text
stringlengths 0
190k
|
|---|
quant-ph9612018.txt |@word consider:2 hats:1 generalize:1 contributions:1 preserves:1 depend:2 b386:1 pˆi:1 deterministic:9 those:1 marks:1 te:1 ta:1 case:4 very:3 wave:8 every:2 matrices:2 entire:1 hamiltonian:14 turns:1 solution:2 large:3 discrete:5 pˆ2:2 small:2 eigenvalues:7 sign:6 approximation:4 dissipation:1 substituting:1 further:2 copenhagen:2 index:2 what:2 foregoing:1 infinitesimal:1 goes:1 construction:1 prescriptions:1 here:7 behaviour:2 objects:1 others:1 along:1 equations:2 appears:1 change:1 box:1 institute:1 shift:1 elaborate:1 allows:2 trial:1 resulting:1 postponed:2 changes:1 emerge:1 useful:1 extra:1 merely:1 explained:1 replace:2 addressed:1 b342:1 summation:1 total:1 use:1 additive:1 takes:2 would:2 positive:7 negative:6 next:2 ψj:6 nucl:2 ψi:9 taken:1 survive:3 stage:2 theoretical:1 more:4 becomes:2 operators:1 odinger:2 reversible:1 varying:1 must:4 ibi:4 crosses:1 equation:2 fock:5 values:9 akij:6 thooft:1 omit:1 renormalization:1 figure:1 give:1 choice:2 sense:1 states:10 numbers:2 arise:1 keep:2 distinguishable:1 occur:1 information:7 end:1 s2:2 s1:6 feature:1 write:3 how:1 pair:1 parameter:2 simplicity:1 intended:1 may:11 oscillators:1 after:1 produce:1 law:1 constants:1 drop:1 whenever:1 sp:1 their:1 sj:1 si:9 so:6 allow:1 suggest:1 order:2 interpretation:1 over:2 inconclusive:1 flips:1 interpreted:1 course:2 paper:3 statistical:1 signs:4 still:2 its:3 envisage:1 εabc:1 chosen:2 interesting:1 writing:1 parts:2 degrees:2 systems:1 mail:1 defining:1 into:3 arguments:1 them:1 within:1 regarding:1 introduce:4 hamilton:1 effects:1 they:1 now:4 discuss:1 nor:1 eigenvalue:1 term:1 netherlands:1 always:1 university:1 level:1 establishing:1 oppositely:1 sufficiently:2 each:1 found:1 entirely:2 2i:1 ei:2 fairly:1 energy:7 expect:1 quantum:15 our:4 eq:8 out:2 emerges:1 matrix:3 factors:1 since:4 interference:1 particles:2 re:1 reader:1 occurs:1 stat:1 theory:6 interactions:1 free:1 standard:1 difficulty:1 complicated:1 imagine:2 wanted:1 interaction:5 could:2 transition:1 quantummechanical:1 turn:1 place:1 δij:1 corrections:3 first:2 features:2 probability:2 variables:4 number:2 iht:1 exact:2 philosophical:1 carry:1 reached:1 passes:2 given:1 iai:4 publication:1 similarly:1 system:1 construct:2 attach:1 too:1 convention:1 scheme:1 final:2 continuous:4 part:1 jump:1 needless:1 future:1 exhibit:1 fig:1 footnote:1 spectrum:3 say:1 substantial:1 seen:2 seem:1 clearly:1 genuine:1 depending:1 note:1 take:2 exactly:4 iwj:1 iwi:1 most:4 aproximation:1 remarks:1 why:1 clear:1 later:7 implications:2 points:3 exp:2 mechanical:3 velocity:6 physics:2 fact:1 sector:1 particularly:1 solutions:3 scarce:1 tend:1 trivial:3 find:3 paradoxes:1 ground:2 q1:1 q2:9 simulating:1 parameters:1 distributed:1 enough:1 only:7 factor:1 circle:1 hamiltonians:2 do:2 his:1 means:3 express:1 overall:1 truly:1 cannot:1 report:1 dt:5 evolution:2 arxiv:1 remove:1 optimally:1 experiments:1 contain:1 qi:11 fixed:2 physically:1 see:4 result:1 best:1 techniques:1 satisfying:1 commutation:1 ways:2 yet:1 importance:2 state:4 between:2 probably:1 boundary:2 before:2 conditions:2 knowing:1 terms:1 statistically:1 nature:2 initially:1 p2i:1 however:1 vanishing:1 concentrate:1 problem:1 many:4 invited:1 according:1 energies:1 connection:1 densely:1 ci:3 point:5 σjb:1 harmonic:1 described:2 claiming:1 been:2 ai:2 much:1 slowly:1 pj:1 ph:2 pi:5 hardly:1 define:1 obtained:2 corresponding:1 concerning:1 observe:1 spin:1 present:1 quotation:1 p2:1 p1:1 look:2 p4:1 will:24 near:1 exist:2 study:1 identical:1 unitary:3 chaotic:2 vi:1 vj:1 thus:1 non:6 iw:2 itself:1 im:1 vanish:1 interacts:1 different:1 things:1 make:1 same:1 any:1 rules:1 complex:2 quant:2 emphasize:1 pauli:1 several:1 higher:1 evolve:1 used:2 infinity:1 effect:2 publ:1 moving:2 delicate:1 potentials:1 infinite:1 paradox:1 hartree:5 lower:3 ckij:6 schr:2 thu:1 without:1 utrecht:2 sets:1 coordinate:2 model:17 usual:3 proposed:1 rosen:1 using:1 eigenstates:1 conclusions:1 had:2 mathematically:1 spread:1 treatment:1 easy:1 relevance:1 iπ:1 iσ:1 generalized:2 real:12 iα:1 big:4 possible:1 fys:1 qj:14 preference:1 vacuum:1 world:1 loss:5 necessary:1 like:1 particle:9 follows:2 unnecessary:1 either:2 arbitrary:1 become:2 works:2 essential:5 mathematical:1 because:5 classical:1 smoothly:1 some:1 back:1 σi3:8 σi2:5 σi1:8 sight:1 realistic:1 legal:1 does:1 σic:1 σia:2 obey:3 bi:2 imaginary:3 permitted:1 ruu:1 freedom:2 o:2 page:1 ensure:1 obeys:2 introduced:1 other:3 own:1 kalitzin:1 h2:3 h3:2 h0:2 h1:3 bound:2 phase:1 references:1 tiny:2 einstein:1 soon:1 iδij:1 her:1 there:8 approximate:3 start:1 way:4 hooft:4 was:2 function:5 form:1 removes:1 but:7 hi:1 line:1 true:1 applying:1 whether:1 wish:3 inside:1 smooth:1 flip:2 us:6 tell:1 below:1 limit:2 distribution:1 called:2 eigenvector:2 defined:2 abstract:1 describe:1 single:1 pˆ:2 moves:1 proceeds:1 physical:4 again:2 functions:4 compared:1 nl:1 dotted:1 no:2 whereas:1 when:2 virtual:1 field:3 interested:3 details:2 draw:1 elements:1 superposition:1 models:1 variation:1 stay:1 important:3 bounded:1 allowing:1 variable:1 needed:1 practically:1 assume:2 space:1 mass:2 time:4 far:1 serious:2 starting:1
|
quant-ph9612019.txt |@word limited:1 concept:1 allowed:1 consider:6 ali:1 rev:5 lack:1 results:5 existing:1 leads:5 roy:3 grateful:1 go:1 gm:1 magnifying:1 golshani:24 nonlocal:1 former:1 investigation:1 those:1 under:3 fax:1 economical:1 orthogonal:1 very:6 splitting:1 fall:1 experimentally:1 bringing:1 founded:1 notes:1 t0:3 large:14 small:14 unifying:2 equation:7 force:5 dealing:1 consistent:1 direct:26 sign:1 second:4 narlikar:7 uncomfortable:1 dynamics:1 linear:1 aim:2 what:1 appear:1 fine:1 section:5 uniform:1 above:6 lifshitz:1 relational:4 method:1 zeits:2 iran:2 chose:1 degree:1 respectively:1 here:2 understanding:1 ranges:1 objects:1 berkeley:1 galileo:2 strong:1 equations:1 box:2 derivable:2 remark:1 arrive:1 nachrichten:1 institute:1 study:1 larger:4 contradiction:3 amount:1 suggestion:1 action:5 suitable:1 studies:1 via:2 ipm:1 brought:1 glance:1 should:1 unit:1 derivatives:1 use:4 eω:6 takes:1 would:1 contains:2 chooses:1 properties:1 doubt:1 therefore:7 mysterious:2 theoretical:2 conse:1 introducing:1 acceptable:2 apparent:2 corrected:2 validity:2 must:11 high:1 none:1 room:1 infinities:3 work:4 london:1 theories:6 reproduce:1 remain:1 assumptions:3 following:7 dec:1 root:2 example:1 beautiful:1 renormalization:1 cosmological:4 stated:1 calculation:1 ak:14 locating:1 accept:1 states:1 lorentz:3 caution:1 arise:1 sharp:1 times:1 absolute:5 information:4 needs:2 travel:1 acts:2 how:1 amazing:1 ensure:2 parameter:3 ensemble:6 derivations:1 simplicity:1 product:1 de:1 tried:1 algebra:1 may:11 after:1 derived:3 different:6 physik:2 cambridge:1 choice:3 meaningful:1 plank:1 stress:1 short:2 natural:2 coupling:1 light:4 separations:4 summing:1 cosmology:2 cannot:2 so:7 fundamental:1 representation:4 discussion:2 typical:5 produces:1 developed:1 over:4 dy:1 interpreted:1 experiments:1 through:2 argued:3 existence:1 kinetic:4 y2:1 its:7 derive:2 thank:1 located:2 chosen:1 relativity:6 fruitful:2 ǫ2n:1 choose:4 remarked:1 wellknown:1 overcome:1 versus:1 freeman:1 them:4 good:1 integral:1 dai:2 introduce:1 landau:1 framework:5 they:6 half:1 oxford:1 formulating:1 now:6 easily:1 term:6 gets:1 dirac:5 always:2 university:2 sufficiently:1 magnitude:1 each:7 2m:4 2n:2 realism:1 glasses:1 homogeneous:2 ann:2 domain:1 square:2 england:1 directly:2 formulate:1 eg:3 gaussian:2 related:2 arrives:1 proportional:1 quantum:15 our:16 special:1 out:4 shown:6 matrix:1 space:8 rep:3 since:2 lagrangian:1 particles:33 behaviours:5 mediated:1 correct:6 shows:3 theory:22 interactions:4 backer:1 standard:1 imagine:1 put:1 definition:1 interaction:33 derivation:2 noted:1 motion:6 thing:1 place:1 isotropic:1 corrections:5 moving:2 unphysically:1 first:8 origin:2 lond:2 xl:3 xm:4 relate:2 wave:1 number:1 approximate:1 done:1 another:2 says:1 little:1 law:1 tetrode:2 interact:2 system:6 approximately:1 their:5 assumption:1 observations:1 statement:1 postulate:6 structures:2 shell:5 schwarzschild:2 tehran:2 believe:1 representing:2 than:6 coefficients:1 distance:5 kind:4 holland:1 showed:1 accordance:1 hoyle:6 sections:1 approximations:1 cimento:2 zero:3 matter:2 supposed:1 were:1 hiley:3 nouvo:2 sees:1 san:1 electrodynamics:1 correction:1 say:1 manner:1 need:1 seen:5 seem:2 apparently:1 any:9 shojai:25 complete:1 routledge:1 paths:1 form:10 depending:1 latter:2 able:4 ideas:1 note:7 potential:23 generalized:1 forces:5 begin:1 broglie:1 shall:5 object:1 most:1 connected:1 nothing:3 mach:1 constructed:1 considered:1 clear:1 later:2 physica:2 order:3 inde:1 feynman:3 points:3 exp:12 velocity:9 physics:14 sum:3 fact:4 show:7 bring:1 relation:8 solutions:1 trivial:2 d3:1 fifth:1 absoluteness:2 x1:4 parameters:3 situations:1 peculiar:1 lemma:1 only:7 postulated:1 local:3 hope:1 continuity:1 do:1 his:1 3m:2 mehdi:1 undivided:1 dependent:2 simplified:1 express:1 ones:1 words:2 new:1 dt:3 areas:1 qp:24 densities:1 fields:1 arxiv:1 mon:1 summary:2 paper:1 aeg:1 contain:2 including:1 dpi:44 view:1 2nǫ:1 38b:1 set:2 constructing:1 achieved:1 physically:1 unpublished:1 uses:1 relative:3 depends:1 radius:2 result:7 discussions:1 led:2 forthcoming:2 nonlocality:3 αs:13 gravitation:5 exponent:1 ways:1 pattern:1 shimony:1 definite:1 propagates:2 symmetric:1 written:7 between:8 invariant:4 reading:1 conditions:1 email:1 terms:16 2αs:1 nature:2 weak:1 configuration:2 distribution:1 suggested:2 both:4 interpretations:1 many:5 taking:1 infinitely:1 equal:5 propagation:2 retarded:1 expression:4 otherwise:1 point:6 lagrangians:2 others:2 addisonwesley:1 constant:6 throughout:1 kp:1 combines:1 transformations:6 addition:3 locally:1 due:1 been:3 ph:1 prototype:8 abstract:1 systems:1 obtained:2 describe:1 corresponding:1 wheeler:3 astron:1 fokker:4 spirit:1 present:3 mashhoon:1 case:5 look:1 exponential:4 existance:1 value:1 will:1 while:3 suppose:4 applies:1 determinism:1 situation:1 property:5 discretize:1 ir:1 thus:7 non:1 itself:1 il:2 elsevier:1 mod:2 technology:1 containing:2 develop:1 etc:1 things:1 make:2 lett:1 same:4 x2:1 unity:1 parts:3 quant:1 viewed:1 finite:3 difficult:1 used:2 infinity:1 see:5 forced:3 upon:2 hand:1 αs2:3 postulation:1 barbour:8 26b:1 infinite:3 identity:3 electromagnetism:4 task:1 acknowledgement:1 well:2 obviously:1 bohm:18 sets:1 position:10 model:5 self:2 charged:2 distances:6 just:3 less:1 observed:1 newton:5 pergamon:1 obtain:1 gravity:5 shape:1 formulated:1 distant:1 predicts:2 spherically:1 facts:1 speed:1 yet:1 previous:3 density:12 photons:4 bell:2 seems:3 leibnitz:5 internal:6 location:2 theorem:1 apart:1 acted:1 identical:2 aspects:2 magnify:1 represents:1 rules:1 sums:1 possible:4 five:1 know:1 press:2 using:5 highly:1 ruled:1 necessary:2 like:8 particle:48 follows:1 reduces:1 unnecessary:1 specific:3 either:3 arbitrary:3 works:1 quantal:6 exceed:1 because:3 classical:2 people:2 squires:2 30r:1 some:16 understood:1 examples:1 choosing:1 proper:1 provided:3 scale:5 describing:2 lead:2 electromagnetic:2 avoid:1 legal:2 instantaneous:1 provides:1 prog:1 prof:1 proc:3 limitations:1 obey:1 equivalent:2 agreement:1 expansion:1 step:1 although:6 found:1 tautological:3 throw:1 publishing:1 about:1 carried:2 instantaneously:1 universe:5 discussed:1 o:2 essential:2 range:2 plus:5 act:1 bertotti:2 introduced:1 differentiable:1 soc:4 own:1 presence:2 h2:1 maxwell:5 obtaining:1 multiply:1 appropriate:1 right:1 references:1 einstein:1 operator:2 factor:6 schrodinger:1 her:1 assumed:3 there:4 u0:12 long:1 accordingly:2 noting:1 physicists:1 way:3 was:5 function:11 elsewhere:2 newtonian:3 phenomena:3 removes:1 but:12 philosophers:1 construction:1 understandable:1 delta:5 true:3 he:5 made:5 born:1 gravitational:3 up:1 us:2 quences:1 below:2 limit:1 problem:1 similar:6 called:1 mechanics:6 ac:1 phil:1 proved:2 worthwhile:1 ai:12 certain:1 universal:1 aj:3 general:1 αl:2 single:1 exist:1 relates:1 physical:5 incorrect:1 functions:1 faithful:1 no:11 when:7 virtual:1 sharif:1 field:6 other:9 role:1 department:1 mathematics:1 company:2 conclusion:2 francisco:1 kinds:1 felt:1 problems:1 transported:1 important:4 camb:1 structure:5 faster:1 assume:5 clauser:1 factors:1 mass:2 time:11 far:1
|
