giazotto:1 relative:6 kind:1 scheme:1 ben:5 amplitude:2 hz:1 ann:1 spectrum:2 slab:1 relatively:2 iben:1 picasso:1 forces:1 schematically:1 electric:1 normal:1 but:1 phase:9 extremely:2 class:1 haifa:1 observation:1 average:1 physicists:1 detectors:2 proceedings:1 fowler:1 physics:2 fact:1 shot:2 astrophys:2 earth:1 find:4 based:1 should:1 factor:1 lobo:1 get:1 dependent:1 beams:3 beam:4 made:1 during:2 gen:1 traverses:1 fields:1 arxiv:1 grav:1 rudiger:1 common:2 monochromatic:1 requirement:2 achieved:1 coccia:1 j1:7 detection:9 intensity:9 electrostatic:1 sec:1 arm:1 gravitation:3 pattern:2 heterodyne:8 between:6 prentice:1 approach:1 edoardo:1 terms:5 weak:2 however:3 jr:1 interfere:1 concentrate:1 analyzer:1 article:1 suggested:3 cos:5 etc:2 refraction:1 cm:1 period:4 conference:1 hawkins:1 described:1 due:3 been:1 reduction:1 expected:2 ph:1 wheeler:1 coherent:1 observe:1 weisberg:1 astron:2 those:1 applied:2 laser:5 developing:1 straight:1 will:9 kawashima:1 centrella:1 technology:1 currents:1 quant:1 split:1 used:1 peaks:1 singapore:2 effect:1 hand:1 saulson:2 tyson:1 cycle:1 fourier:2 changes:3 analysis:2 academic:1 observed:3 sources:1 bandwidth:3 using:8 previous:1 vibration:2 lett:1 shoemaker:1 polarized:1 krolak:1 haus:1 press:4 world:2 advanced:1 disadvantage:1 insert:1 agrav:7 englewood:1 follows:1 signal:1 performing:1 flux:1 output:7 reduced:1 mathematical:1 right:1 often:1 mirror:5 photomultipliers:1 kawamura:1 kdp:1 lead:2 webbink:1 magnitude:1 prog:1 bessel:2 measuring:1 noise:7 scientific:3 problems:1 journal:2 use:4 interferometric:2 periodically:1 getting:1 numerator:1 2eg:1 range:1 wolf:1 cambridge:5 into:4 three:1 references:1 proportional:1 oohara:1 methods:2 pegoraro:1 assumed:1 there:1 transform:2 long:4 strict:1 low:1 forward:1 energy:1 morrison:1 function:5 fundamentals:1 differences:1 jul:1 technion:1 october:1 gravitational:24 crystal:3 astrophysical:1 fluctuations:1 ωg:4 taylor:1 certain:2 abstract:1 functions:1 percent:1 field:2 narrowing:1 other:2 department:1 theor:1 coherence:1 june:1 includes:2 deriving:1 seismic:1 assume:1 veneziano:1 dτ:2 time:8
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quant-ph9907014.txt |@word concept:1 gr:4 chain:15 issued:1 magnetic:2 results:5 chaos:2 leads:1 eds:2 commute:3 latter:4 bohm:1 cooperative:1 crete:7 bosonized:2 expressions:3 localized:2 consider:4 inverse:1 referring:1 duction:1 recurrence:5 company:1 finally:5 γh:1 γn:9 th:2 under:3 worth:2 applied:1 labels:2 amplitudes:1 straightforward:1 evolves:1 very:7 continues:1 springer:2 seemingly:1 choice:2 p1:2 fab:1 fac:1 associated:2 difference:6 exact:4 condition:1 dirac:1 skii:2 hamiltonian:27 issue:1 enol:2 solution:4 large:4 discrete:5 vector:5 minimal:1 recall:2 indices:6 eigenvalues:8 nine:1 selftrapping:7 inspection:1 dimer:20 degeneracy:1 employing:1 grateful:1 concise:1 matrices:1 talks:1 rate:3 orthogonal:2 perspective:1 further:1 dynamics:3 odd:2 canonical:9 even:3 will:13 what:1 nonlinear:6 trapping:1 invertible:1 brackets:1 section:5 near:2 expressed:3 chakrabarti:1 d0:1 suq:15 deal:1 new:4 christiansen:1 method:2 publications:1 coefficient:2 edited:1 drastic:1 systematic:1 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quant-ph9907015.txt |@word represent:1 partial:2 consider:6 both:1 results:3 commute:1 per:1 reasoning:2 simon:3 depend:2 aug:1 auf:1 does:3 th:1 indicating:1 belonging:1 orthogonal:6 kamber:2 verb:1 difference:1 encounter:1 turns:1 michael:3 discrete:1 vector:2 eigenvalues:7 inspection:1 setup:1 direct:1 riesz:1 tex:1 j23:1 j22:17 specker:16 index:1 what:2 appear:2 apparatus:3 diag:2 section:1 axes:3 consistently:1 experiment:4 subspaces:2 expresses:1 annalen:1 leg:1 respectively:4 never:1 answers:1 atoms:2 nicht:1 groups:1 others:1 represented:6 along:5 strong:6 orthomodular:3 vectors:3 contradiction:1 resulting:1 usually:2 conveniently:1 makes:1 der:1 via:2 projection:3 logical:1 outcomes:2 austria:1 boolean:2 unit:1 would:3 distinct:1 negative:1 selecta:1 svozil:6 therefore:3 type:5 diagrams:2 more:4 formally:2 operators:9 berlin:2 particular:4 foundations:2 iii:1 must:3 states:3 springer:3 valued:1 science:1 equation:1 testability:1 besides:1 values:2 publications:1 concepts:1 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quant-ph9907019.txt |@word code:17 consider:2 remarkable:1 similarity:1 rev:2 focus:2 four:2 proposition:4 follow:1 devoted:1 certainly:2 hold:2 depend:1 calculate:1 tr:2 asking:3 those:5 under:2 sent:2 divergent:1 summand:2 very:2 rise:1 results:5 corollary:2 every:7 verd:3 formula:1 exact:1 fakult:1 condition:1 leads:3 din:1 exponential:1 transmission:6 list:1 large:4 small:5 upper:5 smaller:3 direct:3 approximation:1 second:3 rigorous:1 further:2 peredachi:1 canonical:1 even:2 dissertation:1 errors:1 rate:12 ˆw:1 pkn:9 section:10 analogously:1 uniform:6 access:2 version:1 above:3 sup:5 new:2 d1:7 method:3 limsup:2 here:8 refinement:2 represented:1 strong:6 simulating:1 sending:1 remark:16 sender:2 study:1 larger:2 allows:1 contradiction:1 simultaneous:14 schumacher:2 changes:1 uniquely:1 via:4 useful:2 family:2 bounds:2 prefer:1 replace:1 naimark:1 achievable:11 apply:2 resolutions:2 use:8 andreas:1 projector:1 would:8 prove:6 distinct:1 positive:4 negative:1 next:4 vol:9 ψi:2 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quant-ph9907020.txt |@word monte:1 partial:1 consider:2 pointing:1 crucial:1 reversibility:1 results:3 four:2 roy:1 comments:1 computation:9 consists:2 gn:1 primes:11 gk:3 compact:1 whose:2 superpositions:1 re:1 alamos:4 deterministic:1 factoring:3 tn:19 finally:10 tk:8 th:6 under:2 norm:2 conjecture:7 supported:2 amplitudes:1 advantage:1 far:1 springer:1 induce:1 choice:3 unstructured:1 print:3 every:1 summarized:1 li:2 sssr:1 logarithmically:1 condition:3 level:2 did:1 evaluation:3 prototypes:1 large:3 discrete:1 undone:1 dealt:1 small:3 noted:1 programme:1 upper:2 strongly:1 smaller:6 periodicity:4 zk:3 dealing:1 α2k:2 sin2:1 sign:2 second:1 value:2 picked:1 chen:1 further:4 odd:3 gm:4 even:5 errors:2 sub:3 sum:7 3p:2 means:1 witnesses:9 version:3 above:2 referees:1 replaced:1 method:4 exercise:2 full:1 respectively:9 doing:1 here:3 behaviour:2 operating:1 ansatz:1 berkeley:1 directions:1 ratio:1 change:3 digits:2 search:3 institute:3 study:1 larger:6 example:2 exploitation:1 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quant-ph9907021.txt |@word concept:1 consider:6 illustrates:1 results:4 leads:2 proposition:4 entropy:5 increase:1 knill:1 tr:1 participants:1 present:1 worth:1 case:10 conjecture:1 supported:1 orthogonal:2 rise:1 choice:1 exact:1 level:1 transmission:2 turns:4 optics:1 upper:2 smaller:1 findings:1 obsolete:1 fold:1 rate:1 further:2 linear:1 even:2 what:2 unavailable:1 apparatus:1 section:1 analogously:1 networks:1 above:4 shared:1 degree:1 jointly:1 explore:1 plenio:4 based:1 change:3 extreme:1 obtained:3 popescu:1 allows:2 reason:1 ρj:2 amount:6 resulting:2 procedure:2 permutation:3 usually:1 implement:1 schur:1 via:1 spatially:1 projection:1 distinguishability:1 total:1 establish:1 use:4 would:4 prove:2 remains:1 contains:1 negative:1 ψj:15 classically:1 noting:1 therefore:3 taken:3 stage:1 type:2 more:6 separated:1 sharing:4 formally:1 composite:1 distillation:4 operators:1 validity:2 berlin:1 ignorant:1 labelled:1 particular:5 known:4 projective:1 hold:1 kraus:1 springer:1 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quant-ph9907022.txt |@word consider:1 results:1 eds:1 comments:1 foundations:1 issues:1 content:2 tr:2 send:7 answered:1 finally:1 preserved:1 under:2 sent:2 division:1 orthogonal:4 very:2 experimentally:1 matrices:1 school:1 presented:1 large:1 bangor:2 antiunitary:1 says:1 direct:1 hillery:1 zero:1 cost:3 design:1 further:1 even:1 what:1 apparatus:1 assisted:1 expressed:1 steiner:2 version:1 above:2 shared:5 