quant-ph9612020.txt |@word ali:1 magnetic:1 results:3 four:1 preserves:1 calculate:2 golshani:13 finally:1 stable:1 fax:1 very:1 minded:1 experimentally:1 founded:1 presented:2 solution:3 correct:1 manifestly:1 dis:1 ten:1 consistent:2 ted:1 prediction:1 nbt:8 second:2 what:2 section:3 above:1 new:1 increasing:1 body:3 q1:3 iran:2 mr:1 atoms:6 asymmetry:1 others:2 equations:3 change:1 box:2 institute:1 study:1 dri:2 t21:2 studies:1 formulated:1 highly:1 glance:1 use:3 would:2 covariant:1 squires:3 m1:8 m2:9 theoretical:1 sort:2 odinger:2 basically:1 iii:2 must:5 mc:1 equation:4 work:1 mi:4 obvious:1 ρv:1 following:4 dec:1 example:1 stated:1 calculation:2 relativistic:3 involve:1 lorentz:1 want:1 sense:2 hydrogen:6 needs:1 rather:1 write:1 instead:1 ensemble:1 simplicity:1 objectively:1 law:2 natural:1 third:2 light:1 explicit:2 accelerated:3 so:3 order:3 ith:3 move:1 mainly:1 meter:2 experiments:1 london:1 differs:2 satisfies:1 ln:10 coordinates:2 writing:1 degrees:1 fig:1 defining:1 non:1 now:1 easily:2 term:1 always:1 university:2 2x:2 2y:2 sin:2 2c:1 accompanied:1 side:1 domain:1 energy:5 related:1 year:1 quantum:4 beyond:1 out:1 shown:5 rep:1 since:2 rev:1 particles:6 collisions:1 rc:4 rn:1 ri:1 rj:6 shows:2 theory:20 found:1 standard:3 clarify:1 york:1 care:1 definition:1 r0:3 r1:2 r2:3 r3:1 v2:1 times:2 motion:5 mvc:1 first:3 xj:5 xn:6 xc:2 reflected:1 xx:5 done:1 least:1 given:5 checked:1 temperature:1 introduction:1 system:11 relations:2 assumption:1 postulate:1 x2:9 x1:15 than:1 inventor:1 relative:1 holland:1 zero:1 represents:1 seen:1 clearly:2 shojai:14 acceleration:3 self:5 isolated:4 note:3 potential:4 electric:1 shall:1 any:2 calculated:2 heating:1 kt:1 velocity:6 physics:3 sum:1 fact:4 tehran:2 solutions:1 postulates:2 q2:3 iet:2 should:2 local:2 do:1 mehdi:1 means:1 ones:1 dt:2 2mi:3 arxiv:1 investigate:1 paper:1 predicted:3 observed:1 sec:2 result:3 terms:2 fails:1 αt:1 dipole:1 written:2 jth:1 between:2 propagated:1 email:1 recently:1 2αc:5 extent:1 distribution:5 observable:4 cos:3 equal:1 etc:1 retarded:19 contribution:1 estimation:1 point:1 simple:2 simply:1 cr:3 considers:1 leads:3 three:2 ph:1 define:1 quadrapole:1 quantities:1 gas:2 c2:8 present:1 novel:1 rbt:6 evaluated:2 eik:1 vc:2 ir:1 thus:1 according:1 ii:2 technology:1 different:1 same:2 orders:1 strange:1 quant:1 used:1 kelvin:1 effect:4 hand:3 v1:1 moment:2 potentials:1 schr:2 center:9 charges:1 bohm:19 solve:1 components:1 position:2 spherical:2 r03:1 actions:1 via:3 questions:2 previous:1 nonrelativistic:1 seems:1 lett:1 samples:1 east:1 real:1 unstability:3 rnl:1 increases:1 hiley:1 know:1 press:1 using:1 ipm:1 like:8 particle:4 unstable:1 works:1 because:4 classical:2 some:6 respect:1 lead:1 electromagnetic:1 t12:2 eiφ:1 properties:1 about:3 extension:2 2ct:1 universe:1 dependence:1 o:11 2i:2 compatible:1 introduced:1 cambridge:1 right:1 references:1 pl1:1 normalised:1 there:4 question:2 conservation:2 way:1 assumes:1 function:8 hx:1 hy:1 form:1 but:1 heat:1 atom:3 whether:1 us:2 assume:3 converted:1 problem:5 called:1 distance:1 mechanics:2 ac:1 constant:2 defined:1 abstract:1 general:1 formalism:2 physical:1 again:1 no:1 when:2 sharif:1 field:2 other:3 tii:1 tij:5 department:1 mathematics:1 tribution:1 perturbatively:1 age:1 interval:1 equivalently:1 mass:9 time:9 having:1
|
quant-ph9612021.txt |@word distances:1 now:2 since:1 interpretation:5 consider:3 ali:1 guided:1 particular:1 observed:2 four:5 bandwidth:1 underlying:1 relation:2 statistical:1 mentioned:1 momenta:2 macroscopic:2 its:1 section:1 current:1 claim:1 rapidly:1 golshani:10 ln:1 show:4 seems:1 nonlocal:1 mathematically:1 only:1 version:1 imt:1 under:4 jacobi:1 fermionic:1 defining:1 over:1 momentum:4 continuity:1 do:1 non:1 dk:4 mehdi:1 distance:1 far:1 de:1 possible:3 investigated:1 wave:4 ones:1 hamilton:1 they:1 new:1 press:1 experimentally:1 thus:2 unique:1 encounter:1 densities:1 easily:1 necessary:1 like:5 particle:14 level:2 fields:5 university:2 arxiv:1 identified:1 manifest:1 large:1 vector:1 reasonable:1 succession:1 london:1 inter:1 separations:3 typical:1 integrand:3 domain:1 because:1 methods:1 deal:1 energy:2 some:2 solution:5 connections:1 second:1 individual:1 value:1 quantum:3 wavelength:1 kf:1 even:1 shown:3 scale:1 lead:1 space:4 review:1 shall:2 definite:1 ak:2 d3:7 particles:4 may:3 does:1 localized:1 above:1 invariant:2 conditions:4 email:1 contrast:1 shows:2 averaging:1 iran:2 theory:7 localization:1 equivalent:1 ikx:1 mω:2 possibility:1 otherwise:1 behaviour:1 difficulty:1 york:1 inverse:1 no:1 making:1 ratio:1 dictated:1 kd3:2 box:2 both:1 cos:5 numerator:1 r2:6 always:1 institute:1 many:2 region:1 larger:4 accepts:1 so:1 o:2 page:1 motion:14 covariant:2 intervals:1 gordon:5 faces:1 domains:1 argue:1 studies:1 first:2 invalidate:1 already:1 conclude:2 ipm:1 dimensional:2 references:1 least:2 home:1 bosonic:6 causal:6 seen:1 necessarily:1 integrals:1 leads:1 prove:1 introduction:1 positive:1 there:1 construct:1 next:1 dη:2 noting:1 bosons:1 therefore:1 kµ:3 m2:6 ph:1 dx:2 theoretical:1 define:1 function:2 observable:3 becomes:1 concerning:1 factor:1 2r2:1 but:2 long:2 basically:1 authors:1 tehran:2 cases:1 dt:6 than:12 must:1 case:2 iωt:2 xi:1 holland:1 equation:8 see:1 us:1 will:1 nevertheless:1 ωk:1 assumptions:1 suppose:1 universe:1 following:1 demonstrate:1 problem:1 dec:1 dkdk:2 ki:2 mechanics:1 real:1 ac:1 interval:1 constant:1 figure:2 defined:1 relativistic:3 abstract:1 ir:1 neglected:1 argument:1 general:2 hiley:1 ik:1 lorentz:3 exist:1 dxi:2 our:1 been:1 technology:1 clearly:1 shojai:11 absolute:1 routledge:1 again:1 functions:2 any:1 klein:5 zero:1 ghose:1 rather:1 undivided:1 when:1 lett:1 sharif:1 unity:2 occasionally:1 quant:1 emphasize:1 department:1 mathematics:1 ordinary:1 trajectory:1 conclusion:1 happens:1 briefly:1 broglie:1 superluminal:12 less:5 aexp:1 denominator:1 averages:1 what:1 extending:1 paper:1 a2:4 moving:1 letter:1 velocity:9 cambridge:1 invariance:1 normalization:1 suitable:1 faster:2 assume:2 light:4 average:5 sometimes:1 well:1 bohm:5 objection:1 mass:1 exp:6 time:4 serious:1 kx:6 physics:3 order:1 fact:3 laws:1
|
quant-ph9612022.txt |@word concept:2 consider:2 ali:1 lack:2 dynamic:2 results:3 leads:3 roy:1 consists:1 reasoning:1 localized:2 whose:2 presenta:1 calculate:2 golshani:17 tp:2 answered:1 does:3 weakening:1 under:5 analogous:2 fax:1 very:1 translations:2 electron:1 condition:1 irreducible:1 t2:1 solution:1 deals:1 solved:1 vector:4 section:2 eigenvalues:3 foldy:2 dealing:1 zero:3 ǫu1:1 silagadze:1 copenhagen:1 canonical:6 what:2 brackets:2 sum:1 favour:2 d3:3 above:1 new:11 net:1 consisting:1 wavefunctions:1 iran:2 respectively:1 component:1 behaviour:1 desired:1 pub:1 path:1 equations:3 interpret:1 box:2 search:1 arrive:1 institute:1 leaves:1 changed:1 suggests:2 amount:1 survey:1 poisson:3 fourier:1 studies:1 orthonormality:1 ipi:1 ipm:1 unit:2 use:1 would:2 probabilities:1 positive:1 ψq:1 classically:1 linear:1 call:1 therefore:1 m2:1 k0j:1 theoretical:2 th:1 operators:5 apparent:2 appendix:3 known:3 must:7 states:1 springer:1 equation:7 work:4 following:2 dec:1 example:1 stated:1 relativistic:3 high:1 want:1 allowed:1 hydrogen:1 verlag:1 rather:1 write:3 instead:1 ordinary:1 u21:2 simplicity:1 tried:1 algebra:1 may:2 suppose:1 after:3 derived:3 tries:1 representations:3 natural:2 sk:1 sj:1 si:1 so:5 representation:3 first:2 order:1 operations:2 unsolved:1 interpretation:1 reversal:3 constituents:1 move:3 satisfied:1 differs:1 still:2 its:7 roots:1 before:1 group:8 symmetry:1 relativity:1 coordinates:4 forms:1 systems:2 derivative:1 defining:1 overcome:1 symmetrization:1 non:4 good:1 propose:1 introduce:1 framework:1 they:3 now:4 discuss:1 easily:2 inversion:2 dirac:1 always:2 university:1 identified:3 reasonable:1 found:1 side:2 doing:1 energy:2 related:1 operator:60 used:3 poincare:7 measurement:1 quantum:8 our:6 special:1 shown:8 space:8 nuovo:1 since:2 rev:3 particles:28 acting:1 correct:5 math:1 antiunitary:2 theory:1 differ:1 free:1 standard:5 difficulty:1 reason:1 term:1 derivation:1 starts:1 could:1 days:1 introduction:1 massive:3 δij:3 july:1 heuristically:1 initial:1 probability:1 done:1 least:1 precisely:2 angular:1 1p:1 given:1 bracket:1 πj:1 system:7 relations:6 their:3 πp:1 assumption:1 calculations:1 final:1 speaking:1 lot:1 jordan:1 tehran:2 translation:5 than:1 unfortunately:1 accordance:1 cimento:1 second:3 determined:1 recovered:1 represents:1 enables:1 symmetries:1 unchanged:1 argument:1 peculiar:1 conjugate:1 seen:3 clearly:1 shojai:18 forced:1 able:1 note:3 k2:1 k0:4 finding:4 accuracy:1 heisenberg:1 added:1 shall:3 object:1 simplify:1 rigidly:1 why:1 inconsistency:1 localizable:1 hj:1 subtracted:1 consequences:1 kk:1 kj:3 clear:1 tγ:1 ks:1 points:1 principle:2 exp:1 kt:1 velocity:4 effect:1 physics:4 notion:1 fact:3 omnes:1 show:3 delta:1 foregoing:1 ki:6 relation:22 wigner:8 find:1 postulates:1 q2:3 causality:3 knowledge:1 spite:2 should:1 only:5 generators:1 factor:1 mehdi:1 means:1 expectation:1 cannot:1 words:1 during:1 dt:1 dp:1 dq:1 qt:1 arxiv:1 qi:11 qh:1 qk:1 qj:3 set:1 constructing:1 reference:5 achieved:1 physically:1 frame:9 observed:1 argued:1 depends:1 result:4 pryce:6 satisfying:1 commutation:14 review:1 definite:1 rejecting:1 state:3 boosts:2 between:3 encounters:1 email:1 terms:2 august:1 jt:1 comi:1 ji:5 jj:1 jk:2 observable:2 last:1 uncertainty:5 according:4 quantization:1 april:1 casimir:1 mourad:2 hσ:1 experimental:2 nonrelativistic:1 simple:1 lpthe:1 pq:2 transformations:2 basis:1 been:2 change:1 pj:19 pk:1 ph:1 pi:10 empty:1 choose:1 obtained:2 direction:5 corresponding:1 concerning:1 photon:3 c2:2 c1:1 careful:1 spin:2 present:1 case:6 p1:2 look:1 ǫj:1 value:1 will:1 while:1 replaced:1 property:3 procedure:1 unitary:1 iq:1 ip:4 ir:1 thus:8 equal:5 ih:3 reads:2 eˆ2:1 il:1 technology:1 orbital:1 φq:8 verified:1 began:1 any:7 complex:1 quant:1 arguments:1 constructed:2 events:1 independent:1 arrives:3 peaks:1 see:2 slac:1 iǫijk:6 hand:2 v1:2 v2:2 uses:1 center:1 nevertheless:1 well:3 solve:1 components:9 coordinate:1 position:65 manifold:1 newton:7 rest:2 proposes:1 via:2 facts:1 momenta:3 macroscopic:1 eigenstates:1 previous:1 intersection:1 preprint:2 localizability:4 photons:1 conclude:1 character:1 except:1 transformed:1 lett:1 mod:1 transformation:3 momentum:13 eigenfunction:1 eigenvalue:4 dφq:1 possible:1 early:1 helicity:4 birth:1 using:5 unique:2 formal:1 like:1 particle:15 follows:3 works:3 essential:1 therein:1 because:4 classical:6 people:1 some:3 nonzero:1 affects:1 investigations:1 behave:1 proc:1 inserting:1 eigenfunctions:3 meanings:1 dictates:1 although:1 about:3 o:2 compatible:1 covariant:1 involving:2 soc:1 h2:1 lenght:1 rotations:1 down:1 hermitian:3 right:2 references:2 elementary:8 56a:1 technically:1 iδij:2 there:4 u1:3 transform:2 u2:9 restricts:1 way:3 translate:1 function:3 himself:1 complete:2 form:1 ht:1 volume:1 atom:1 instructive:1 attached:1 up:2 us:1 until:1 below:1 limit:3 problem:9 called:1 mechanics:7 ac:1 constant:1 worthwhile:1 defined:1 abstract:1 measure:1 meaningless:2 general:3 exist:2 moves:1 commuting:8 physical:2 no:5 wavefunction:3 when:6 sharif:1 other:3 role:1 department:1 mathematics:1 you:1 massless:27 conclusion:1 picture:1 mechanical:1 bacry:1 generated:1 important:2 observables:3 longer:1 assume:3 rule:1 investigated:1 mass:1 volumes:1 time:10 serious:2 having:4
|
quant-ph9612023.txt |@word represent:2 customary:2 consider:5 remarkable:1 ali:1 squared:1 pte:1 results:8 leads:11 αr1:2 generalize:4 contains:1 transversally:1 consists:3 follow:1 reasoning:1 seemed:1 whose:1 depend:2 calculate:3 indices:1 golshani:46 similarity:1 created:3 presents:3 answered:1 charge:4 present:2 stable:4 eβ:7 norm:2 fax:1 straightforward:2 very:6 kcl:1 assuming:1 αrn:2 wave:16 chooses:2 interpreting:1 fall:1 zµ:2 ln:1 difference:3 matrices:3 rn:14 four:6 annihilated:2 y1:8 presented:4 positions:1 applicable:5 large:2 vector:3 guiding:2 small:2 eigenvalues:1 equation:16 configurations:1 governing:1 unexpected:1 force:76 dealing:1 direct:25 sign:6 go:2 second:11 concludes:1 copenhagen:18 choices:1 permutations:1 eigenspaces:1 canonical:2 even:1 aim:1 what:3 causally:1 incompatible:3 section:8 foregoing:3 expressed:1 d3:9 current:4 version:3 above:8 new:6 method:3 contrast:2 satisfy:1 simultaneously:1 degree:4 respectively:1 here:8 understanding:5 behaviour:4 free:1 groups:1 others:1 represented:3 path:3 xα:2 equations:23 z1:1 change:6 box:6 great:1 ref:1 zr1:2 difficulty:1 institute:1 until:1 larger:2 contradiction:1 leaving:1 spins:3 usually:1 suitable:2 studies:1 writes:1 emerge:4 via:3 useful:1 merely:3 explained:1 logical:4 objectively:9 immediately:1 total:3 tools:1 causal:6 derivatives:7 use:9 takes:1 would:9 formulated:1 positive:3 give:1 predictions:1 next:2 classically:1 approach:3 call:3 therefore:7 m2:24 conservation:4 ηk:1 tell:1 reflects:1 more:9 introducing:2 rgµν:1 relax:1 outputs:2 company:1 under:2 corrected:2 odinger:3 appendix:13 varying:1 known:2 cases:3 producing:1 must:26 fly:1 high:3 account:2 tachyonic:1 word:1 anything:1 mc:1 effectively:1 setup:1 work:2 modified:1 theories:2 ρp:1 remain:2 lorentz:2 values:1 following:8 making:1 dec:1 example:3 decoupled:1 stated:2 process:4 relativistic:68 choice:1 allowed:2 states:2 indicates:2 slit:2 assumptions:4 something:1 sense:2 hydrogen:1 calculated:1 absolute:1 end:3 e2q:1 rather:1 s2:2 discussion:1 acts:1 feature:1 write:6 how:2 answer:1 instead:5 axis:1 ensemble:8 inputs:2 untill:1 description:1 superluminal:5 may:14 after:2 derived:12 tries:1 produce:1 1993b:2 1993a:5 cambridge:1 law:2 constants:2 goal:1 short:2 natural:2 effective:9 departure:1 element:2 accelerated:1 ones:1 so:34 fundamental:4 parti:1 lξ:1 representation:4 order:6 gµν:5 origin:1 ohanian:2 interpretation:3 ith:3 produces:1 laboratory:1 move:4 expects:2 stability:1 paper:1 through:4 statistical:5 hµν:4 argued:2 kinetic:1 y2:4 its:12 roots:1 before:2 lg:1 derive:2 τj:1 symmetry:1 fit:1 τi:2 chosen:3 cle:1 relativity:1 coordinates:1 him:1 microscopic:1 systems:3 jacobi:2 derivative:2 overcome:1 yi:5 symmetrization:1 them:3 yj:2 return:1 integral:5 practice:2 evolution:2 introduce:4 framework:4 hamilton:2 they:9 half:8 foot:1 advantage:1 ys:4 now:11 represents:5 term:2 finite:2 dirac:5 name:1 publication:1 always:3 university:2 level:2 possibilities:4 radial:1 2m:6 higher:1 2h:4 mean:2 spinor:1 domain:3 differential:1 directly:2 lam:3 doing:3 energy:9 mv:2 reduce:2 gaussian:2 related:3 solution:3 antiparticle:4 extended:2 obtains:4 measurement:5 quantum:143 our:10 beyond:1 event:2 out:4 deals:1 shown:11 matrix:2 space:6 furthermore:1 since:4 lagrangian:10 semi:2 particles:41 behaviours:3 investigation:1 performs:1 reader:1 formula:4 get:1 evaluation:1 correct:2 shows:1 theory:55 barrier:1 interactions:7 mω:3 differ:2 possibility:2 standard:3 extraordinary:1 completely:3 advantages:1 intermediate:1 e2:1 definition:1 interaction:26 r1:15 r2:1 αs2:5 could:1 pictures:1 times:2 motion:37 thing:1 gordon:2 circuit:2 signature:1 corrections:9 uses:1 x1:14 first:13 xj:2 there:17 probability:2 spoken:1 relate:1 confuse:1 number:6 approximate:1 multiplying:1 done:5 approximately:1 another:6 impossible:1 apparent:1 open:2 given:9 necessarily:1 antiparticles:6 discussed:1 πe:1 introduction:1 leading:4 ǫr1:1 system:11 relations:5 their:2 assumption:4 observations:2 calculations:3 smoothen:1 postulate:5 electromagnetism:1 final:2 gives:3 relationship:2 explanation:1 exactly:1 interesting:1 absorbed:1 part:5 predictable:1 too:1 authors:1 tehran:2 eliminated:1 believe:2 than:3 character:1 expanding:1 kind:2 determines:1 holland:7 sections:2 zero:10 submitted:1 peculiar:1 annihilation:4 matter:1 therfore:1 were:1 negatively:1 enables:4 treated:1 remembers:1 descriptions:2 pre:1 plus:1 sees:2 electrodynamics:1 measure:1 locations:1 generalization:5 summing:1 say:5 manner:1 need:4 seen:5 seem:2 saw:3 any:23 shojai:60 gspin:2 forced:1 depending:1 convenient:1 latter:3 responsible:1 gravity:3 note:15 mix:1 potential:46 square:1 generalized:1 forces:3 xi:6 gravitons:2 spacetime:1 heisenberg:1 begin:1 broglie:17 electric:3 shall:5 denominator:1 αs:2 z2:2 gravitation:1 plan:1 claims:1 phase:3 lagrangians:2 measured:3 why:2 xµ:2 zrn:2 found:2 don:1 consequences:1 considered:2 clear:1 later:2 steady:3 looked:1 points:1 electrons:6 principle:4 exp:16 αx:2 iaµ:1 velocity:7 left:1 physics:8 calculates:1 fact:11 laws:3 undivided:1 show:2 delta:3 categorize:1 favour:1 discovered:1 x2:10 relation:10 solutions:2 d4:19 find:1 postulates:1 finally:3 based:1 parameters:1 situations:1 guidance:2 distributed:1 written:9 should:2 lemma:2 only:10 experiment:3 black:4 summarizing:1 factor:2 integrate:2 µi:1 circle:1 local:1 continuity:1 do:7 mehdi:1 means:4 familiar:1 de:17 antisymmetrization:1 soon:1 cannot:6 negative:1 words:3 invariant:2 during:1 dt:2 aκ:1 klein:2 geometric:1 produced:2 processes:1 densities:4 fields:17 µ2n:4 arxiv:1 xµi:1 rotationally:1 investigate:1 experiments:4 predicted:2 contain:2 including:1 fixed:1 terminology:1 view:4 kernel:10 set:3 predicts:2 exists:3 achieved:1 clarified:2 exerted:1 2c:1 j0:9 j1:1 arrives:1 up:7 observed:4 differentiation:2 depends:4 result:16 discussions:1 iran:2 j2n:2 dpµ:2 αr:1 draws:1 tensor:5 ways:1 jumped:1 away:1 definite:2 state:8 determined:1 ermions:1 discovers:1 closed:1 between:6 noting:2 boundary:1 conditions:4 email:1 choose:1 notice:2 terms:10 2αs:1 extend:2 nature:1 importance:1 however:1 ltd:1 jn:4 multiplies:1 group:1 atoms:9 problem:9 succesful:1 τk:1 suggested:1 observable:2 interpretations:1 prescription:1 xµ1:1 many:4 region:1 uncertainty:1 according:2 minus:2 etc:3 faces:2 argue:1 coloumb:1 experimental:1 otherwise:4 co:1 hausdorf:2 nonrelativistic:9 simple:1 seems:3 acted:1 xν:4 directions:1 ψi:1 simply:2 consideration:1 cancel:2 constant:9 accordingly:3 testable:1 considers:3 speak:1 ensures:1 described:1 publishing:1 puts:1 basis:2 addition:2 three:4 ai:14 reduction:3 describes:1 interpret:1 basic:1 expected:1 ph:1 abstract:1 empty:1 define:2 wants:3 obtained:4 aj:2 corresponding:2 deeper:3 both:2 quantities:4 thousand:1 writting:1 convert:1 argument:1 understand:1 c2:21 careful:1 spin:46 former:1 those:1 case:29 eis:2 p1:1 look:2 exponential:2 appearance:1 conserved:4 evaluated:1 transformation:4 will:8 rests:1 suppose:5 situation:3 property:5 identical:1 century:3 almost:3 ne:2 metric:5 ir:2 thus:11 non:2 equal:3 reads:1 sudden:1 curved:2 technology:1 currents:3 begining:1 different:10 develop:1 halfinteger:1 suggest:2 make:1 norton:1 radiation:1 same:8 clearly:1 κtµν:1 parts:2 quant:1 viewed:1 several:1 couple:1 difficult:2 status:1 routledge:1 used:3 infinity:2 hαβ:1 see:8 absorb:1 logic:3 upon:1 hand:5 action:9 moment:1 moving:5 hγδ:1 potentials:1 infinite:1 invariance:1 cµ:1 recent:1 task:3 schr:3 pµ:2 charges:2 expression:1 motions:1 simplicity:1 well:6 deal:2 bohr:1 bohm:29 without:1 sets:1 position:9 simplified:1 charged:5 things:1 world:1 1994b:1 departed:1 just:1 1994a:2 being:1 guided:1 newton:1 obtain:3 rest:8 homogeneity:1 sources:1 shape:1 underlying:3 transforms:1 questions:2 using:9 facts:4 sharif:1 scattering:2 yet:1 previous:6 accepted:1 flying:1 density:13 photons:2 point:3 had:1 source:2 setting:3 ρu:1 location:2 versa:1 theorem:2 input:1 eigenstate:1 momentum:9 take:1 real:9 iλ:1 spinless:5 around:3 rev:2 easily:5 rules:1 evaluate:1 λe:1 decomposed:2 xs:6 possible:4 dewdney:2 hiley:1 background:1 rµν:1 press:1 integer:5 ipm:3 gr:1 domains:1 like:8 particle:69 tµν:1 obvious:3 δr:1 isotropy:1 noted:4 specific:2 δl:5 unstable:1 either:5 arbitrary:1 output:1 ie:2 works:1 stationary:3 quantal:5 towards:3 mathematical:2 satisfactory:1 because:12 methods:1 classical:14 creation:4 some:18 understood:1 repeat:1 respect:3 complementarity:1 provided:2 scale:2 describing:1 lead:3 electromagnetic:12 avoid:2 opposite:1 integration:1 ak:7 does:8 eliminate:1 provides:3 timelike:1 ct:1 minimal:1 backer:2 object:1 measurment:5 reaching:1 fermions:3 equivalent:3 each:4 expansion:1 defines:1 step:2 departures:1 although:4 accompanied:1 refers:2 properties:2 stage:1 about:4 kinematical:1 carried:2 extension:5 instantaneously:1 universe:1 ranges:1 dependence:1 o:4 essential:2 covariant:1 range:3 nothing:1 obeys:1 j2:3 introduced:4 slightly:2 nµ:1 considerations:1 own:1 follows:5 maxwell:7 into:3 radiate:3 ηi:1 balances:1 down:4 device:6 appropriate:5 right:2 references:1 determine:2 einstein:1 proportional:2 smoothening:1 forget:1 statistics:5 additional:1 infinitesimal:1 initial:3 question:2 u0:8 long:2 u2:2 aν:5 restricts:3 much:1 bosons:5 physicists:2 way:6 scientific:1 was:5 assumes:2 third:1 function:29 himself:3 elsewhere:1 form:7 energies:1 last:2 but:17 aµ:23 atom:2 line:1 role:1 raising:1 coupling:1 sourceless:2 made:1 places:1 instructive:2 minkowski:1 smooth:3 maximum:2 us:7 theoretical:1 ieα:1 exerts:1 limit:2 decomposable:2 distribution:2 similar:7 called:6 mechanics:21 ac:2 sometimes:1 successfully:1 worthwhile:4 lowering:1 defined:7 implications:1 universal:2 describe:1 meaningless:1 general:4 proper:1 engineering:1 exist:4 formulation:5 formalism:5 physical:2 again:2 functions:3 faithful:1 no:17 uµ:1 wavefunction:3 when:4 detail:1 reality:2 field:18 other:17 electrical:1 department:1 mathematics:1 you:1 conclusion:7 picture:4 elements:2 problems:2 variation:3 ǫr2:1 replace:2 important:5 nucleus:3 serious:1 variable:3 correlated:1 auxiliary:7 prevalent:1 vice:1 assume:12 dτ:2 packets:4 4m:2 mass:9 time:12 far:1 observables:4 quantity:1 rep:1
|
quant-ph9612024.txt |@word limited:1 concept:2 homomorphism:2 crucial:1 global:1 results:2 existing:1 adjective:1 jawaharlal:1 supplement:2 overlap:3 houches:1 follow:1 expressions:4 whose:1 replacements:1 integral:2 paris:1 concerned:2 finally:1 indicate:1 adjoin:2 elliptic:1 under:1 hermann:1 analogous:3 characterised:2 norm:2 p2:2 straightforward:1 orthogonal:1 very:1 translations:1 noncommuting:1 dokl:1 wave:5 cot:1 novel:1 every:1 emphasized:3 little:1 matrices:2 founded:2 irreducible:3 solution:1 deals:1 convenience:1 vector:7 phase:2 avoiding:1 eigenvalues:1 optics:4 foldy:2 ten:1 sℓ:1 dealing:1 lubanski:1 zero:3 pass:1 iσ3:1 iσ2:2 choices:6 eik3:2 theory:2 even:1 employ:1 what:2 down:1 diag:1 section:6 expressed:1 find:3 indian:2 subspaces:1 obvious:1 boost:1 contrast:1 degree:2 respectively:6 component:2 here:14 diagonal:1 behaviour:1 guise:1 identifications:2 les:1 particules:1 separation:3 others:1 alone:1 obtained:1 ref:1 institute:2 involved:4 leaves:1 vectors:9 amount:1 products:1 pick:1 action:10 birefringent:1 makes:1 helps:1 involves:1 emerge:1 via:1 useful:1 projection:1 kinematically:1 eiφ:1 replace:1 addressed:1 total:1 unit:2 standing:1 use:5 handled:1 would:3 nehru:1 distinct:1 positive:8 contains:1 definiteness:2 noting:1 therefore:2 centre:2 m2:4 taken:2 doubling:2 theoretical:1 more:1 orthochronous:1 becomes:1 operators:14 factor:2 nontriviality:1 carrying:2 rigid:1 labelled:1 particular:5 known:2 iii:1 must:3 obeying:1 account:2 include:1 extension:1 science:2 work:4 infinitesimal:1 values:2 three:1 following:3 nonsingular:1 dec:1 example:1 numbers:2 gµσ:1 gµρ:2 omit:1 relativistic:5 choice:1 preserving:1 india:1 purposes:1 states:16 effectively:1 lorentz:9 something:1 arise:2 unphysical:1 handle:2 tan:1 pν:3 conversely:1 occur:1 axis:1 respective:1 pseudovector:1 end:1 s3:18 switches:2 six:1 feature:1 write:1 how:2 nontrivial:7 pure:2 familiar:1 answer:2 explains:1 sin:6 circular:3 upto:1 inputs:1 de:1 description:7 algebra:4 may:7 suppose:1 earlier:6 singularities:2 containing:2 tied:1 hence:1 plane:1 representations:6 law:1 changes:1 physical:3 dynamical:1 four:6 light:5 correspond:2 su:30 mjk:1 sk:1 sj:1 switch:1 ones:3 so:16 allow:1 sl:16 definitions:4 se:1 acts:1 wigner:6 indeed:3 over:3 choose:1 stability:2 introductions:1 paper:3 including:2 mentioned:1 existence:1 jℓ:1 its:2 refs:1 before:2 supplemented:1 group:11 chosen:1 bringing:1 fix:1 pct:1 systems:6 arguments:1 correspondence:2 constructible:1 rotations:3 polarizations:3 introduce:1 framework:1 effects:1 they:1 half:2 rotation:5 now:9 easily:1 2p:4 2s:2 invariants:3 traced:1 revert:1 each:11 accommodated:1 quarter:1 lorentzian:1 homogeneous:3 domain:1 ellipsometry:1 another:2 ed:1 energy:20 reduce:2 related:3 conventions:2 elementary:5 used:1 connect:1 measure:1 quantum:2 gµν:1 operation:2 special:2 out:6 respects:1 ultimately:1 realising:2 space:37 restricted:1 tried:1 since:8 squared:2 research:1 particles:3 acting:7 reader:1 denoted:1 get:3 cause:1 math:1 shows:1 benjamin:1 exactly:2 after:1 linear:3 written:2 differ:1 free:3 standard:3 york:1 usual:2 beginning:1 generate:3 additional:1 r4:1 definition:2 qj:1 r3:3 could:1 transition:2 times:2 turn:3 relativistically:1 massive:4 consequence:1 exhibited:1 south:2 first:5 already:1 features:6 symmetry:1 omitted:2 variables:3 primary:1 sssr:1 done:3 construct:3 directly:2 carry:1 impossible:1 open:1 angular:1 computed:1 given:7 discussed:1 needed:1 introduction:1 leading:1 cited:1 relations:5 1a:1 their:5 1b:1 too:1 calculations:2 eqn:14 unambiguously:1 recovered:1 dutta:1 accompany:1 statement:1 continuous:1 immediate:1 j1:1 optical:1 natural:1 eliminated:1 representing:2 than:1 polarized:2 third:1 likely:1 ǫh:1 classes:1 ap:1 were:2 treated:2 ann:2 argument:1 say:2 manner:7 unaltered:1 need:6 seen:1 element:6 linked:3 contents:1 lie:2 constructions:6 angle:2 built:3 convenient:1 separate:2 able:1 polarization:27 k2:1 ideal:1 take:3 timelike:7 new:1 wonder:1 subscripts:1 begin:2 towards:1 unless:1 fundamental:2 opposite:1 any:8 consistency:1 paid:1 algebraic:1 involving:1 but:3 representation:5 remarks:2 intrinsic:3 shirokov:2 eigenfunctions:1 consequences:1 kj:1 clear:2 later:2 face:1 kp:1 electrons:2 principle:2 clean:2 subgroup:7 physics:2 naively:1 fact:3 12a:1 12b:1 show:1 appearing:1 notations:2 bring:3 wµ:6 spaces:1 relation:2 trivial:2 d3:2 based:2 behind:1 topological:6 should:1 freedoms:1 only:6 going:1 generators:14 arvind:1 developed:2 equally:1 preliminaries:1 do:2 sense:1 notation:1 means:2 dependent:4 simplified:1 express:2 aim:1 cannot:4 actions:1 closely:1 pǫ:11 combinations:1 reconstruct:1 ds:2 holland:1 fields:1 arxiv:1 wightman:2 doubled:1 nauk:1 though:2 through:2 fixed:9 view:1 ik3:4 set:6 constructing:1 notational:2 physically:5 smooth:1 frame:2 geometrical:1 notice:2 j2:1 j3:2 mνµ:1 intensity:1 result:2 inequivalent:1 iu:1 alternative:3 subject:1 phases:1 exploited:1 commutation:2 ways:1 representatives:2 eigenstates:1 state:2 various:3 between:1 invariant:1 avoidance:1 approach:1 checks:1 available:3 pcan:1 terms:2 nature:1 confusion:2 attention:1 jp:1 however:8 implementing:1 nǫ:1 topology:2 observable:2 essentially:2 σn:18 many:4 taking:2 etc:2 context:1 casimir:4 σs:19 otherwise:1 relevant:3 groups:1 point:2 reasons:1 hutchinson:1 inc:1 dimensional:7 concluding:2 pole:3 moreover:3 appeared:1 second:1 described:2 transformations:10 kinematic:2 basis:12 union:1 create:2 imagine:1 markedly:1 been:4 much:1 treat:1 basic:2 expected:1 pk:1 ph:1 helicities:1 enable:1 corresponding:4 both:4 photon:10 cos:7 ordering:1 angles:1 c2:4 c1:4 spin:19 spirit:2 present:2 aid:1 case:9 p3:2 p0:25 p1:1 subsets:1 eiv:1 leave:1 accommodating:1 examine:1 value:2 eigenstate:1 will:7 while:3 replaced:1 fiducial:2 shall:1 situation:2 iφ:1 σa:6 focussed:1 unitary:5 spacelike:2 played:2 metric:1 ir:1 thus:2 them:1 iv:1 ii:1 examined:1 cone:2 vanish:2 ie:2 orbital:1 explicitly:1 different:2 recover:1 develop:2 media:1 make:1 same:7 poincar:2 highlighted:2 complex:2 quant:1 split:1 pauli:5 pramana:1 plates:2 finite:12 naive:1 independent:2 extended:3 see:6 numerical:2 hand:2 domains:1 uses:1 purpose:2 infinite:1 eigenvectors:3 suitable:1 undefined:1 pµ:19 studies:1 well:10 analysis:1 without:1 machinery:1 components:2 sets:1 position:4 kets:1 latter:1 left:3 spherical:1 just:2 being:1 tip:1 aǫ:4 newton:1 obtain:2 rest:5 reviewed:1 mρσ:1 questions:1 part:1 momenta:4 singularity:3 multiples:1 cut:1 instance:2 mµν:6 photons:6 iϕ:1 k1:1 mathematically:1 simple:1 setting:2 treatment:3 iπ:5 mod:1 transformation:3 momentum:26 build:2 real:2 iθ:1 aspects:2 rotators:1 exploiting:1 rules:1 couple:1 handling:1 possible:5 helicity:14 using:5 emergence:1 unique:1 usually:1 advanced:1 apart:1 necessary:2 like:8 particle:2 identifying:1 follows:6 δs:1 separately:3 steps:1 either:1 always:2 iδjk:1 topologically:4 spins:2 therein:1 parity:21 right:5 often:1 classical:1 polar:1 obliged:1 some:6 back:2 pρ:1 analogues:1 normalisation:2 proper:1 multiple:2 gνρ:2 nonzero:2 specific:1 describing:1 lead:2 electromagnetic:1 unavoidable:1 per:1 does:1 connecting:1 entails:1 provides:1 assuming:1 eiϕ:1 scientific:1 perpendicular:3 step:4 departures:1 2m:2 ross:1 bangalore:3 hilbert:7 simpler:1 chapter:1 comparison:1 about:2 working:1 anything:1 freedom:4 eqns:5 energymomentum:2 dependence:2 essential:3 nonvanishing:1 mukunda:3 act:2 slightly:1 primitive:2 rev:2 statements:1 within:2 m0j:1 due:2 accommodate:2 pair:1 hermitian:2 references:1 operator:12 amsterdam:1 statistics:1 deal:2 prepare:1 assumed:1 suffice:1 there:9 question:2 why:1 dispersion:1 pa:1 inner:1 way:2 was:1 azzam:1 function:3 north:2 form:2 simplifications:1 overlapping:1 somehow:1 construction:2 removed:1 considerable:2 absent:1 coset:5 arranged:1 inhomogeneous:1 whether:2 wish:1 welldefined:1 up:11 us:2 ur:1 simplifying:1 problem:3 define:3 similar:2 called:1 eigenvector:1 precedes:1 mechanics:2 associated:1 ln:8 defined:12 universal:1 describe:1 general:13 globally:3 gνσ:1 single:7 uir:39 our:4 constructed:2 again:5 functions:1 compared:2 lightlike:4 no:7 whereas:1 when:3 vanishes:1 handed:1 streater:1 other:4 role:5 details:2 spatial:2 department:2 massless:3 solely:1 acceptable:1 eiα:2 briefly:1 elements:3 exp:3 emerges:1 subspace:1 symbol:2 problems:1 includes:1 enlargement:2 meaning:2 important:2 realised:1 included:1 structure:3 matrix:3 building:1 implies:1 longer:1 assume:1 factors:2 pseudo:1 rule:2 equivalently:1 implied:1 mass:5 lying:1 time:7 far:2 starting:5 having:1 once:1