ever:3 chose:3 teleportation:19 here:2 iσy:4 represented:2 change:1 obtained:1 sending:6 great:2 remarks:1 cbit:17 popescu:3 vectors:1 amount:1 resulting:4 bob:36 suitable:1 involves:1 buˇzek:1 useful:3 projection:1 extra:2 outcomes:1 brought:1 hardy:3 aimed:1 apply:2 total:1 univ:1 use:3 would:1 massar:1 probabilities:2 contains:2 chooses:1 therefore:2 type:1 theoretical:1 more:2 possession:2 sharing:1 formally:1 knows:1 india:1 operators:1 known:16 projective:2 cases:1 reconstructed:1 science:3 soul:2 minimum:3 following:3 example:2 compare:2 boschi:2 process:2 bennett:4 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quant-ph9907023.txt |@word limited:2 gs:4 consider:3 rev:6 merced:1 results:4 leads:1 ciudad:1 go:1 expressions:6 looking:1 inverse:2 eα:1 affirmative:1 ıa:1 finally:2 those:1 th:1 under:4 maryland:3 magnetic:26 applied:1 belonging:1 straightforward:3 far:1 focus:1 every:2 interpreting:1 entries:1 exact:10 condition:9 level:11 solution:7 try:1 vector:11 specified:1 possibility:1 sin2:1 direct:2 consists:1 second:1 tangential:1 dynamics:9 carlo:1 even:1 what:1 appear:1 giving:1 expressed:1 new:17 apply:1 method:4 satisfy:4 simultaneously:1 notions:1 relates:1 respectively:2 fields:5 here:9 free:1 along:2 strong:2 equations:2 appears:1 interpret:1 rests:2 involved:2 study:1 vectors:5 allows:2 completely:1 periodic:1 bhandari:1 hospitality:1 suitable:1 composed:2 formulated:1 followed:1 projection:1 family:1 namely:3 pietri:1 ask:1 abdel:1 use:2 takes:1 usa:2 covariant:7 peri:1 mexico:1 dni:1 next:2 call:1 therefore:3 means:3 type:4 theoretical:1 possible:1 more:2 kˆ:3 ublica:1 becomes:1 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quant-ph9907024.txt |@word precise:2 consider:2 cussed:1 crucial:1 alternatives:1 results:3 leads:2 bayesian:1 follow:1 remarkably:1 research:1 decisions:2 reasoning:1 payoff:2 whose:1 depend:1 deterministic:1 acting:1 including:2 chaps:1 helps:2 under:1 include:2 statespace:1 ingredient:2 case:7 supported:2 amplitudes:4 transitively:2 tends:1 choice:1 school:1 prize:1 cause:1 list:1 accidentally:1 deals:2 vector:1 cooke:1 eigenvalues:1 caltech:1 strongly:1 deutsch:42 consistent:4 past:1 second:4 substituting:1 further:1 envisions:1 linear:1 index:1 what:4 preferences:10 section:4 lawrence:1 subspaces:1 embodied:1 new:4 increasing:2 ever:1 equivalent:1 seeks:2 cleaner:1 simultaneously:1 lee:1 never:1 here:1 understanding:1 akin:2 consideration:1 along:4 equations:2 celebration:1 naval:1 suitably:1 institute:4 shift:1 vectors:1 p2:5 amount:1 resulting:1 published:1 hospitality:3 proof:1 studies:2 maker:3 involves:1 uniquely:1 formulated:1 prefer:2 outcomes:6 amherst:1 vols:1 unit:1 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quant-ph9907025.txt |@word camacho:4 concept:1 gr:1 similarity:1 interference:6 forbidden:7 results:3 go:1 follow:1 expressions:1 hole:1 consider:9 astrophysikalisches:2 depend:2 calculate:1 equivalence:4 nonlocal:13 finally:1 program:1 present:3 under:4 magnetic:1 hibbs:1 very:6 wave:2 puzzles:1 dxdt:1 probability:1 noninvariant:1 experimentally:1 condition:1 riemann:1 level:10 vector:7 small:1 relation:1 mangano:1 der:1 smaller:1 force:2 measurable:1 second:3 qualitatively:1 dynamics:3 even:2 plays:3 appear:1 deeply:1 section:2 experiment:6 goes:1 boundary:1 renders:1 acknowledgments:1 movement:2 lukierski:1 lef:4 whose:1 respectively:2 never:1 modify:1 here:9 cylindrical:3 them:3 possibility:1 address:1 xβ:3 path:3 along:5 xα:4 equations:5 appears:1 interpret:1 spite:1 allows:1 controversy:1 sternwarte:1 action:2 hospitality:1 spacetime:10 emerge:1 unit:1 readily:1 derivatives:1 use:1 takes:5 would:2 prove:1 remains:1 contains:1 classically:1 therefore:3 more:3 successful:1 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quant-ph9907026.txt |@word represent:1 monte:1 measurements:43 sci:1 consider:5 ali:1 rev:13 particular:5 results:10 leads:5 rapid:1 emch:1 