|
quant-ph9612025.txt |@word consider:8 pointing:1 focus:2 illustrated:2 follow:1 expressions:4 centers:1 whiting:1 compact:1 ihes:1 violate:1 noncompact:1 present:5 dλ2:1 analogous:1 include:2 presentation:1 applied:1 virtue:1 very:2 implicitly:1 choice:2 every:2 summarized:1 difference:5 encounter:1 leads:6 school:1 quantitatively:1 hamiltonian:6 irreducible:2 notes:2 solution:8 dκ1:1 discrete:2 convenience:2 vector:1 dealt:1 indices:1 relation:2 concluded:1 upper:1 approximately:1 insignificant:1 dealing:1 consistent:2 coefficient:2 sign:1 second:10 evaluated:1 further:1 dynamics:3 odd:3 canonical:2 even:8 what:1 section:5 foregoing:1 expressed:2 version:3 above:1 new:6 order:3 satisfy:3 focuses:1 led:3 degree:1 respectively:1 never:1 here:3 path:15 along:2 quite:1 equations:19 change:2 obtained:1 pleasant:1 great:1 gruber:1 involved:1 approaches:1 p2:34 poisson:2 action:12 suitable:5 changes:1 cancellation:1 involves:2 appropriately:1 shorthand:1 projection:4 family:2 extra:2 namely:3 integrations:1 austria:1 issue:1 summation:1 should:2 unit:2 readily:1 conventional:1 would:1 commun:1 distinct:2 positive:2 next:2 comparing:1 circumstances:1 therefore:1 usp:1 taken:1 det:1 theoretical:2 more:3 sort:1 formally:2 incorporates:1 ap2:1 ap3:1 operators:5 ap4:1 normalized:3 particular:6 cases:5 hold:1 must:2 springer:1 te:3 defines:2 quartic:1 henneaux:2 science:2 equation:3 when:6 oscillator:1 regularity:1 theories:1 following:6 cab:3 dec:1 example:14 yeshiva:1 shabanov:3 introduces:1 states:2 effectively:2 arise:4 nonnegative:2 evidently:4 verlag:1 p4:2 iλ2:1 rather:4 discussion:3 holds:2 b139:1 how:2 criterion:1 fourth:1 symposium:1 parameter:5 sin:4 influence:1 simplicity:1 product:6 may:10 after:1 derived:1 expectation:1 applications:2 representations:1 fl:1 arnold:1 constants:1 short:2 natural:1 dynamical:2 third:1 lines:1 spectral:1 maintain:1 so:4 ultimate:1 fundamental:1 representation:8 integrand:1 divergences:1 forced:1 interpretation:1 dx:1 indeed:1 over:4 despite:1 satisfied:1 course:3 including:1 hypersurface:1 differs:1 still:1 its:2 before:2 djp:1 group:3 φa:29 chosen:1 φb:5 coordinates:1 actually:1 forms:1 complex:1 systems:10 covered:1 eventually:1 teitelboim:1 entire:1 numerically:1 introduce:3 effects:1 they:2 instead:4 documented:1 now:4 discuss:3 maintaining:1 represents:1 term:9 dirac:3 hereafter:1 characterizes:2 university:4 2a:1 each:1 entirely:1 2j:1 constraints:42 domain:1 differential:1 doing:1 series:1 energy:5 reduce:1 related:2 frequency:1 measure:4 quantum:20 our:6 beyond:1 adequately:1 out:2 category:1 large:7 shown:1 matrix:1 space:24 restricted:1 furthermore:1 since:3 projected:2 denotes:6 studying:1 seriously:1 multiply:1 dλ1:1 lecture:1 ref:4 correct:1 math:2 shows:2 earlier:2 theory:9 easily:1 enforcing:1 given:22 standard:3 admits:1 difficulty:2 completely:1 york:2 ask:2 dubna:1 remainder:1 generate:3 ecx:1 definition:2 discussing:1 seeking:1 impose:1 florida:1 times:1 motion:18 turn:3 iλ1:2 consequence:2 view:9 onto:4 first:17 initial:5 ik2:1 variables:9 powerful:1 number:2 iht:2 engenders:1 clear:1 multiplying:1 choose:1 least:2 another:2 impossible:1 open:2 differ:1 requirement:1 introduction:2 adjoint:3 speci:1 system:11 relations:2 iat:2 john:1 final:3 continuous:7 reflecting:1 focusing:1 than:1 coefficients:1 kind:1 princeton:1 dy:1 zero:1 limiting:1 project:1 determined:3 sec:1 treated:1 exhibit:1 fashion:1 symmetries:1 acknowledged:1 spectrum:6 generalization:1 discussions:1 say:2 analysis:1 qualitatively:5 need:1 seen:1 seem:1 constrained:2 any:5 paths:1 traditionally:1 lim:8 self:3 curvilinear:1 note:5 k2:4 k1:3 potential:1 take:2 reproducing:15 heisenberg:1 subscripts:1 exactly:3 normal:1 measures:1 extending:1 satisfying:1 connected:1 significant:2 phase:9 mechanically:1 future:1 inserted:1 class:12 involving:1 commutation:2 ka:3 cause:1 especially:3 surprising:1 average:1 adopt:3 ko:3 face:1 bracket:2 principle:1 χa:2 typically:2 fact:5 ambiguities:1 incorporate:1 timedependent:1 brief:1 iǫ:1 spaces:1 gauge:7 solutions:4 rough:1 find:2 ground:1 q1:2 q0:1 q2:3 based:4 parameters:2 aφ:1 commutators:1 appended:1 written:1 considerable:3 only:5 explicitly:1 bfv:1 factor:3 hamiltonians:1 local:3 do:1 his:1 temporarily:1 dk:4 means:3 dependent:3 express:1 dc:4 unacceptable:1 unimportant:1 cannot:1 words:1 international:1 dt:26 procedures:1 dp:11 dq:13 normalizable:1 continuum:1 conditions:6 arxiv:1 yield:1 prokhorov:1 though:1 gribov:1 qk:4 qj:3 automatic:1 ql:7 qn:1 kernel:16 ik1:1 set:8 notational:1 imposing:1 hγ:2 opposite:1 see:8 p21:1 result:9 p22:1 fail:1 dµ:9 brst:1 analog:4 subject:1 said:2 dk2:1 imposition:1 dk1:1 review:1 initially:1 state:13 difficulties:3 bruno:1 closed:5 between:3 invariant:2 αk:4 previous:1 approach:2 αl:2 ka1:1 preserve:1 terms:3 august:1 cλ2:1 importance:1 attention:4 jp:1 however:8 interfere:1 gratefully:1 vanishing:2 multiplier:6 picking:1 ikl:1 both:3 cos:2 prescription:2 irregular:11 ill:1 termed:1 quantization:11 fulfilled:2 etc:1 admit:2 straint:1 dkl:1 expression:13 sake:1 among:1 point:12 simple:4 harmonic:1 insist:1 dimensional:6 chap:1 diverges:1 lagrange:10 constant:4 kp:1 conference:1 kernels:1 most:1 pq:9 described:2 raise:1 inadmissible:1 addition:1 due:1 been:2 iκ1:1 reduction:4 interest:2 basic:1 pj:17 pk:5 enlarging:1 pn:1 ak:1 pl:5 define:2 determinant:2 k3:1 corresponding:1 observable:1 quantities:1 sufficient:1 subspace:4 covariance:1 belfer:1 coherent:14 observe:4 understand:1 representative:3 last:1 resultant:2 those:2 quantisation:1 case:20 p3:3 p0:1 p1:15 look:1 unlike:1 appearance:1 examine:1 value:5 iτ:2 will:3 while:2 suppose:1 behavior:2 property:1 procedure:1 ix:1 aw:1 iq:1 refs:1 conjugate:1 thus:8 iw:1 ik:2 itself:2 properties:1 vanish:1 ie:1 different:5 develop:2 make:2 formulations:2 connection:1 same:5 clearly:2 rules:1 unity:3 φc:2 quant:4 emphasize:1 widely:1 several:2 difficult:1 independent:6 used:2 again:5 hand:5 arose:1 infinite:1 frequently:1 passing:1 normalization:1 fully:1 variety:3 well:10 deal:2 without:2 sets:1 dimension:1 usual:3 λp:3 just:5 gainesville:1 rule:1 con3:1 λa:18 thanks:2 klauder:2 λj:1 alternative:4 graduate:1 λl:1 polarization:1 generator:2 instance:1 hab:3 conclude:4 had:1 remaining:2 real:3 depends:2 iξ:2 read:3 possible:4 corresponds:1 possibly:1 press:3 necessary:1 unique:1 moreover:2 formal:4 desire:1 imposed:2 like:3 particle:1 follows:11 qualitative:1 popov:1 ignore:1 communications:1 yields:1 starting:1 integrals:1 alternatively:1 become:2 reduced:3 mathematical:2 because:3 often:2 classical:36 lectures:1 some:5 linearly:1 examples:6 specified:1 proper:1 small:1 provided:4 vol:1 dense:1 lead:2 shall:1 integration:3 per:1 does:2 decomposition:1 eliminate:1 ct:7 faddeev:3 equivalent:6 illustration:1 although:2 hilbert:16 comparison:1 about:1 kinematical:1 constraint:34 freedom:1 discussed:6 dependence:2 o:4 costs:1 nonvanishing:1 remains:1 regular:5 ensure:2 characterized:1 efforts:1 introduced:2 h2:1 pays:1 into:2 integral:18 functional:3 lies:1 appropriate:2 leuven:2 references:1 determine:2 sov:1 operator:15 proportional:3 lastly:1 methods:3 acknowledgements:1 additional:1 strictly:1 there:8 question:1 nucl:1 long:2 inasmuch:2 quadratic:1 inner:6 way:4 jinr:1 resulted:1 was:2 propagator:4 assumes:1 function:10 annals:1 form:17 singer:1 but:7 volume:1 repeatedly:1 russian:1 subsidiary:1 line:3 true:1 ph:4 he:1 evident:1 wish:1 up:1 us:13 placed:1 below:3 limit:6 hp2:1 problem:3 similar:1 called:2 mechanics:3 sometimes:1 ordered:1 defined:4 certain:3 abstract:1 condition:1 general:6 dξ:2 ap:7 single:1 exist:1 dλ:1 interchanged:1 formulation:8 kl:2 proceeds:2 physical:4 grassmann:1 functions:9 compared:2 ideally:1 no:7 fixing:1 generally:2 vanishes:4 multipliers:4 started:1 other:8 details:1 becomes:1 mathematics:1 theor:1 acceptable:1 govaerts:2 briefly:2 elements:2 denote:4 exp:28 symbol:1 time:7 problems:1 deriving:1 generated:1 important:3 bounded:1 allowing:1 additionally:1 included:1 structure:3 algebraic:1 suffers:1 implies:2 using:2 assume:2 physics:4 orbit:1 departments:1 implied:1 remarked:1 once:4 resolution:4 original:2 augmented:1
|
quant-ph9612026.txt |@word code:4 partial:1 consider:3 remarkable:1 illustrates:1 squared:1 cooperative:1 edu:2 go:1 certainly:1 depend:1 calculate:1 edward:1 under:1 kθ:5 random:1 advantage:1 sitting:1 very:2 2re:1 difference:2 solves:1 hamiltonian:12 list:1 solution:1 large:2 item:1 vector:11 eigenvalues:2 computation:7 sin2:1 discover:1 consists:1 what:4 appear:1 sum:1 increasing:1 told:1 satisfy:1 evolving:1 full:1 here:2 agreement:1 cos2:1 others:1 along:2 wait:1 search:1 ctp:1 institute:1 items:1 vectors:3 allows:2 pick:3 hospitality:1 implement:2 marked:1 iet:1 linearly:1 use:2 superpositions:1 would:2 positive:3 ψw:21 next:1 process:1 program:5 call:2 therefore:1 taken:1 tell:2 more:1 appendix:2 normalized:3 particular:1 must:5 ma:2 equation:1 work:2 grover:10 dec:1 example:3 proof:3 give:2 calculation:1 december:1 bennett:2 states:1 sphere:1 sense:1 goal:1 locates:1 orthogonal:1 write:3 how:4 optimal:2 ordinary:6 sin:5 brassard:2 product:2 after:3 collection:1 designed:2 evaluations:4 grow:2 short:2 element:1 so:5 farhi:2 order:7 operations:2 acts:2 course:1 paper:1 differs:1 its:1 group:1 thank:1 chosen:1 smolin:1 actually:1 differently:1 might:1 them:1 framework:1 effects:1 they:1 rotation:1 now:11 discuss:1 eigenvalue:2 2ex:1 university:1 orthonormal:3 sufficiently:2 2en:2 each:3 found:2 2n:3 domain:1 independent:6 energy:3 idea:1 operator:3 expect:1 substantially:2 our:3 operation:1 beyond:2 out:1 divincenzo:1 ultimately:1 driving:1 space:6 since:3 interference:1 particles:1 acting:1 illustrate:1 suffices:1 shows:2 weaknesses:1 theory:1 given:8 vazirani:1 could:2 computers:2 times:1 length:2 place:1 think:1 initial:4 probability:3 number:6 iht:1 restrict:1 supressed:1 size:1 differ:2 unknown:1 πn:1 system:3 unspecified:1 their:2 siam:1 bits:1 gives:2 part:1 x2:6 than:1 showed:1 gotten:1 require:1 database:1 were:1 sam:1 boston:1 turned:1 outperforms:1 weinfurter:1 any:6 viewed:1 lie:1 angle:1 note:1 fitting:1 εn:1 absorbed:1 take:1 finding:4 strengths:1 mit:2 roma:1 phase:1 don:1 average:2 ext:5 principle:1 mechanical:1 physics:1 fact:1 shor:1 show:4 supported:1 analogue:4 find:4 tapp:1 explain:3 written:1 only:1 bernstein:1 do:1 quantph:1 get:1 de:1 dt:7 evolution:2 neu:1 arxiv:1 summary:1 optimally:2 fixed:1 nε:1 margolus:1 bounds:1 see:4 computer:15 result:2 discussions:1 close:2 analog:4 definite:1 sites:2 state:10 barenco:1 terms:1 ability:1 attention:2 however:4 sleator:1 cos:7 universit:1 uncertainty:1 equal:1 boyer:1 relevant:1 simple:1 acted:1 northeastern:1 dimensional:7 described:1 transformations:3 basis:6 been:1 quickly:1 defined:1 slowly:1 expected:3 ph:3 controlled:1 subspace:3 else:1 spin:3 case:1 value:4 choices:1 will:3 while:1 suppose:2 di:1 property:1 procedure:2 unitary:5 almost:1 thus:3 obeying:1 im:1 technology:1 different:1 make:1 same:1 complex:1 quant:3 evaluate:2 grows:4 evolve:3 used:2 upon:1 drives:1 appreciable:1 implements:3 task:2 shortly:1 center:1 acknowledgement:1 well:1 solve:4 sets:1 paradigm:2 usual:1 gates:1 just:1 when:1 rotated:1 obtain:1 speed:2 yet:2 letting:1 adding:1 tight:1 add:2 transformation:2 real:1 rev:1 big:1 possible:3 spanned:2 know:2 using:4 bit:3 apart:1 necessary:2 like:5 steps:4 output:1 works:1 spins:1 gutmann:1 because:1 classical:2 sequence:2 some:5 searching:1 erase:1 specified:2 happens:1 2e:1 2xe:1 does:2 unit:1 power:4 journal:1 conventional:1 step:1 although:1 hilbert:1 takes:2 integers:1 unsorted:1 act:2 a4:1 cambridge:1 into:2 references:2 determine:2 elementary:3 proportional:2 schrodinger:1 classically:1 assumed:1 support:1 there:1 fast:2 start:1 accordingly:1 inner:2 was:1 function:9 form:3 enough:2 tm:2 hw:11 but:1 hd:10 infn:1 algorithm:19 wish:1 up:3 us:9 theoretical:1 problem:6 uf:8 calculated:1 eigenvector:1 computing:2 ai:2 certain:2 abstract:1 general:1 quantum:23 single:1 constructed:1 again:1 generally:1 envisaged:1 application:1 digital:2 department:2 mathematics:1 you:3 confine:1 uniformly:1 a1:1 cleve:1 a3:1 a2:1 a5:1 massachusetts:1 a7:1 a6:1 a8:1 implies:2 calls:2 assume:1 requires:5 required:6 equivalently:1 reversible:3 time:12 oracle:1 n1:1 starting:1