computation:1 reasoning:1 zeh:2 subjected:1 tr:6 braginsky:1 intensive:1 preserved:1 under:3 must:2 alber:1 applied:2 random:2 worse:1 advantage:3 returning:1 very:1 springer:3 choice:1 crosses:1 resonant:3 fakult:1 condition:2 beginning:1 level:5 knight:2 michael:1 solution:2 t0:4 t1:11 try:1 solved:1 convenience:1 vector:1 fourier:3 small:13 unsharp:5 equation:4 upper:6 smaller:1 oscillation:1 pulse:9 approximation:1 konstanz:5 design:1 evaluated:2 growing:1 further:2 dynamics:8 implemented:1 carlo:1 even:3 employ:1 what:5 apparatus:1 brackets:4 giving:1 section:8 brief:1 overwhelmed:1 above:1 new:3 full:1 simultaneously:1 chose:1 degree:4 modify:3 here:1 beige:1 behaviour:1 desired:1 selective:1 address:3 represented:1 path:1 strong:5 obtained:5 remark:1 institute:1 study:1 studied:1 allows:1 amount:2 survey:1 narrow:2 makes:1 plotted:2 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quant-ph9907031.txt |@word consider:1 alternatives:1 results:2 illustrated:3 commute:1 go:1 expressions:6 reasoning:1 whose:4 depend:2 concerned:1 tain:1 finally:1 exposition:1 must:1 necessary:1 amplitudes:44 straightforward:2 r11:2 choice:16 mixing:1 matrices:3 condition:1 presented:3 did:1 vector:12 yale:1 eigenvalues:11 employing:1 sin2:42 direct:1 consists:1 zero:1 even:1 what:3 appear:2 giving:1 section:4 uniform:1 above:1 new:11 method:6 satisfy:1 led:2 respectively:7 component:18 here:1 bj:3 along:1 implicit:1 change:12 deduced:1 obtained:8 great:1 technical:1 changed:1 leaving:1 resulting:2 procedure:1 permutation:1 via:1 projection:9 apply:2 total:2 unit:2 use:5 would:2 remains:1 positive:1 negative:1 permitted:1 m1:1 therefore:1 m2:1 taken:1 more:4 formally:1 becomes:3 operators:26 correspondingly:1 particular:1 known:1 foundations:3 cases:1 given:7 r1:5 ma:3 mc:2 mb:3 mn:17 mi:16 mj:8 remain:1 obvious:2 following:4 specialized:1 example:1 2iϕ:11 give:1 calculation:1 organized:1 states:10 sense:3 r12:2 r22:2 r21:2 axis:7 respective:2 discussion:2 means:1 evidently:1 how:1 sin:209 product:1 may:3 ladder:6 earlier:1 derived:4 constants:1 remember:1 joachain:1 explicit:3 used:2 definitions:1 order:4 terms:2 interpretation:1 subsections:1 indeed:1 over:1 course:2 paper:5 through:8 mentioned:1 fortunate:1 its:7 before:1 chosen:1 exact:1 forms:20 resort:1 choose:2 emphasize:1 them:3 rotations:2 they:3 now:4 possess:1 easily:2 always:2 university:3 2e:26 each:1 found:2 2i:6 characterized:1 square:1 ei:34 reduce:2 principles:2 related:1 owing:1 measurement:2 quantum:10 our:3 special:1 out:1 shown:1 matrix:6 since:6 squared:1 formula:1 rn:4 ref:4 correct:2 after:1 theory:4 diagonal:2 standard:13 reason:2 derivation:2 r2:5 thing:1 place:1 derivations:1 hence:4 first:2 there:4 probability:47 relate:1 number:4 relations:1 another:1 calculational:1 illustrate:1 differ:2 similarly:1 introduction:2 unknown:2 system:1 adopted:1 obtainable:3 observations:1 calculations:1 eqn:13 perfectly:1 gives:2 focusing:1 than:1 cyclic:1 e2iϕ:3 depends:3 submitted:1 matter:1 amplitude:2 result:2 unchanged:2 measure:2 argument:2 already:1 say:1 manner:1 need:3 seen:1 seem:1 confirms:1 their:14 angle:2 able:2 concerns:1 generalized:30 finding:1 so:2 formulas:5 sure:1 shall:3 most:2 involving:1 but:8 phase:29 measured:2 probable:1 clear:1 χy:1 mechanical:1 physics:2 fact:3 quantity:1 precise:1 purely:1 solutions:1 find:9 commutators:1 explain:1 state:2 should:1 iei:4 only:2 explicitly:1 subsection:5 factor:2 achieve:1 do:3 goes:1 get:2 expectation:1 ones:2 combinations:1 runs:1 arxiv:1 expansions:2 yield:1 investigate:1 though:1 set:6 computed:1 observed:1 collectively:1 namely:1 projections:1 close:1 labour:1 commutation:1 written:1 affecting:1 conditions:1 multiplied:1 recently:1 initially:2 attention:1 however:3 key:1 alters:1 σk:1 both:2 cos:160 accident:1 prescription:1 σc:24 many:1 taking:1 according:1 quantization:3 σz:4 σy:20 σx:22 cos2:39 ck:1 cn:4 point:1 seems:3 corresponds:1 whatever:2 anti:1 respect:7 longman:1 transformations:3 three:6 defined:1 reduction:1 expected:1 ph:4 dualism:1 direction:6 describe:1 corresponding:6 σj:2 quantities:13 σi:2 θe:4 observe:1 angles:7 general:8 spin:56 those:3 case:7 expanded:1 appearance:1 value:5 choices:1 will:7 while:3 suppose:1 property:1 characterizing:1 remembering:1 vectors:5 refs:6 thus:16 equal:1 different:3 recover:2 perhaps:1 make:4 belong:1 same:11 any:5 shorter:1 unity:1 quant:4 arguments:6 pauli:3 units:1 hermiticity:1 literature:1 see:3 upon:2 effect:3 hand:2 moment:1 changing:3 laborious:1 eigenvectors:47 off:1 well:3 concrete:1 without:1 components:14 sets:1 arising:1 usual:1 arbitrarily:1 just:1 being:2 accurate:1 rotated:2 obtain:19 actions:1 underlying:1 alternative:3 yet:1 iϕ:39 other:4 transformation:3 match:1 identical:2 eigenvalue:8 possible:4 know:1 press:4 using:12 apart:1 rotate:1 appearing:1 follows:3 either:1 arbitrary:3 become:1 inter:1 old:2 methods:1 deal:1 ξy:7 some:2 deduce:2 happens:1 describing:1 lead:2 measurements:3 does:2 connecting:1 eliminate:1 demonstrated:1 refer:1 eiϕ:20 scientific:1 expansion:5 substitution:1 properties:2 plug:1 about:2 eqns:13 discussed:1 obc:1 probabilities:2 introduced:3 considerations:1 cambridge:2 into:2 obtaining:5 down:2 references:1 determine:1 operator:18 suffice:1 initial:1 transform:1 way:2 call:1 was:3 function:2 form:18 jul:1 eϕ:4 rjj:2 applying:1 wish:1 up:5 limit:5 called:1 eigenvector:1 mechanics:3 computing:1 ai:5 sketched:1 proven:1 denote:3 work:1 tedious:1 no:1 nc:2 when:11 setting:2 conclusion:2 ξx:9 polar:6 elements:21 kinds:1 needed:1 structure:2 land:8 values:1 required:1 together:2 original:1 dot:1 time:1 observables:4 having:1
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quant-ph9907032.txt |@word limited:1 katz:1 consider:2 pointing:1 interference:1 varying:1 splitting:1 four:5 quadrature:1 garching:1 causes:1 gr:1 gases:1 calculate:2 does:1 squeezing:1 th:1 stable:3 stochastic:1 analogous:1 include:2 amplitudes:4 downstream:1 very:6 frequencies:10 unchen:2 ed2:5 anonymous:1 upstream:1 mixing:5 condition:7 leads:1 level:2 schawlow:1 yin:1 eigenmodes:1 solution:2 itamp:1 standards:2 large:10 solved:1 differential:1 demonstrated:1 science:1 small:13 optics:6 noted:1 fleischhauer:4 upper:1 smaller:1 oscillation:10 sin2:1 pulse:1 approximation:1 second:2 exter:1 dynamics:2 even:1 nonlinear:7 sub:1 rate:3 sum:1 cell:7 lukin:4 experiment:1 pershan:1 above:7 new:2 consisting:1 contrast:3 κl:7 magnetometry:2 respectively:1 here:5 atoms:4 cos2:1 κz:1 relaxation:1 represented:2 ratio:1 equations:4 woerdman:1 naval:1 technical:1 shift:1 study:1 losses:3 resulting:2 resonance:1 narrow:5 makes:3 via:1 spatially:1 vapors:1 electromagnetically:1 welch:1 traversing:1 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quant-ph9907033.txt |@word represent:1 evidence:1 magnetic:1 results:22 four:1 expressions:5 row:1 devoted:1 whose:3 depend:1 calculate:1 those:2 applied:1 amplitudes:17 implicitly:1 seemingly:1 wave:3 difference:2 presented:2 applicable:1 vector:15 succession:1 eigenvalues:2 dealing:1 sin2:2 literature:6 rate:1 further:2 theory:2 subscripts:1 index:1 what:4 appear:1 section:12 current:6 new:11 contrast:1 satisfy:1 full:1 respectively:4 even:1 component:3 equals:1 here:5 cos2:2 represented:2 along:1 strong:1 obtained:5 technical:1 inspired:1 vectors:5 allows:1 prior:1 accomplished:1 resulting:1 changes:1 involves:1 projection:16 explained:1 brought:3 logically:1 unit:5 use:5 proceed:1 would:1 positive:2 contains:1 call:1 therefore:5 m2:2 more:3 becomes:1 operators:10 validity:1 labelled:1 foundations:3 cases:7 must:3 states:22 mf:2 mi:15 values:8 following:1 making:2 specialized:1 example:1 dedicated:1 give:5 calculation:1 expanding:1 choice:3 organized:1 involve:3 numbers:1 arise:1 axis:1 respective:1 discussion:3 get:2 how:4 sin:48 description:2 derived:2 representations:5 