|
quant-ph9612027.txt |@word limited:1 externally:1 consider:2 illustrates:1 separates:1 results:4 go:1 expressions:1 centers:1 compact:1 whose:2 calculate:2 baym:1 opportunities:1 must:3 rokhsar:2 bakker:1 under:1 analogous:1 spinpolarized:1 periphery:2 applied:1 supported:2 straightforward:2 frequencies:1 implicitly:2 focus:1 every:1 exact:3 condition:1 squares:1 unlike:1 level:2 anisotropy:3 large:6 discrete:1 small:3 noted:1 andrews:1 dilute:4 force:1 direct:2 approximation:11 surrounding:1 zero:12 what:1 stoof:1 section:1 axes:1 remain:2 d3:8 cell:4 axial:3 3n:1 above:2 ground:2 thin:1 coefficient:1 simultaneously:2 ranged:1 respectively:2 spacing:6 here:1 atoms:2 met:1 isotope:1 2kb:1 berkeley:2 directions:2 along:1 quite:3 hkf:1 change:4 obtained:1 precursor:1 study:2 larger:1 excursion:2 suitable:1 plotted:1 diameter:2 via:1 useful:2 scales:4 vii:1 scaled:7 rkf:1 summation:1 total:1 cloud:8 use:1 would:3 negative:1 few:1 therefore:2 associated:1 theoretical:1 more:4 comparison:1 becomes:2 validity:1 appendix:2 excellent:1 known:1 aligned:1 iii:1 fermionic:1 states:11 ma:1 science:2 equation:1 work:3 oscillator:2 flight:1 labeled:1 temperatures:9 following:1 dec:1 example:1 compare:1 figure:8 calculation:1 december:1 near:2 high:4 numbers:1 degenerate:12 sense:2 evidently:1 axis:1 respective:1 provide:4 describes:1 holds:3 feature:1 chemical:9 varies:1 2rf:2 parameter:2 isn:1 profile:2 sommerfeld:2 may:7 after:2 different:3 plane:1 physik:1 cambridge:1 wave:2 constants:1 kurn:1 short:2 third:1 grant:1 explicit:1 summing:1 neglect:1 interpolates:1 rather:1 so:4 allow:1 enter:2 increase:1 sackett:2 order:4 typical:3 six:1 gradual:1 over:3 vary:1 choose:1 experiments:1 through:1 statistical:2 satisfies:1 lx:1 its:2 before:1 strikingly:1 rapidly:1 exclusion:5 energies:1 interesting:1 encompasses:1 decreases:1 li:1 forms:3 complex:1 systems:3 lz:1 kasevich:1 aeff:2 ly:1 correspondence:1 them:1 good:1 greater:4 integral:1 ωr2:2 fig:4 introduce:1 scaling:3 tails:1 effects:3 ensher:1 densities:1 easily:2 dirac:1 always:1 university:2 hamiltonian:4 crudely:1 magnitude:1 trap:13 radial:5 2m:5 2ef:1 mean:3 square:4 ℓm:1 doing:1 series:1 energy:18 ef:27 gaussian:2 related:2 bradley:1 inhomogeneous:1 frequency:1 measure:1 quantum:7 laboratory:1 eq:13 ketterle:1 shown:5 container:1 exponential:1 space:8 since:14 rev:5 research:1 particles:5 rf:10 rb:5 sloan:1 induced:2 ref:1 shows:1 foundation:1 linear:1 interactions:5 free:1 effect:1 approaches:1 california:1 imagine:1 matthews:1 e2:1 interaction:1 widths:1 transition:1 david:1 length:8 isotropic:2 davis:1 quadratically:1 eqs:3 first:1 origin:1 xi:1 omitted:1 variables:3 number:7 transform:1 xy:1 directly:2 appl:1 size:5 equating:1 given:7 perturbation:2 temperature:26 similarly:3 introduction:1 xii:1 top:2 system:4 their:1 perturbations:1 fermions:5 realization:1 perfectly:1 unpublished:1 speaking:1 gives:1 shell:2 kf2:2 kf3:1 trapped:22 zeroth:1 accurately:1 manipulation:1 x2:2 than:8 center:3 observed:1 polarized:4 effective:6 approximations:1 depends:1 limiting:1 determined:3 merits:1 evaporated:1 treated:2 δkf:1 spectrum:1 crossover:1 need:1 seen:1 occupied:1 any:3 viewed:2 prohibits:1 strength:1 studying:1 able:1 predominantly:1 note:5 k2:1 ideal:4 potential:22 amusing:1 silvera:4 stringari:1 experienced:1 opposite:1 goldman:1 condensate:2 satisfy:1 interatomic:1 δef:4 boltzmann:1 thank:1 position:3 phase:4 acknowledgements:1 intrinsic:1 eigenfunctions:1 kb:20 unequal:1 kf:23 calculated:1 phil:1 brought:1 electrons:1 principle:7 exp:1 velocity:4 ueff:1 physics:1 tollett:1 wavenumber:4 thomas:6 particularly:1 show:1 delta:1 radii:1 pethick:1 thickness:2 find:4 occupation:1 rf3:3 symmetric:1 ratio:3 ellipsoid:1 committee:1 unwieldy:1 analytic:1 only:5 factor:1 local:6 do:1 quantph:1 distance:2 dependent:1 familiar:3 de:1 nearly:1 despite:1 evolution:1 continuum:1 conditions:2 arxiv:1 nλ:1 mewes:1 fixed:2 occupy:1 body:1 requirement:1 computed:1 veselov:1 undergoes:1 national:1 box:2 up:1 relative:1 see:6 radius:3 result:4 sea:5 discussions:1 close:2 fails:1 capacity:2 interacting:4 dmr:1 µm:3 state:5 various:1 µk:1 between:5 fermi:53 approach:2 across:1 multiplied:2 comparable:1 terms:1 attention:2 weak:1 however:6 butts:2 reproduces:1 rapid:1 houbiers:1 ike:1 bose:17 suppressed:1 problem:1 p2z:2 both:8 σn:1 limits:1 many:1 region:1 uncertainty:1 against:1 ln:1 hω:1 leggett:1 exceeds:1 σr:5 expression:1 otherwise:1 azimuthally:1 adjusted:1 point:1 simple:3 ca:1 harmonic:10 semiclassical:11 simply:3 ae:1 atmosphere:1 described:3 p2y:2 px:1 due:5 been:1 p2x:1 much:3 slowly:1 treat:2 anisotropic:2 ph:1 define:2 interparticle:2 contribute:1 corresponding:4 gas:34 dramatic:2 evidence:1 spin:6 case:4 hωr:1 reciprocal:1 expanded:1 mimicked:1 value:1 rectangular:1 will:3 while:6 replaced:1 viii:1 behavior:1 applies:2 ix:1 vi:1 refs:2 thus:1 non:2 iv:1 ii:1 characterize:1 vs:8 vanish:2 containing:1 pseudopotential:2 perhaps:1 make:1 lett:5 same:8 clearly:1 selfconsistent:1 shifts:1 unity:4 noninteracting:1 quant:1 wavepacket:1 pauli:6 dimensionless:3 lithium:1 grows:1 higher:1 independent:1 used:1 numerical:2 monotonic:1 levels:1 moving:1 lower:1 fourier:1 traps:1 safely:1 well:4 roughly:1 sets:1 quantitative:1 dimension:1 sec:1 less:1 when:2 accurate:1 druten:1 atomic:4 aspect:2 scattering:4 eigenstates:1 visualization:1 enters:1 preprint:1 density:21 cornell:1 weiss:1 confirmed:2 wavevector:2 valid:2 treatment:1 easy:1 theorem:2 momentum:20 real:3 casting:1 2u:1 sums:2 possible:1 possibly:1 increases:2 confined:2 using:3 rf2:1 dimensional:1 particle:18 δv:4 follows:1 adiabatic:1 δr:1 isotropy:3 harmonically:7 specific:6 envisioned:1 eβ:2 yields:1 integrals:2 polikarpov:1 become:1 nucleons:1 waltham:1 right:1 old:1 classical:13 discontinuities:1 interact:1 understood:1 linearly:1 expected:2 respect:1 happens:1 δn:2 tracked:1 integration:1 per:4 does:1 unit:1 proc:1 restoring:1 core:1 equipartition:3 bold:1 liquid:1 each:1 expansion:2 notably:1 pressure:2 step:1 although:1 found:1 110b:1 exciting:1 properties:5 integers:1 about:1 inter:2 neurobiology:1 discussed:2 walraven:1 o:4 range:1 repulsion:3 soc:1 own:1 lowtemperature:1 h2:2 into:1 within:4 numerically:2 functional:1 nsf:1 appropriate:3 because:1 einstein:1 proportional:1 mark:1 van:1 heated:1 there:1 approximate:1 gases:19 width:3 anderson:1 quadratic:3 bosons:1 low:9 way:1 spring:1 was:3 function:6 elsewhere:1 form:8 but:2 volume:6 hk:1 heat:7 atom:3 line:2 observation:2 partitioning:1 ωz:1 durfee:1 characteristic:7 cells:1 ωr:5 maximum:2 quantitatively:1 hulet:2 paired:1 below:3 exerts:1 limit:11 spectroscopy:1 distribution:18 uc:1 regimes:1 48n:3 constant:4 computing:1 defined:1 universal:7 combining:2 metals:1 general:2 single:5 physica:1 our:1 controlled:1 distributions:9 regime:2 again:1 functions:3 compared:3 dotted:1 dashed:1 nb:2 generally:1 vanishes:2 thomasfermi:1 nx:2 ny:3 nz:2 setting:1 spatial:12 department:1 heats:1 pitaevski:1 conclusion:1 brandeis:2 calculating:1 separate:1 uniformly:1 variation:2 condensation:1 factors:1 curve:3 equivalently:1 mass:2 fact:1 time:1 observables:1 nuclei:1 expands:1
|
quant-ph9612028.txt |@word represent:2 monte:1 code:26 consider:8 impression:1 interference:1 results:2 leads:2 p02:3 scalar:1 computation:15 transversally:1 go:5 follow:2 integrity:2 causes:1 gr:1 compact:1 increase:3 certainly:1 inverse:1 depend:2 calculate:3 knill:2 combinatoric:1 finally:1 program:5 present:1 under:3 stochastic:1 analogous:1 include:2 case:9 belonging:1 worse:1 advantage:1 orthogonal:1 very:10 void:12 dragged:1 differently:1 every:5 telling:1 affect:4 1s:1 exact:1 dim:4 differentiated:1 dominate:1 level:18 t6:1 positions:2 applicable:1 fewer:1 try:7 sand:1 especially:2 small:4 possibilities:2 barbara:1 accumulation:1 prevent:1 smaller:3 occurrence:1 practically:1 consistent:1 estimates:1 past:1 consists:2 second:4 htr:2 further:2 ǫl:4 carlo:1 shining:1 even:8 what:9 errors:69 xor:31 stands:2 rate:17 contributions:2 lead:2 version:2 goes:1 new:1 row:1 ever:1 method:1 justification:1 led:1 degree:3 whose:1 ǫt:4 here:8 understanding:1 p12:3 desired:1 free:4 strategies:1 november:1 observing:3 z1:4 change:2 simulating:1 obtained:4 suitably:1 involved:1 elaborate:1 changed:1 allows:4 leaving:1 suggests:1 amount:1 resulting:1 characterizing:1 within:1 tolerantly:2 complicated:3 changes:2 engineer:1 followed:2 santa:1 timestep:1 namely:1 worthwile:1 logical:1 9f:2 brought:1 patience:1 printf:8 apply:12 counts:3 total:1 redo:1 unit:1 clifford:1 qcs:6 use:5 proceed:2 would:16 codewords:8 probabilities:9 readable:1 next:5 estimated:1 opposed:1 memory:4 taken:3 means:5 stage:1 type:3 tell:1 more:21 introducing:3 becomes:1 acceptable:1 potentially:1 corrected:2 occurred:1 concatenation:4 carrying:2 particular:2 e2b:2 kǫ2:1 must:1 me:1 states:11 account:1 word:2 err:5 science:1 originally:1 work:1 cat:30 remain:2 paragraph:2 values:2 hope:1 following:9 making:6 abandon:1 crude:1 my:12 control:1 claim:3 months:1 dual:2 figure:3 give:5 calculation:8 programming:1 did:1 copying:2 high:1 indicates:3 assumptions:2 fprintf:1 numbers:3 want:2 sense:1 times:5 occur:1 gcc:1 requirements:1 recovery:1 provide:2 verify:3 divided:1 acts:1 machine:1 till:2 behave:1 pure:2 answer:1 instead:5 revisions:1 ensemble:4 isn:4 simplicity:1 xors:1 transforming:1 stop:1 after:3 variant:1 imaginable:1 diagram:2 wrong:4 produce:1 multiplication:1 data:8 parallel:1 constants:3 efficiently:1 shortcomings:1 physical:2 effective:4 computations:1 many:1 lines:1 sv:6 su:1 think:2 destroying:1 so:13 fundamental:7 threatens:1 order:13 sd:5 operations:42 longer:1 help:3 produces:1 over:1 mainly:1 flips:14 years:1 produced:2 course:4 paper:1 restore:2 sqrt:3 statistical:1 mentioned:3 still:1 its:3 before:5 write:1 ld:1 difference:1 group:1 thank:1 how:6 chosen:1 interesting:1 ǫ2t:1 actually:15 better:6 estimating:1 detected:2 choose:1 listing:1 mail:1 main:2 might:1 happened:2 eventually:4 non:4 good:3 return:3 pauli:1 combination:2 propose:1 evolution:2 introduce:5 break:5 p11:2 steane:2 they:8 gate:33 own:1 rotation:1 now:7 nop:10 p01:3 easily:1 february:1 gets:7 verifying:1 always:2 reasonably:1 loosely:1 adrian:1 orthonormal:1 sufficiently:2 theory:1 magnitude:1 trap:2 reasonable:2 each:13 2m:1 repeating:1 taylor:2 side:1 individually:1 square:1 directly:1 hard:1 reduce:2 frequency:1 expect:3 measurement:15 quantum:36 our:1 happen:2 transitions:2 special:1 out:25 category:1 large:1 dominates:1 matrix:4 space:2 rep:2 crucial:2 looking:2 may:9 multiply:1 adapt:1 rb:5 gov:1 cause:2 correct:4 math:1 shows:3 foundation:1 linear:5 attempt:2 possibility:1 quite:1 alternatingly:1 unwanted:1 term:10 besides:1 imagine:2 put:1 estimate:9 muller:1 care:3 depolarizing:5 interaction:1 v1:5 starts:1 could:9 computers:2 diminished:1 tolerant:25 motion:1 turn:1 length:1 levels:8 place:1 isotropic:1 assumed:1 quadratically:1 diminishes:1 resetting:1 neglect:1 first:22 initial:1 probability:38 encoding:9 xb:1 number:21 clear:1 erroneous:3 done:5 construct:2 another:7 carry:5 xp:1 clarity:1 zalka:2 reliable:1 aharonov:1 size:1 given:6 uncorrectable:10 likely:1 needed:4 introduction:1 leading:3 least:1 their:3 assumption:6 california:1 too:3 calculations:1 scheme:6 bits:14 1l:7 speaking:1 gives:6 collapse:2 mostly:2 continuous:1 took:1 forward:1 part:4 somewhat:2 natural:5 representing:1 than:18 coefficients:3 center:1 serv:1 approximation:1 kind:1 critically:1 last:6 participated:1 double:3 depends:1 preparation:4 minimize:1 individual:2 contrary:2 store:1 amplitude:1 were:1 7f:1 motivation:1 sees:2 takes:2 ran:1 7n:1 correction:24 argument:2 bitwise:8 correspond:2 eps:5 say:4 distorted:1 need:7 seen:2 seem:2 null:1 any:8 viewed:1 qb1:6 qb2:6 astonishingly:1 sdr:6 zero:2 patterns:1 check:4 lim:2 self:1 able:3 mechanism:1 note:4 potential:1 best:1 simplified:2 bus:1 schematically:1 destroy:5 outlook:1 wonder:1 channel:5 accuracy:4 play:1 added:1 multiple:1 allow:3 opposite:2 track:1 keeps:1 thoroughly:1 harmful:1 most:9 optimized:2 propagate:2 but:12 preliminary:1 nothing:1 adds:1 acknowledgements:1 probabilistic:1 why:4 deviations:1 don:4 observation:4 won:1 considered:3 average:6 later:1 points:2 principle:2 inaccuracies:1 toffoli:18 quadratic:1 justify:2 physics:1 away:3 quantity:3 optimal:8 shor:10 particularly:1 simulate:2 show:6 supported:1 minimizing:1 diminish:1 threshold:28 rough:6 determined:1 guideline:1 find:3 feedback:1 specifically:2 knowledge:1 parameters:4 implementation:8 enough:5 should:12 only:24 going:3 admixture:1 adequate:1 accurate:1 achieve:3 equilibrium:1 exchanged:1 do:3 dm:6 handle:1 above:5 quantph:2 get:22 zurek:1 db:5 soon:1 beam:1 ones:4 preparing:1 words:2 combinations:1 during:5 target:1 runs:1 estate:2 dpr:3 fields:1 arxiv:1 yield:1 summary:1 qc:5 qb:8 though:2 clean:1 e1b:8 view:1 set:3 k02:9 achieved:3 float:2 national:1 up:5 observed:1 intensity:1 computer:16 result:5 discussions:1 analog:1 techniques:1 probable:1 pattern:1 review:2 targeted:1 state:43 smallest:1 between:12 affecting:1 progress:1 neither:1 tolerance:2 knowing:2 terms:2 