derives:1 constants:1 joachain:1 explicit:3 correspond:4 so:4 order:2 interpretation:8 indeed:1 pointed:1 insight:1 course:1 paper:4 satisfies:1 its:1 before:5 exclusion:1 interesting:1 fruitful:1 forms:10 setting:3 them:4 outlined:1 mention:2 they:2 now:3 eigenvalue:4 always:2 university:3 possibilities:3 token:1 each:2 found:2 characterized:3 ei:12 principles:3 related:1 owing:1 obtains:3 measurement:16 quantum:11 our:3 special:5 out:1 bility:1 shown:1 matrix:8 since:2 formula:1 belief:2 yale:1 differ:1 standard:34 completely:1 derivation:1 could:1 hence:1 first:4 initial:7 seeming:1 probability:26 relate:1 hitherto:1 done:1 another:2 angular:1 illustrate:1 given:7 similarly:2 introduction:2 system:2 least:1 their:4 eqn:13 final:5 gives:2 exactly:1 representing:1 than:1 coefficients:3 double:1 submitted:1 amplitude:4 result:1 spectrum:1 talking:2 need:1 seen:2 seek:1 any:3 viewed:1 angle:1 depending:1 pursued:1 ideas:1 instance:1 take:2 finding:8 formulas:4 continuous:1 shall:5 most:5 but:5 pair:2 measured:3 surprising:1 considered:1 clear:1 later:1 principle:1 physics:2 review:2 fact:3 quantity:1 precise:1 show:3 labels:1 relation:1 find:3 explain:3 should:3 only:4 explicitly:2 achieve:1 do:1 means:4 expectation:21 truly:1 ones:2 closely:1 despite:1 compute:3 approach:7 arxiv:1 expansions:1 yield:1 summary:2 twice:1 common:1 pertains:1 view:1 requirement:1 set:5 reference:9 clarified:1 projections:1 ignores:1 terms:1 closes:1 eigenfunctions:2 away:1 label:1 state:21 various:4 between:6 reproducible:1 drawn:1 conditions:1 recently:1 initially:2 complement:1 however:3 key:1 dualism:1 both:5 cos:54 prescription:1 σc:1 many:3 according:2 quantization:1 σz:3 connection:2 concentrates:1 expression:2 among:2 seems:1 directions:4 respect:8 considering:1 longman:1 ensures:1 basis:2 addition:1 due:1 been:1 attaching:1 describes:1 interest:1 recognize:1 ph:5 direction:20 corresponding:4 observable:1 quantities:15 θe:1 observe:1 angles:13 general:10 spin:73 present:1 case:26 straight:1 expanded:1 value:16 choices:1 will:3 while:13 situation:1 characterizing:2 thus:6 equal:3 characterize:1 different:4 perform:1 make:1 same:9 unity:1 quant:5 arguments:2 pauli:6 units:1 used:2 upon:4 expand:1 eigenvectors:13 undefined:1 well:4 without:1 arising:1 usual:2 just:2 being:2 obtain:6 alternative:1 iϕ:2 valid:1 treatment:3 save:2 generalized:40 identical:1 eigenfunction:1 possible:1 press:4 using:6 vague:1 success:1 alternatively:1 indication:1 either:2 arbitrary:1 methods:3 understood:1 deduce:2 repeat:1 describing:1 lead:2 confirm:1 measurements:9 exposition:2 refer:2 eiϕ:7 scientific:1 elucidate:2 expansion:5 properties:1 takes:2 comparison:2 about:4 actual:1 column:1 certainty:1 eqns:15 recognizes:1 introduced:1 cambridge:2 obtaining:4 three:1 down:7 phase:2 references:1 determine:1 operator:20 prepare:1 there:2 way:3 m1:2 function:4 complete:1 form:11 jul:1 idea:2 failure:1 made:1 arranged:1 whether:1 characteristic:1 up:8 us:1 below:3 called:1 expect:1 mechanics:6 defined:3 certain:1 measure:1 denote:2 formalism:1 defines:3 again:1 functions:1 no:1 fixing:1 when:4 other:3 conclusion:2 polar:5 briefly:1 elements:8 kinds:1 superposition:1 symbol:1 primed:1 variation:1 structure:3 land:10 already:1 original:1
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quant-ph9907034.txt |@word limited:2 consider:2 global:3 brownian:1 results:3 abramovici:1 leads:2 finesse:1 expressions:3 2r2:2 gillespie:2 depend:1 paris:1 braginsky:1 recurrence:1 finally:2 sound:1 llp:2 πcl:1 very:3 frequencies:5 brossel:1 geometrical:1 every:3 experimentally:2 deformations:2 large:4 solved:1 science:1 small:2 heidmann:4 averaged:5 force:4 direct:1 approximation:6 zero:2 even:1 brackets:2 section:1 while:1 expressed:3 thickness:17 axial:1 sup:1 contributes:1 erieure:1 coefficient:1 respectively:3 cylindrical:14 2kb:3 interferometric:1 path:1 quite:2 equations:1 appears:2 change:3 