ability:1 qubits:48 come:1 distribution:1 improve:3 received:1 essentially:1 improved:5 fault:29 taking:3 equal:2 flipped:1 propagation:5 marked:1 figures:3 qubit:64 whole:2 0l:10 con:1 relevant:1 point:1 simple:7 pow:1 cx:1 simply:5 linux:1 cv:2 considering:1 destroyed:1 pp:10 described:2 basis:17 addition:1 simplification:2 ben:1 three:6 been:4 strategy:1 int:30 reduction:1 much:7 pf:1 combined:3 equation:2 expected:3 threaten:1 ph:6 wait:1 hardly:2 pro:1 define:2 resting:4 direction:2 describe:2 corresponding:3 versa:1 both:8 concerning:2 coherence:1 precision:2 observe:2 unified:1 systematic:4 c2:3 c1:3 those:1 applied:13 5f:1 laser:1 look:4 gentle:1 operational:1 straight:1 value:2 transformation:6 will:37 while:5 theoretical:1 error:117 irrespective:1 procedure:3 optimize:1 schweizerischer:1 unitary:6 laflamme:2 thus:43 them:2 correctable:7 middle:1 exterior:1 turns:3 cyclicly:1 sequentially:1 binary:1 different:10 confirms:1 verified:1 parabola:1 author:1 pay:2 make:8 same:16 clearly:2 benign:1 parts:1 quant:6 arguments:2 diagonalize:1 accumulating:2 units:1 several:6 higher:10 independent:5 used:6 raymond:1 see:7 i1:13 i3:7 i2:30 upon:1 occurence:1 hand:7 ion:3 v2:5 v3:5 v4:1 v5:1 nationalfonds:1 workings:2 ab:8 contribution:2 keep:1 lower:4 off:4 modes:1 smallness:1 nevertheless:3 expression:1 preceeding:1 well:2 roughly:4 deal:1 obviously:1 thought:2 efficient:2 without:6 comes:3 simulated:1 swiss:1 model:9 usual:2 gates:7 calderbank:2 just:9 less:1 being:2 generally:3 resp:1 half:1 obtain:1 proposes:1 transforms:2 using:1 compared:1 nǫ:3 density:3 seems:3 except:1 improvement:1 source:2 conjugated:1 inner:2 easy:1 save:2 tolerable:1 take:11 real:1 makes:1 around:1 psb:3 big:1 possible:7 early:1 possibly:2 increases:2 know:3 performance:1 immediately:1 bit:61 correcting:2 usually:1 occurring:2 necessary:4 like:8 particle:1 university:1 follows:5 machinery:2 steps:11 either:3 arbitrary:5 become:2 reduced:1 preskill:2 parity:5 sketch:1 because:6 often:4 classical:4 sequence:1 some:12 back:1 sure:2 duration:1 little:2 dc3:1 reasons:2 provided:2 undisturbed:4 affects:1 measurements:8 per:13 counteracts:1 does:1 exit:1 tends:1 yields:1 prob:1 refer:1 measuring:6 destroys:1 run:1 equivalent:2 bh:1 conventional:1 expansion:1 step:30 although:2 hadamard:13 transported:1 throw:2 simpler:2 comparison:1 about:12 actual:1 carried:9 getting:1 capable:1 o:3 simulation:13 practical:1 statement:1 plus:1 mixed:1 introduced:6 block:1 equally:1 computational:8 pays:2 into:15 codeword:37 due:6 down:5 phase:16 appropriate:3 right:3 references:1 determine:1 elementary:3 proportional:1 reducing:1 initially:1 methods:2 realisation:1 k12:6 institut:1 additional:5 prepare:1 combinatorics:1 measured:2 there:15 transform:5 long:3 start:3 cats:2 low:1 way:7 var:4 analyze:1 function:1 form:1 concatenated:2 becoming:1 jul:1 encode:2 reed:1 larger:3 encoded:38 trying:1 true:7 faster:2 count:1 made:5 applying:6 full:8 whether:5 characteristic:1 negating:1 flip:16 us:2 until:1 below:3 limit:1 verification:1 iterated:2 dv:7 problem:2 called:1 strongly:1 required:2 constant:3 computing:4 defined:1 certain:1 abstract:1 measure:11 doesn:2 denote:1 single:6 exist:3 file:1 dragging:1 operation:13 four:1 constructed:2 grv:1 again:7 codes:9 discriminate:1 no:4 when:10 application:1 other:9 role:1 test:1 really:5 christof:1 sufficient:1 presenting:1 deviation:1 picture:1 elements:5 superposition:1 includes:2 important:2 stab:2 fraction:1 auxiliary:9 algorithm:1 vice:1 assume:13 lanl:3 rather:1 together:1 having:2 phonon:1 mass:1 parallelism:7 time:11 far:4 decoherence:8 requires:1 original:4 once:6
|
quant-ph9612029.txt |@word replacing:1 limited:3 externally:2 partial:1 consider:5 represent:1 rev:8 magnetic:2 results:7 afosr:1 four:1 privman:8 particularly:1 expressions:3 research:2 issues:1 row:1 inverse:1 referring:2 aug:1 σyb:7 factoring:1 preprint:3 answered:1 finally:1 program:4 those:4 eiα:5 division:1 supported:2 straightforward:2 far:1 continues:1 choice:4 refine:1 putting:1 entries:1 affect:1 manageable:1 matrices:17 condition:1 obvious:2 hamiltonian:15 issue:2 proposals:1 large:2 adjust:1 avoiding:1 small:1 eigenvalues:6 force:2 computation:7 deutsch:1 direct:2 literature:2 likely:1 design:12 eiβ:5 follow:1 further:3 choices:2 even:2 what:2 errors:1 xor:19 sub:2 apparatus:1 section:3 σxb:4 u34:1 u33:1 above:2 international:1 acknowledged:1 body:1 condensed:2 proliferation:1 chose:1 respectively:1 component:3 here:8 desired:3 operating:2 relaxation:1 along:1 standard:2 calculate:2 obtained:3 search:1 accomplishes:1 involved:5 larger:4 suggests:1 resulting:2 studies:2 involves:2 composed:1 spatially:1 addresses:1 family:3 semiconductors:1 explained:1 prefer:1 logical:5 highly:1 boolean:2 analyzing:1 apply:1 unit:6 use:3 additive:1 superpositions:1 would:4 contains:1 nonsymmetric:1 next:1 a51:1 going:1 call:1 therefore:4 assistance:1 theoretical:1 today:4 more:5 brings:1 operators:4 apparent:2 reversible:3 normalized:1 particular:1 known:1 given:1 must:9 involve:2 keeping:1 rotational:1 vladimir:1 pursue:1 recall:1 work:9 reviews:1 values:2 following:4 trans:1 example:3 initial:3 compare:1 computers:1 calculation:4 u61:1 bennett:2 haroche:1 states:7 numbers:3 guarantee:1 information:1 rather:5 verify:1 write:1 numerous:1 instead:2 ordinary:1 parameter:5 sin:12 u21:1 inputs:1 product:2 algebra:1 may:2 demonstrates:1 earlier:3 derived:1 lengthy:2 nullify:1 explored:2 designed:1 representations:1 namely:1 realized:1 short:4 attempt:1 clarkson:2 lines:1 correspond:4 element:1 provide:1 algorithms:1 allow:1 σzb:2 representation:2 σza:10 order:13 operations:3 gershenfeld:1 serving:1 indeed:3 over:1 turchette:1 soon:1 symbols:1 course:1 experiments:2 london:1 omitting:1 mentioned:1 still:3 its:2 roots:1 before:1 derive:1 chosen:1 conjugation:1 forms:3 absence:1 complex:4 itano:1 systems:8 decreased:1 main:1 might:1 arguments:1 them:1 good:2 diagonalize:2 combination:2 seeking:1 propose:2 evolution:7 introduce:2 steane:1 nonzero:2 effects:1 they:7 twoparticle:1 now:4 realize:1 2u:1 term:2 w4:1 university:2 level:2 sufficiently:1 2ei:1 trap:1 each:6 found:2 2h:1 subset:1 tensor:1 schemes:1 ei:26 independent:3 house:1 reduce:1 dima:1 extended:1 reached:1 quantum:21 laboratory:2 operation:3 special:1 out:3 divincenzo:4 accomplish:4 network:1 space:6 iα:4 furthermore:2 since:1 interference:2 denotes:1 semiconductor:1 attracted:1 ref:3 gate:17 after:1 linear:4 interactions:25 diagonal:14 quite:3 approaches:1 carried:2 complicated:2 york:2 put:2 jozsa:1 care:1 interaction:7 benioff:1 derivation:2 could:1 impose:1 positioning:1 unitarity:2 american:1 produce:2 undesirable:3 u22:1 timed:1 v4:1 first:9 feed:1 already:1 features:1 symmetry:2 omitted:1 number:5 lond:1 xy:2 adopted:1 calculational:1 electronic:1 hood:1 size:1 guess:2 necessarily:2 their:3 introduction:1 interact:1 smoother:1 system:5 least:1 ukn:1 zeros:1 too:1 calculations:2 convention:1 programmable:1 bits:1 final:1 a32:1 stars:1 schwarzschild:1 explanation:1 exactly:2 required:1 part:1 hillery:1 kept:1 than:6 king:1 determines:1 was:1 require:3 second:4 matter:2 determined:2 pairwise:1 solely:1 fashion:1 symmetries:1 explicit:3 correction:2 modern:1 need:2 seen:1 cumbersome:3 weinfurter:1 seek:1 any:2 built:1 zero:3 convenient:1 latter:3 note:5 instance:2 materials:1 take:1 so:1 smolin:1 heisenberg:2 subscripts:1 added:1 though:2 mimics:1 most:1 abc:2 eight:2 phase:4 analytically:1 measured:1 stands:1 calculated:1 later:1 hi:2 principle:1 exp:3 mechanical:2 physics:8 notion:1 fact:4 precise:1 shor:2 shot:1 show:2 probe:1 relation:1 lloyd:2 indicate:1 make:1 symmetric:1 specifically:1 based:2 parameters:10 favor:1 written:1 should:1 only:13 explicitly:1 factor:1 hamiltonians:7 do:1 mixture:1 notation:2 get:1 familiar:2 overall:1 uniaxial:2 satisfied:1 cannot:1 nearly:1 new:2 during:1 symmetrically:1 processes:1 conditions:6 arxiv:1 yield:1 summary:2 nonrigorous:1 contain:5 analytical:2 valid:1 set:2 aspect:1 reference:1 sensitivity:1 margolus:1 topics:1 see:6 computer:9 result:5 recently:1 analog:1 subject:1 appear:1 phases:1 interacting:1 ways:2 pattern:1 review:1 µm:1 initially:1 state:10 future:1 identification:1 simplest:3 tens:1 probably:1 approach:3 choose:2 admittedly:1 barenco:2 terms:13 reproduced:1 tensorial:1 qubits:2 lange:1 attention:2 focus:1 however:6 science:3 gratefully:1 succeed:1 article:2 cirac:1 remaining:3 motivations:1 restrictions:1 cos:12 reverse:1 many:2 according:2 isotropic:1 etc:3 σy:1 σx:2 raimond:1 context:1 logic:1 qubit:1 whole:2 experimental:2 otherwise:1 conclude:1 simple:3 address:1 corresponds:2 grants:1 sleator:1 respect:1 throughout:1 factors:1 better:1 transformations:2 basis:5 three:16 been:4 difference:2 much:3 interest:1 expected:1 ph:1 u15:1 u14:1 define:2 suggested:1 controlled:2 both:4 offers:1 coherent:3 external:3 angles:1 denote:3 spin:28 former:2 present:1 case:2 eiδ:1 survey:1 unlike:1 kimble:1 air:2 will:15 while:8 σxc:5 replaced:1 error:3 property:2 couplings:1 landauer:1 real:3 planar:2 unitary:8 iq:1 ip:1 refs:3 formulation:1 thus:8 encountered:1 ih:1 obstacle:1 contract:1 ic:2 ib:1 technology:2 seem:1 monroe:1 binary:1 different:5 eiµ:2 trial:1 perhaps:1 realizing:1 σz:1 same:1 rules:1 parts:1 quant:1 emphasize:2 pauli:7 units:5 products:1 several:2 start:1 evolve:1 used:2 numerical:1 mozyrsky:8 counterparts:1 hand:1 parametrized:1 ion:1 moving:1 expand:1 recent:3 eigenvectors:1 a52:1 task:1 off:4 exploratory:1 well:4 magnified:1 rome:3 command:1 components:6 consistency:1 firstly:2 entry:1 gates:13 protocol:1 proposed:1 being:1 when:1 identically:1 atomic:2 questions:1 using:1 useful:4 alternative:1 yamamoto:1 macroscopic:1 eigenstates:1 multiples:1 secondly:1 interestingly:1 zoller:1 seems:1 parametrization:1 improvement:1 iω:1 reasons:1 other:8 lett:5 technological:1 input:7 solvable:2 transformation:4 chuang:2 identical:3 march:1 depends:1 iξ:1 read:1 advances:2 iγ:5 iβ:4 possible:2 philos:1 five:1 know:1 world:2 bit:2 unique:2 vague:1 mod:2 imposed:1 like:2 particle:3 sizes:1 follows:2 reduces:2 performing:2 u42:1 collect:1 imposes:1 steps:2 arbitrary:6 multiplicative:1 output:12 reduced:1 spins:13 grouping:1 accessible:1 because:3 classical:5 some:2 examples:1 specified:1 diagonalizing:2 happens:1 provided:2 eiγ:4 scale:1 dimensions:2 eiη:1 2e:3 affects:1 avoid:2 measurements:1 equal:2 proc:1 refer:2 presented:2 noise:1 scientific:1 june:1 journal:1 conventional:1 illustration:1 eiρ:1 step:1 become:1 manufacturing:1 stage:2 about:1 actual:1 usa:2 algebraic:2 column:1 introduces:1 dependence:2 page:1 financial:1 range:4 involving:1 ensure:1 introduced:1 processor:1 soc:2 computational:2 wineland:1 into:2 numerically:1 due:1 down:2 appropriate:3 references:2 steven:1 operator:5 proportional:1 refined:1 acknowledgements:1 deal:1 treated:1 there:5 question:1 transform:1 fast:2 spread:1 describes:1 way:3 perform:1 analyze:1 sections:2 function:9 considerably:1 medium:1 form:8 multispin:7 but:2 anisotropic:1 underlined:1 construction:1 related:1 dissipative:1 u13:1 coupling:2 october:1 instructive:1 whether:1 up:1 miniaturization:1 lead:3 below:2 sum:1 problem:2 u16:1 similar:6 ab:1 constant:4 int:1 certain:4 universal:2 describe:2 general:10 peres:1 multiparticle:1 single:5 our:11 corresponding:2 august:2 functions:2 us:4 no:5 ekert:1 generally:5 meekhof:1 field:1 interested:1 potsdam:1 department:1 picture:1 stat:1 elements:5 intend:1 superposition:2 separate:1 problems:1 includes:1 chance:1 important:4 ising:2 studied:2 included:1 structure:5 matrix:13 faster:1 practically:1 photonics:2 interval:2 persistent:1 original:2 time:9 cleve:1 failures:1 having:1
|