obtained:9 great:1 shift:4 study:3 studied:5 allows:1 thicknesses:1 resulting:2 usually:2 resonance:10 fourier:1 composed:1 diameter:9 followed:1 hermite:1 replace:2 visible:1 decrease:1 total:1 use:2 feb:1 takes:1 would:6 contains:1 arms:2 france:1 few:1 nucl:1 noting:1 m3:1 taken:1 robertson:1 resonator:1 more:1 ecole:1 becomes:1 about:1 curvature:7 degrade:1 particular:1 iv:1 iii:1 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quant-ph9907038.txt |@word secondly:1 sci:1 consider:2 switched:1 rx:1 equalities:2 excellent:1 results:1 chiao:1 four:2 eds:1 computation:1 transversally:1 transmittances:1 reasoning:1 whose:1 depend:2 violate:1 tx:1 ty:1 optimization:1 efficiencies:4 tj:1 under:4 division:1 far:9 frequencies:1 distort:1 figs:1 mattle:1 condition:2 splitter:17 presented:2 ref:1 proposals:3 fewer:1 t1:2 dealt:1 smaller:1 ten:1 sin2:8 past:2 second:2 enhancement:4 pass:4 eik2:1 substitute:1 even:3 will:3 nonlinear:3 appear:2 analogously:3 t2y:2 t2x:2 waiting:1 experiment:16 above:4 new:2 paviˇci:6 increasing:1 method:5 counters:1 outgoing:1 simultaneously:2 chose:1 nonmaximal:3 adelberger:1 respectively:2 spacing:1 here:3 delivering:1 cos2:4 along:1 z1:5 z2:5 obtained:1 thirty:1 changed:1 completely:1 contradiction:1 simultaneous:2 m3k:1 walther:1 pick:1 usually:1 narrow:2 makes:1 emerge:2 adjustable:1 although:3 elaborated:1 app:1 polarizers:7 hardy:6 counts:8 total:2 univ:1 planck:1 use:5 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quant-ph9907039.txt |@word ibid:1 represent:1 partial:1 consider:1 crucial:1 equalities:7 results:4 four:4 gf:1 computation:1 transversally:1 consists:1 sci:1 expressions:1 increase:1 inverse:2 terms:1 violate:4 tx:3 ty:3 technique:1 containing:1 efficiencies:4 device:1 those:4 under:2 include:1 worth:1 eliminate:1 entangle:3 rx:3 far:3 frequencies:3 wave:5 every:1 orientations:1 experimentally:1 difference:1 enter:1 condition:3 subsystems:1 splitter:13 presented:2 turns:1 proposals:3 fewer:1 t1:3 leave:1 vector:2 phase:1 harry:1 small:2 optics:2 application:1 unexpected:1 compensated:2 ten:2 dealing:1 ready:1 sin2:11 unpolarized:3 past:1 zero:1 chopping:1 enhancement:2 pass:2 zu:1 eik2:2 eik1:2 even:4 aim:1 what:1 nonlinear:1 appear:1 section:1 selected:1 near:1 consequent:1 t2y:6 t2x:6 experiment:15 intersect:1 new:2 paviˇci:9 increasing:1 ever:1 method:6 counters:1 satisfy:1 outgoing:1 full:3 simultaneously:2 nonmaximal:5 whose:3 respectively:4 never:1 spacing:1 equals:1 here:6 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quant-ph9907040.txt |@word represent:1 sci:1 rev:5 magnetic:1 decays:1 activated:1 results:2 gf:1 go:3 follow:1 reasoning:3 row:1 particles:2 calculate:1 efficiencies:1 excluded:1 under:3 attenuated:1 case:3 amplitudes:1 very:5 wave:6 electron:1 sons:1 every:1 refractive:2 resonant:1 difference:1 splitter:1 disturb:2 progression:2 presented:2 supports:1 large:1 harry:1 small:1 round:18 prevent:1 smaller:3 direct:1 second:1 chopping:2 functioning:1 even:4 index:3 what:3 plays:1 appear:1 apparatus:3 brackets:1 section:1 waiting:1 experiment:19 destroyed:1 new:3 paviˇci:5 contributes:1 method:1 filled:1 full:1 exchange:16 never:1 here:2 bi:1 objects:7 possibility:1 groups:1 path:4 widening:1 obtained:4 sending:1 incoming:7 rests:1 involved:1 losses:3 allows:1 exiting:1 m3k:1 walther:2 action:2 resonance:7 narrow:1 changes:1 plenum:1 highly:1 visible:1 photonics:1 counts:1 total:10 planck:2 use:3 would:5 remains:1 next:1 few:1 doubt:1 call:1 therefore:3 doubling:1 resonator:16 until:1 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quant-ph9907041.txt |@word epeau:1 partial:10 consider:3 remarkable:1 four:2 preserves:1 terms:1 calculate:2 nonlocal:1 environment:7 e78:8 include:1 γe:1 conjecture:2 random:1 straightforward:1 far:2 2e12:2 choice:1 every:1 difference:1 matrices:1 swapping:2 level:1 transmission:1 knight:1 fragile:1 eigenvalues:1 kim1:1 maximization:1 direct:1 further:2 theory:1 even:3 what:1 ˆx:1 ˆy:1 ˆz:1 contributed:1 analogously:2 new:1 contributes:1 body:7 full:1 simultaneously:1 lee:1 degree:1 respectively:1 teleportation:39 plenio:2 represented:5 equations:1 appears:1 box:1 sending:1 sender:1 rigorously:1 study:1 studied:3 schumacher:2 studies:2 plotted:3 via:3 family:1 marginal:2 explained:1 highly:1 hardy:1 analyzing:2 total:6 linearly:4 feb:1 would:1 prove:1 remains:1 negative:2 ψi:1 call:1 a57:1 noisy:12 theoretical:1 more:1 linden:1 becomes:2 operators:1 normalized:1 ward:1 ρa:2 brukner:2 science:1 work:2 reproduce:1 example:2 purity:11 boschi:1 bennett:3 share:1 dependence:2 states:11 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conditions:1 bt7:1 korea:2 recently:1 nature:2 qubits:1 however:3 dissipates:4 jl:1 both:4 σn:4 σm:1 according:1 attributed:1 whole:1 unitarily:1 ci:1 bell:5 wootters:1 dimensional:1 werner:8 maximize:1 respect:2 uck:1 considering:3 better:1 transformations:2 locally:1 due:3 been:2 defined:3 a210:1 much:2 basic:1 ph:2 define:4 obtained:1 contribute:1 corresponding:1 sorensen:1 zeilinger:5 pαβ:2 c2:1 c1:1 maximally:6 spin:6 applied:4 e46:3 pacs:1 solid:1 kimble:2 value:3 will:1 teleport:2 while:4 property:2 procedure:2 unitary:4 against:1 dual:1 weinfurter:2 ewc:4 make:2 same:7 clearly:1 parts:1 quant:1 pauli:2 pan:2 independent:3 extended:1 hand:2 purpose:1 kim:1 entanglement:71 totally:1 numbered:1 purer:1 hwang:1 epr:2 analysis:2 vaidman:1 does:1 drawing:1 know:1 popescu:5 less:1 obtain:1 thanks:1 using:2 belfast:1 density:9 source:2 interested:1 lett:16 real:3 eigenvalue:1 koashi:1 showing:2 decomposed:1 possible:2 increases:1 zukowski:1 entangled:25 confined:1 world:1 bit:2 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teleported:2 observables:1 decoherence:1 original:4 degrade:1
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quant-ph9907042.txt |@word secondly:2 code:1 partial:2 consider:6 caused:2 results:1 illustrated:1 stochastically:1 consists:1 perturbations:1 denotes:3 gk:8 gj:2 row:1 maximally:3 producing:1 subjected:2 disturbances:2 tr:27 contained:1 factoring:1 containing:2 environment:9 wmi:2 th:2 include:1 norm:6 supported:1 amplitudes:1 straightforward:2 orthogonal:1 very:1 implicitly:1 springer:2 otteler:1 print:2 corollary:9 sons:1 every:30 emphasized:1 difference:3 matrices:7 condition:3 partitions:1 leads:1 beginning:1 quantitatively:1 level:8 positions:3 manyparticle:1 fragile:4 correct:1 large:15 convenience:1 vector:2 enclosing:2 small:7 eigenvalues:2 mahler:2 upper:2 work:1 appearance:1 fragility:7 prediction:1 fold:4 likely:1 invariant:1 cat:7 substitute:1 canonical:6 even:1 what:1 errors:2 rate:1 sun:1 sum:10 selected:2 access:1 above:3 sup:4 new:2 increasing:1 contrast:2 κi:1 respectively:1 never:2 modify:1 here:1 diagonal:3 behaviour:1 plenio:1 address:2 represented:1 stamatescu:1 ascending:1 obtained:9 great:1 technical:2 root:2 study:1 changed:2 allows:2 commonly:2 gl:13 su2:3 permutation:1 schack:1 projection:2 family:9 bounds:2 convexity:2 wii:1 highly:5 unitary:6 summation:1 detecting:1 use:4 superpositions:4 would:3 prove:6 distinct:7 positive:2 eρ:20 cauchy:1 ψj:1 ψk:4 linear:1 doubt:1 call:4 therefore:12 ψl:15 endowed:3 taken:1 type:4 today:1 more:4 conclusions:3 operators:4 corrected:1 depolarizing:10 berlin:2 known:1 foundations:1 cases:1 iv:1 iii:4 alexei:1 high:1 account:3 word:5 ρi:1 science:1 equation:4 ρj:3 mi:10 ρn:1 macroscopically:3 zhan:1 values:5 following:21 averages:1 example:6 proof:17 f1:2 weaker:1 challenging:1 give:3 calculation:2 preserving:1 states:43 assumptions:1 νa:1 numbers:1 want:2 sense:5 triangle:1 simple:1 νj:2 end:1 g1:3 rather:3 s1:1 holds:4 rippin:1 terhal:1 machine:2 maps:3 criterion:2 pure:16 instead:3 verlag:2 parameter:5 dominance:1 map:12 product:13 algebra:1 may:2 after:3 minimized:1 fi:9 fj:2 fk:8 unentangled:2 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