quant-ph9612030.txt |@word represent:1 consider:2 splitting:1 illustrated:1 research:1 reasoning:1 certainly:1 2n0:1 violate:1 disposal:1 technique:1 those:1 th:1 under:2 include:1 instytut:1 case:5 straightforward:1 orthogonal:2 far:1 none:3 seemingly:1 wave:3 every:1 selleri:1 decide:1 bringing:1 entire:3 solves:1 large:1 small:4 optics:1 equation:2 configurations:1 upper:2 too:1 sapienza:1 foundation:1 second:3 chopping:1 situated:1 belief:1 even:2 index:2 what:3 apparatus:1 selected:1 near:2 experiment:5 above:4 new:2 ever:1 method:2 full:1 respectively:4 never:3 here:1 following:4 others:1 directions:5 based:1 along:5 quite:1 observing:2 obtained:1 great:1 incoming:4 institute:1 popescu:2 vectors:2 contradiction:1 yˆ:2 usually:1 studi:1 suitable:3 caro:1 formulated:3 followed:1 extra:1 explained:1 outcomes:1 analyzing:1 counts:2 total:4 causal:1 use:4 would:5 prove:1 probabilities:5 give:1 forcefully:1 riv:1 explicitly:2 proposes:1 therefore:1 means:1 type:8 more:3 dλρ:2 started:1 operators:3 holt:2 occurred:1 drown:1 normalized:1 particular:1 known:1 cases:20 must:2 high:1 account:3 eberhard:1 effectively:1 originally:1 values:1 beam:3 believed:2 making:1 arrive:2 example:1 claim:1 ready:7 mirrors:1 relativistic:1 states:2 indicates:1 performed:2 degenerate:1 misalignments:1 counting:1 axis:3 normalize:1 information:2 end:5 rather:1 discussion:1 holds:1 xˆ:2 feature:1 regions:1 very:3 justifiably:1 instead:2 ordinary:2 ensemble:4 simplicity:1 product:1 may:1 wrong:1 produce:1 summarize:1 choice:1 data:1 parallel:2 realized:1 short:2 joint:1 register:3 departure:1 quotes:1 cannot:2 negligible:1 correlation:1 putting:1 acknowledges:3 divided:1 typical:1 horne:5 saturated:1 indeed:3 years:1 produced:1 experiments:20 through:1 unfavorable:8 still:1 its:3 before:2 perfect:2 rapidly:1 thank:1 la:1 sergienko:2 polarizing:7 subensemble:6 actually:3 better:1 detected:6 fig:2 isaac:1 hidden:7 loophole:1 them:3 propose:1 reject:1 introduce:1 obeyed:1 effects:1 they:8 now:3 day:1 bigger:1 represents:2 february:1 fizyki:1 always:2 university:2 advent:1 sufficiently:1 inequality:6 transmitted:1 each:12 universit:1 uniwersytet:1 ports:1 realism:9 another:1 map:1 doing:1 energy:1 idea:2 sandu:1 used:5 entering:1 quantum:7 our:2 event:12 out:3 shown:1 space:3 rep:1 since:6 rev:12 denotes:1 particles:2 investigation:1 shows:1 marek:1 linear:2 localization:2 fisica:1 possibility:4 standard:4 reason:1 term:3 beginning:2 generate:1 pairs:5 employing:1 starts:1 could:5 chiao:1 hence:4 retain:1 onto:1 first:5 placing:1 features:1 probability:4 variables:4 number:5 smaller:2 directly:1 biasing:1 passes:1 dipartimento:1 their:4 rates:1 normalization:1 low:2 grant:1 employ:1 optical:2 favorable:2 authors:1 yurke:1 than:8 distance:2 polarized:4 double:1 bother:1 see:3 preparation:1 supposed:1 were:2 toward:1 projections:1 footnote:1 argument:2 alley:4 correspond:3 randomly:2 say:1 sentences:1 need:1 any:5 paths:1 conversion:5 genuine:1 zero:2 polarization:11 mix:1 take:2 so:3 detector:5 towards:1 multiple:1 shall:1 collaboration:1 outcome:4 most:2 involving:1 propagate:1 plenty:1 pair:7 measured:1 class:3 especially:1 considered:2 detectors:7 face:1 principle:1 distinctive:1 physics:1 review:1 fact:2 emerging:1 selection:6 show:1 violation:1 nτ:2 purely:1 carefully:1 d2:2 d1:2 teoretycznej:1 just:7 state:8 should:7 only:6 going:1 equipped:1 local:21 interested:1 plate:2 his:3 subspaces:1 notation:1 di:2 beams:3 de:1 overall:1 expectation:2 famous:1 ones:1 words:1 probably:2 during:6 subscript:1 aξ:30 runs:2 settings:1 conditions:1 arxiv:1 yield:1 paper:2 set:1 computed:1 observer:21 violated:3 correlations:6 bounds:1 detection:1 namely:1 us:6 contains:1 violates:1 techniques:1 inequalities:9 nondegenerate:1 pattern:3 shimony:4 symmetric:1 enough:2 between:2 progress:1 justified:2 approach:3 polarizer:1 knowing:1 gives:1 terms:3 do:2 premises:1 emitted:4 however:5 analyzer:1 efficiency:4 wp:1 analyzed:1 ket:2 distribution:1 suggested:1 both:5 essentially:1 enables:1 last:4 many:1 taking:2 equal:5 contract:1 chosen:6 receives:7 interesting:1 expression:1 experimental:3 comment:1 splitters:1 author:1 bell:8 appeared:1 corresponds:1 distinguish:2 grants:1 simply:2 nsk:2 considering:1 configuration:1 tremendous:1 been:4 much:2 goes:1 ph:1 pl:1 define:1 wants:1 direction:2 describe:1 corresponding:4 fire:1 dismiss:1 photon:20 remark:1 bs1:1 observers:1 cee:1 doubts:2 careful:1 present:5 p2:3 p1:3 look:1 nski:1 value:3 aξi:2 will:10 technical:1 while:8 steinberg:1 rotator:1 situation:3 procedure:1 stoler:1 studied:1 almost:3 refs:1 thus:4 non:6 according:2 ii:1 claimed:1 result:1 different:3 italy:1 etc:1 make:3 same:4 drawback:1 quant:1 orientated:1 widely:2 weakness:1 events:11 independent:2 investigated:1 effect:1 hand:1 phy:1 identity:1 recent:1 lower:1 off:2 poland:1 obstacles:1 well:2 analysis:1 obviously:1 thought:1 solve:1 roma:2 model:3 parametric:4 usual:6 kiss:1 proposed:1 being:3 generally:1 newton:1 obtain:1 rest:1 gda:3 intervals:2 integer:1 paul:1 yielding:1 oriented:2 superficial:1 photons:28 point:1 discuss:1 signals:1 source:2 other:12 lett:8 versa:1 theorem:1 input:1 violations:2 apart:1 remaining:1 build:1 tests:6 insensitive:1 depends:1 eigenvalue:2 big:1 possible:3 spanned:1 increases:1 zukowski:2 know:1 vacuum:8 using:1 aξ1:1 desire:1 imposed:1 like:1 particle:2 follows:4 signal:1 associate:1 discarded:1 either:2 arbitrary:1 revisiting:1 works:1 lucien:1 because:2 often:1 deal:1 successfully:1 some:3 examples:1 choosing:1 duration:1 home:1 happens:1 specific:1 tmr:1 lead:1 avoid:1 per:1 magnitude:1 exit:1 assuming:1 prog:1 equivalent:1 perpendicular:1 how:1 bw:2 revtex:1 although:1 bs:1 post:3 hilbert:1 about:2 stations:2 firing:1 generated:1 o:4 practical:1 kwiat:3 nothing:1 discard:3 ou:2 consequently:1 equally:1 cambridge:2 beamsplitter:9 previously:1 into:7 obtaining:2 bound:1 nsf:1 down:5 included:3 appropriate:1 references:1 raises:3 operator:2 rely:1 degli:1 her:1 assumed:2 support:2 there:7 long:1 why:1 restricts:1 mandel:2 way:9 analyze:2 was:1 function:2 form:2 phenomena:1 registered:3 regard:1 jun:1 but:9 idealized:3 true:4 he:1 directed:3 made:1 beamsplitters:2 versions:1 whether:4 prevents:1 inside:1 up:1 devices:1 record:1 limit:1 problem:7 similar:1 gisin:1 mechanics:2 shih:4 interval:6 defined:3 certain:3 abstract:1 10ns:1 general:3 peres:1 clauser:6 single:4 together:1 typeset:1 eigenstate:1 cim:1 no:15 ekert:1 when:7 setting:3 sponding:1 test:2 clicks:1 denote:2 calculating:1 models:3 subspace:2 mechanical:1 problems:1 prepared:2 cb3:1 meaning:3 observables:1 variable:3 complications:1 else:1 sides:1 zeilinger:1 happening:1 vice:1 resolution:1 tricks:1 required:1 rule:1 time:7 n0:6 serious:2 chsh:9 original:2
|
quant-ph9612031.txt |@word partial:1 consider:3 pointing:1 rev:1 fa1:2 leads:2 ga:2 consists:1 c1:3 inverse:1 depend:1 critical:1 alvarez:2 present:2 analogous:1 lack:1 choice:1 isomorphism:1 mixing:1 matrices:3 convexity:2 illustrated:1 solves:1 hamiltonian:3 solution:1 vector:1 math:2 manifestly:1 eigenvalues:1 grateful:1 consistent:1 imply:3 ρa1:2 perspective:2 dynamics:5 even:1 index:2 xψ:1 nonlinear:8 gβγ:2 brackets:2 lexicographic:2 version:3 new:2 equivalent:1 satisfy:1 nonlinearly:1 ibid:3 respectively:1 ρan:1 here:1 identifications:1 separation:1 equations:3 implicit:1 knowledge:1 larger:1 allows:1 suggests:1 simultaneous:1 poisson:7 published:1 usually:1 complicated:1 therein:1 spacetime:1 formulated:1 depart:1 explained:1 summation:2 use:4 would:1 probabilities:2 positive:2 few:1 therefore:2 ψa:2 theoretical:1 more:3 composite:1 inclined:1 odinger:1 appendix:2 particular:2 cases:1 must:1 ρa:3 ρb:1 ρd:1 ρi:5 equation:11 ρn:1 following:4 dec:1 example:1 ρe1:1 dn:2 weaker:1 figure:3 abelian:1 preserving:1 dependence:2 states:4 mixture:1 hyperplane:3 exclude:1 counting:1 pure:4 acta:1 ordinary:1 ensemble:1 algebra:1 may:1 earlier:1 fk:1 constants:2 natural:2 correspond:2 greek:2 ones:2 so:1 fundamental:3 order:4 typical:1 interpretation:1 mielnik:2 over:2 interpreted:1 its:3 group:1 thank:1 fruitful:1 forms:1 systems:1 matematyki:1 derivative:1 might:1 them:2 introduce:1 framework:1 hamilton:3 arriving:1 now:3 february:1 dirac:7 fizyki:1 invariants:3 requires:1 subsystem:4 spinor:1 en:2 financial:1 independent:1 quantum:3 our:1 eq:1 out:2 matrix:7 space:1 induces:1 denotes:1 particles:3 jadczyk:1 acting:1 δρa:1 δρb:2 δρc:2 independence:1 marek:1 reformulation:1 linear:5 guess:1 free:1 standard:3 difficulty:1 ρii:3 subalgebras:1 e1:1 transition:1 kuna:1 hence:1 separable:1 philosophical:1 indices:3 svetlichny:1 given:3 system:3 least:1 their:2 convention:4 scheme:2 structures:1 shell:6 tool:1 off:5 july:1 than:1 gγα:1 kind:1 gγβ:2 second:1 preparation:1 gii:3 argument:1 generalization:3 say:1 conjugate:1 any:7 lie:9 subsystems:4 latter:1 generalized:1 analogy:1 forming:1 εa:8 εc:1 kab:1 begin:2 gα:5 ρd1:1 germany:1 remarks:2 manifested:1 nonlinearity:2 average:1 gβα:1 proceedings:1 bracket:10 principle:2 typically:1 fact:1 threshold:1 d4:2 d1:1 gαn:2 inspiring:1 ensembles:1 situations:1 written:1 should:2 experiment:1 continuity:1 do:2 dm:4 means:1 de:1 cannot:1 evolution:1 gbc:1 arxiv:1 maciej:1 consisting:1 garcia:2 marciniak:1 qm:1 gα2:1 gα1:1 view:1 exists:1 hα:2 latin:1 result:1 discussions:1 tensor:2 liouville:1 symmetric:1 state:4 boundary:1 αn:5 nambu:5 ωabc:3 terms:1 comm:1 tensors:4 both:1 interpretations:1 goldin:2 many:2 attributed:1 bispinor:5 symplectic:1 casimir:3 whole:1 ck:3 unclear:1 cn:6 cm:1 point:1 simple:1 cf:1 ce:1 dimensional:1 simply:1 respect:1 indefinite:4 conference:1 described:2 raise:1 basis:2 pk:7 ph:1 abstract:2 define:1 wants:1 arises:1 corresponding:1 covariance:1 gan:2 gak:2 c2:2 xxi:1 gad:1 gab:1 those:1 case:3 nska:1 will:1 replaced:1 property:1 vectors:1 spacelike:1 played:1 von:1 ii:3 skipping:1 triple:8 ia:1 noninteracting:1 quant:1 mixtures:1 physical:1 composition:1 higher:2 evolve:1 used:1 permutation:1 hand:1 infinite:1 lower:1 schr:1 possibly:1 nevertheless:1 poland:1 thought:1 stating:1 usual:1 deltas:1 obtain:3 gda:2 density:10 regarded:1 seems:1 mathematically:1 belongs:1 lett:2 theorem:8 guarantees:1 polon:1 nonoverlapping:1 corresponds:2 ρb1:5 ga1:1 particle:12 follows:1 δs:1 manifest:1 separately:1 δh:8 arbitrary:2 δf:6 reduced:3 mathematical:1 methods:1 classical:3 phenomena:1 b1:2 convex:2 proper:3 proofs:1 provided:1 integration:1 overlap:1 does:3 bd:1 bc:3 bn:7 bk:8 evolutions:1 step:2 hilbert:1 theorems:1 discussed:1 generated:1 covariant:1 organizers:1 em:4 nsk:1 down:1 pair:1 hermitian:1 references:2 elementary:1 neumann:2 aparicio:1 support:1 there:2 question:2 way:2 assumes:1 opposed:2 function:4 form:8 some:2 regard:1 but:3 repeated:1 ha:2 he:1 versions:1 whether:1 differentiable:1 ul:1 below:1 ωa:3 problem:2 ωd:1 mechanics:1 ab:12 associated:1 defined:1 czachor:4 ak:4 general:4 single:2 formulation:2 formalism:7 metric:11 constructed:1 no:2 acknowledgments:1 other:2 role:2 denote:2 a1:4 meaning:1 allowing:2 structure:2 jones:1 implies:1 longer:1 physics:1 rule:1 mass:2 time:3 observables:4 gαγ:1 gαβ:2 gαα:2
|
quant-ph9612032.txt |@word caused:1 reversibility:1 leads:1 houches:1 expressions:1 causes:1 looking:1 certainly:2 amplification:1 referring:1 4ns:1 technique:1 environment:1 th:1 marks:1 analogous:2 tb:17 ta:20 case:5 g4:1 very:2 kω:2 wave:4 electron:1 difference:1 splitter:5 proposals:1 fewer:1 smb:1 leave:1 adjust:1 phase:2 barbara:1 measuring:3 work:1 undoes:1 approximation:1 second:7 cost:2 pass:4 functioning:1 port:1 even:2 what:1 apparatus:1 section:4 current:1 experiment:12 goes:2 sixth:2 replaced:3 acknowledgments:1 contrast:1 edited:2 full:2 simultaneously:1 respectively:3 component:4 here:1 atoms:1 inverse:2 free:1 address:1 path:3 calculate:1 obtained:1 great:1 dec:1 institute:1 through:8 leaving:1 amount:1 commutators:1 suitable:2 involves:1 cˆ1:1 appropriately:1 formulated:1 useful:1 although:1 ions:1 plenum:2 herzog:1 total:1 superpositions:2 usa:1 representing:1 positive:1 escapes:1 arms:6 france:1 associated:1 type:1 theoretical:1 reflects:1 more:3 ecole:1 becomes:4 operators:6 visibility:1 absorptions:1 carrying:1 cases:1 hold:1 iii:2 must:3 permits:1 setup:2 reα:1 modified:1 arrive:1 example:2 performed:1 f1:4 f2:5 polaritons:1 figure:7 give:1 process:2 december:1 franson:2 slit:5 numbers:1 tab:1 sense:1 junctions:1 information:11 united:2 destroying:1 discussion:1 acts:1 delay:3 how:1 instead:1 ordinary:1 may:1 db:5 earlier:1 epsrc:1 applications:1 produce:1 ou:1 constants:1 joint:1 packets:2 perform:1 so:4 keeps:1 howard:1 holds:1 interpretation:1 produces:1 over:2 τr2:2 years:1 produced:2 course:2 experiments:5 london:2 wolf:2 differs:1 still:1 its:2 before:2 group:2 thank:2 scully:1 polariton:2 destroyed:5 absence:1 permanent:1 microscopic:2 systems:5 stephen:1 τr:5 them:2 good:1 irreversible:2 conversations:1 uhl:1 eˆ:3 penetration:1 effects:1 they:2 identically:1 now:4 realize:1 dielectric:28 suppose:2 term:2 brightness:1 always:1 university:3 drop:1 registrations:1 fringes:2 2b:1 each:4 inserts:1 ei:2 energy:1 barnett:5 related:1 interferometer:12 frequency:6 measure:2 quantum:24 out:3 large:3 shown:1 reinstating:1 space:1 interference:22 particles:2 re:5 vector:2 ancilla:2 get:1 plotting:1 wiley:1 linear:2 undo:1 quite:1 california:1 york:3 detecting:1 e1:3 dω1:2 dω2:2 care:1 pairs:2 interaction:6 retained:2 derivation:1 optics:4 could:5 iω2:2 diminished:2 times:2 filter:1 exponentially:1 chiao:3 first:3 initial:2 probability:10 number:3 huttner:1 improvements:1 done:1 given:3 ian:1 likely:1 similarly:1 introduction:1 interact:3 system:12 their:1 tune:1 passed:3 destruction:1 final:1 mandel:3 continuous:1 took:1 tapster:1 optical:1 somewhat:2 manipulation:1 x2:11 x1:12 photographic:1 than:2 specify:1 determines:1 rate:3 loudon:2 probe:3 strathclyde:1 amplitude:1 were:1 identical:1 solely:1 dielectrics:4 recover:1 conversion:3 rochester:2 zero:2 physique:1 extracted:1 k1:2 internal:3 absorbed:7 take:1 analogy:1 destroy:1 detector:3 begin:1 electric:4 though:4 measures:2 falls:1 pair:2 observation:1 detectors:2 proceedings:2 points:1 electrons:1 principle:1 exp:5 mechanical:1 velocity:2 usual:1 physics:6 queen:1 bright:1 relation:1 substituting:1 find:1 emulsion:1 ground:2 based:3 just:1 dissipative:1 pump:2 only:5 integrate:2 plate:1 above:1 means:1 zurek:1 de:1 overall:4 da:6 beam:6 new:3 reconstruct:1 dr:1 him:1 fields:2 arxiv:1 europhys:1 common:1 pulses:1 set:6 human:1 eˆ1:6 eˆ2:6 correlations:2 relative:1 see:4 individual:3 college:1 us:1 discussions:1 recently:1 rarity:1 arm:12 ways:2 pattern:16 tend:1 state:8 closed:1 between:5 neither:3 transfered:1 glasgow:1 terms:4 ability:2 do:1 modify:1 screen:1 combining:1 however:5 efficiency:1 selectively:1 eˆa:1 understanding:1 suppressed:4 both:3 essentially:1 eˆi:1 many:4 connection:1 improves:1 figures:1 absorption:1 passing:2 expression:3 experimental:8 detailed:1 relevant:1 ca:1 coincidence:7 cancel:1 moreover:1 actually:1 suppressing:1 conference:2 described:3 tuning:1 aˆ:1 due:1 been:4 pc:2 reduction:2 eraser:7 degrees:5 ph:1 mary:1 describe:1 coherence:6 photon:17 zeilinger:1 coherently:2 c2:2 c1:4 present:3 applied:2 replaces:1 josephson:1 might:1 britain:1 will:4 while:1 steinberg:3 situation:2 real:1 examines:1 les:1 played:1 almost:1 vi:2 thus:5 ii:3 itself:1 im:12 eberly:2 hong:1 weinfurter:1 lengths:4 make:2 same:1 complex:2 quant:1 events:1 day:1 coincidences:7 published:1 effect:5 entanglement:2 expand:1 recent:1 narrow:3 off:1 traps:1 nevertheless:1 whole:1 well:3 bohr:3 without:1 components:1 parametric:3 left:1 restore:5 stores:1 proposed:2 being:2 captures:1 vanishes:1 bandwidth:3 lossy:5 atomic:1 aspect:1 nicolas:1 adding:1 similarities:1 photons:12 had:2 discuss:1 spread:1 slits:1 lett:3 wiseman:1 unprecedented:1 kingdom:2 increased:1 depends:1 insert:1 evaluate:1 survival:1 measurement:17 possible:7 dark:4 eorique:1 entangled:4 vacuum:2 using:1 loss:2 like:3 lost:1 performing:1 benefit:1 integrals:2 fully:1 become:1 works:1 reduced:1 because:3 classical:4 creation:4 phenomena:1 choosing:1 jeffers:3 mirror:2 nonzero:1 provided:1 electromagnetic:4 measurements:5 langevin:1 wooters:1 overlap:2 manipulations:1 does:1 demonstrated:1 inserting:4 destroys:1 object:1 power:1 retains:1 santa:1 imaginary:1 gained:5 about:6 would:5 freedom:5 fringe:3 dependence:1 o:1 kwiat:4 range:1 a2:1 plus:1 greatly:2 2x1:2 ic2:1 ic1:1 financial:1 rev:10 into:7 within:2 implications:1 down:5 device:2 appropriate:4 references:1 determine:1 operator:3 proportional:1 support:1 there:4 dispersion:2 brun:1 quadratic:1 low:1 way:1 was:8 knowledge:1 naturally:1 function:2 medium:2 some:1 adjusting:1 differences:2 but:6 repeated:1 delta:1 true:1 count:3 absent:1 whether:1 up:5 devices:2 tell:1 ωi:2 converted:1 demonstrate:1 percival:1 piece:1 similar:5 gisin:1 mechanics:1 storing:1 constant:5 b2:1 defined:1 certain:1 abstract:1 todd:1 substantially:1 single:5 arises:1 formalism:1 correlation:1 functions:3 no:2 wavefunction:2 when:1 cˆ:3 field:6 narrowing:1 other:9 role:1 department:1 permitting:1 superposition:2 important:2 allowing:1 variable:2 auxiliary:5 dω:1 assume:2 required:2 pseudo:4 unscathed:1 reversible:1 experimenters:1 time:3 westfield:1 restored:4
|
quant-ph9612033.txt |@word sector:1 measurements:1 consider:2 a23:1 caused:1 results:2 leads:5 roy:1 commute:5 subclass:1 contributions:1 factorizing:1 compact:1 choquet:5 depend:1 calculate:1 disposal:1 bx2:1 tr:4 environment:5 charge:3 under:3 decomposition:6 norm:14 orthogonal:5 very:2 wave:2 puzzles:1 difference:2 matrices:1 condition:2 level:1 tra:1 tre:7 solution:2 large:3 vector:3 small:3 eigenvalues:3 markov:1 trw:5 upper:1 originate:1 consistent:2 estimates:2 approximation:1 zero:3 dynamics:9 estimated:1 theory:12 spectral:5 what:2 projectors:1 sum:2 uniform:4 experiment:1 subspaces:2 values:4 contrast:2 satisfy:6 full:2 never:1 modify:1 here:7 met:1 objects:2 address:1 represented:6 november:1 coupling:1 extreme:2 remark:1 wesley:1 institute:2 vectors:4 periodic:1 definitively:1 usually:1 hospitality:1 uniquely:3 emerge:1 via:1 projection:10 explained:1 limt:2 highly:4 unitary:2 decrease:1 total:11 univ:1 linearly:1 use:2 superpositions:1 would:2 probabilities:4 positive:4 negative:1 properties:5 few:3 therefore:4 type:5 theoretical:2 more:9 separated:1 weight:1 started:1 india:1 operators:29 apparent:1 odinger:2 berlin:2 normalized:1 known:1 foundations:1 cases:1 hold:1 ρa:1 springer:2 balls:2 originally:2 r3:2 δm:1 obvious:3 following:10 dec:1 example:2 proof:1 give:1 process:1 arise:1 organized:1 purposes:1 states:13 assumptions:2 sense:2 δmn:1 subsystem:3 axis:1 information:2 rather:5 ie:6 discussion:1 holds:1 how:2 pure:9 parameter:1 simplicity:1 specifications:3 derived:2 mapping:3 ball:4 hence:5 produce:1 physik:2 representations:2 geometrical:2 constants:1 short:1 natural:1 sectors:10 lines:1 correspond:2 su:1 element:3 extremal:13 so:2 sect:9 allow:4 representation:14 talk:3 restriction:1 logunov:1 interpretation:3 september:1 over:4 satisfied:1 course:1 cambridge:1 statistical:23 differs:1 satisfies:2 still:2 its:6 before:1 derive:2 group:3 thank:1 chosen:1 coordinates:1 permanent:1 choose:1 mail:1 schmidt:3 kupsch:3 h0:2 arguments:1 yi:5 non:7 affected:1 thereby:1 yn:1 introduce:1 bound:5 iht:4 rotation:2 now:2 discuss:2 easily:1 term:1 dirac:1 always:2 university:1 hamiltonian:12 possibilities:1 sufficiently:4 inequality:1 l2:4 found:2 eighties:1 side:3 subset:1 tensor:1 arbitrariness:4 principles:2 related:2 investigated:2 expect:1 measure:4 quantum:31 relates:1 eiht:1 out:1 matrix:4 space:31 restricted:3 nuovo:1 since:12 rx:4 research:2 laid:1 investigation:4 spacing:1 denoted:1 lecture:1 rn:3 induced:10 correct:1 shows:1 benjamin:1 linear:5 localization:1 diagonal:4 free:1 approaches:1 complicated:1 york:1 estimate:7 trs:2 forbids:1 interaction:4 derivation:1 language:1 english:1 could:2 transition:4 consequence:4 onto:1 assign:1 first:1 separable:1 already:2 probability:10 pn1:2 omitted:1 xf:1 number:1 rank:4 restrict:1 done:1 another:2 precisely:1 open:1 given:9 necessarily:1 exists:1 their:1 introduction:1 interact:1 behaves:1 tata:2 system:18 least:2 needed:1 assumption:1 normalization:2 statement:3 recovered:2 observations:1 ih0:2 exactly:5 speakable:1 part:4 norms:1 off:3 translation:1 x1:4 than:1 specify:1 e3:6 kind:1 effective:4 princeton:1 approximations:1 cimento:1 imply:1 nevertheless:1 wheeler:1 distinguished:1 result:3 explicit:2 dynamically:2 spectrum:8 need:1 seen:3 any:8 lie:1 subsystems:3 refute:1 lim:1 polarization:4 emphasis:1 potential:3 bogolubov:1 objective:2 negligible:1 even:1 continuous:3 fundamental:3 trace:10 shall:3 ıve:1 barycentric:1 most:1 involving:1 germany:1 quantitative:1 phase:1 segment:1 class:2 singled:1 especially:1 consequences:2 calculated:2 coincides:2 vertices:2 kl:1 points:8 principle:5 exp:5 mechanical:3 χm:4 physics:3 section:1 fact:2 precise:1 show:3 violation:1 notations:2 x2:4 spaces:2 gauge:1 decompositions:1 trivial:1 agrees:1 based:1 knowledge:1 state:29 contraction:1 giulini:1 only:15 explicitly:1 ambiguity:1 araki:5 zeh:2 achieve:1 dn:2 do:4 triangle:1 above:3 zurek:6 de:1 beltrametti:1 expectation:3 cannot:3 kiefer:1 new:1 unfortunately:1 closure:1 evolution:2 podolsky:1 conditions:3 arxiv:1 wightman:1 investigate:2 valid:1 kernel:2 set:18 aspect:1 reference:1 mentioned:1 see:9 w2:4 w1:4 dµ:3 closer:1 inequalities:2 kaiserslautern:2 symmetric:1 enough:2 closed:2 between:4 αi:3 limit:1 boundary:17 reading:1 approach:1 terms:1 importance:1 wn:2 complement:1 inclusions:1 distinguish:1 suppressed:2 topology:1 concentrated:1 observable:3 essentially:1 many:2 invited:1 cup:1 against:2 approximative:1 sensitive:1 context:1 logic:1 uni:1 whole:1 arbitrarily:1 point:6 simple:3 others:1 corresponds:3 dimensional:4 alone:1 respect:2 superselection:34 stamatescu:1 speak:1 selfadjoint:5 strong:2 110b:1 second:2 addition:1 due:1 been:2 mirman:1 workshop:1 asymptotics:3 ph:1 originates:1 pn:17 pm:34 addison:1 direction:1 corresponding:1 commutes:1 concerning:1 formed:1 subspace:2 coherent:1 understand:1 demand:1 c2:8 spin:5 those:3 case:6 p1:1 splits:1 subsets:1 tetrahedron:1 appearance:1 will:2 euclidean:1 irrespective:1 property:1 a21:1 a22:1 larger:1 ve:14 almost:1 metric:1 them:2 ii:1 reads:1 vs:14 vanish:1 interacts:1 different:1 formulations:2 concluding:1 quant:1 emphasize:1 pauli:2 finite:4 higher:1 independent:1 calculation:1 used:1 comprehensive:1 dimh:1 hand:3 purpose:2 potentials:1 infinite:2 invariance:1 totally:1 identity:3 lower:1 joos:2 schr:2 acknowledgement:1 charges:1 epr:1 analysis:1 todorov:1 without:1 components:2 sets:5 ωu0:2 model:6 usual:3 proposed:1 being:1 obtain:3 vanishes:3 questions:1 facts:1 λi:7 scattering:5 λn:5 λm:11 recapitulated:1 kluwer:1 density:1 bell:2 except:1 smoothness:1 belongs:1 solvable:3 real:2 asymptotically:2 aspects:1 depends:3 eigenvalue:3 rules:21 evaluate:1 decomposed:1 possible:5 early:1 b59:1 press:1 world:1 emergence:6 unique:7 decomposes:1 vague:1 semiclassical:1 modifications:1 like:4 follows:1 reduces:1 separately:1 continue:1 yields:2 integrals:1 λx1:1 become:1 reduced:8 mathematical:7 satisfactory:1 right:3 often:1 classical:14 lectures:1 absolutely:2 some:5 understood:1 examples:2 convex:9 practical:1 vol:1 uniqueness:1 dimensions:3 realistic:1 fachbereich:1 investigations:1 joachim:1 does:4 connecting:3 unit:4 provides:1 prog:1 unstable:1 refer:2 measures:4 slight:1 uniformly:2 equivalent:1 arbitrary:2 restrictive:2 substituted:1 simplex:6 cγ:6 hilbert:11 about:4 kinematical:2 discussed:6 o:8 essential:5 compatible:1 remains:2 regular:1 mixed:1 2x2:1 book:1 therein:1 rev:2 suppression:3 unbounded:1 into:5 within:1 integral:5 isomorphic:1 three:1 remarks:1 appropriate:3 references:3 einstein:1 operator:25 statistics:3 additional:4 there:5 question:1 u0:4 long:1 start:1 much:1 sections:1 function:3 complete:1 form:3 hs:33 but:15 construction:1 hm:6 line:2 he:14 made:3 smooth:3 up:3 us:1 below:1 ρpn:1 problem:4 called:2 mechanics:18 constant:2 defined:6 stronger:2 abstract:2 measurement:2 general:3 chap:1 proves:1 initial:7 dλ:2 our:1 physical:2 again:5 differentiable:1 no:6 naturwiss:1 rosen:1 detail:2 field:3 other:3 role:1 papers:1 theor:1 picture:1 elements:6 superposition:4 models:13 problems:2 generated:2 important:2 bounded:6 establish:1 structure:13 implies:2 longer:2 practically:1 assume:8 interval:1 rule:3 d26:1 weights:1 time:5 far:2 observables:5 decoherence:4 resolution:1 unspeakable:1
|
quant-ph9612034.txt |@word limited:2 sci:1 consider:3 maximum:1 rev:6 magnetic:12 varying:1 results:2 eds:1 entropy:22 computation:2 edu:1 go:1 faster:1 issues:2 depend:1 violate:2 transferred:3 technique:2 send:1 presents:1 isentropic:1 quasi:1 tj:7 swap:2 th:1 under:2 hermann:1 analogous:1 appleton:1 case:1 adiabatic:1 advantage:1 without:4 far:1 frequencies:1 springer:1 should:1 experimentally:6 emphasized:1 difference:1 cool:1 entire:1 disturb:1 incoherent:3 vibrational:1 presented:1 altering:1 turns:1 t2:33 t1:28 hartle:1 convenience:1 phase:2 epstein:1 destroying:1 noted:2 still:2 upper:1 strongly:1 version:1 zj:3 deutsch:1 consistent:1 isolate:1 sin2:2 pulse:16 cash:2 approximation:2 consists:1 second:14 cost:4 dev:1 functioning:2 eigenspaces:1 even:2 section:3 dephasing:1 supplied:3 experiment:1 causes:1 above:11 flowing:1 new:8 net:1 increasing:1 contrast:1 sout:4 exchange:2 continuing:1 kept:1 lange:1 here:2 diagonal:1 selective:1 operating:3 cos2:2 alone:1 along:2 z1:2 change:2 wait:2 obtained:3 convert:2 naval:1 institute:2 allows:8 contradiction:1 leaving:2 amount:7 resulting:1 professor:1 resonance:17 suitable:1 makes:2 involves:1 useful:3 projection:1 extra:5 plenum:1 private:1 highly:1 visible:1 addressed:1 suffered:1 decrease:1 translational:1 apply:8 total:3 readily:1 environment:8 use:2 takes:3 would:1 probabilities:4 jozsa:1 negative:1 properties:1 mation:1 taken:2 theoretical:1 today:1 more:4 clever:1 readers:1 operators:1 apparent:2 envelope:1 particular:3 known:1 iii:3 potential:1 must:4 states:4 keeping:2 ibm:1 science:1 originally:7 work:36 london:1 remain:1 temperatures:2 following:2 making:2 dec:1 example:6 ions:2 process:22 discussed:1 bennett:1 high:5 effectively:2 minimum:1 performed:1 sense:1 validated:1 µj:4 simple:4 axis:1 information:52 respective:2 straightforward:1 provide:2 interacts:5 discussion:1 acts:1 machine:1 how:8 zaxis:1 pure:1 frontiers:1 instead:4 verlag:1 eµ1:1 sin:7 oscillatory:3 redwood:1 flip:8 thermodynamic:8 after:4 santa:1 explored:1 fe:1 law:7 parallel:1 times:1 realized:3 ot:3 physical:1 third:2 eµj:2 light:1 sq:3 author:1 yielding:2 sj:1 completed:1 negligible:1 allow:1 decreasing:2 operate:1 equation:4 haus:3 erasing:1 integrated:1 help:1 office:1 indeed:3 over:2 insight:1 flips:11 produced:1 course:3 thermal:2 paper:6 pulses:5 statistical:1 converting:1 suffer:1 its:10 before:3 s2:16 group:1 ln:1 scully:1 compelling:1 systems:7 communication:1 quant:1 alter:1 inefficiency:12 s1:20 them:1 good:1 return:3 greater:3 thereby:3 practice:3 introduce:2 number:1 slichter:1 effects:2 they:1 half:1 oxford:2 now:6 nor:1 university:4 hamiltonian:1 sideband:1 carnot:13 iff:8 mode:4 each:5 repeating:2 directly:1 ej:2 doing:1 series:1 energy:41 hard:1 idea:1 perpetuum:1 frequency:11 static:1 measurement:24 quantum:72 laboratory:1 operation:9 extract:6 out:10 divincenzo:1 shown:1 container:1 matrix:5 quantify:1 since:2 crucial:1 research:1 increase:3 re:2 investigation:1 flowed:1 performs:1 formula:1 occurs:2 shows:2 decoherent:1 creating:1 performing:3 log2:1 theory:2 written:1 maintains:1 mechanisms:1 pumping:2 free:4 york:2 put:3 e1:11 milburn:1 e2:5 verify:1 interaction:3 created:1 could:9 running:1 decohering:1 quantummechanical:1 motion:3 place:1 due:3 investigates:1 undergo:1 onto:1 first:7 initial:1 features:1 probability:1 swapped:1 flipping:6 clear:1 set:4 done:7 long:2 another:7 precisely:2 affords:1 city:1 given:2 temperature:12 width:2 introduction:2 leading:1 system:6 least:1 intense:1 their:3 delay:1 perfectly:1 bits:3 reversed:2 acquire:3 immediate:1 sciences:1 part:1 absorbs:1 hood:1 than:8 intrinsically:1 modes:4 begins:1 king:1 kind:1 polarized:1 correlate:1 cyclic:2 double:4 zero:3 accordance:3 wheeler:1 tipping:3 extracting:2 exhibit:1 fashion:3 generality:1 unchanged:2 spelled:1 discussions:2 confirms:1 any:4 conversion:2 strength:1 angle:2 thoroughly:1 εq:5 complexity:2 thorough:1 note:1 extracted:6 contact:6 take:2 so:6 acquires:2 mit:3 εc:7 hyperfine:1 decoheres:1 added:4 fundamental:1 opposite:2 trρ:1 who:1 techniques:7 device:22 acknowledgements:1 measured:1 why:1 refrigerator:3 kb:37 mobile:1 average:6 flow:1 repeated:1 order:2 points:4 principle:13 mechanical:8 typically:1 mabuchi:1 reprinted:1 laws:1 operations:1 cyclically:1 intensity:1 show:2 violation:1 supported:1 contemporary:1 disturbs:1 lloyd:3 decade:1 ground:1 slow:1 reservoir:25 much:1 pump:1 elucidated:1 short:1 moments:1 only:7 going:3 molecules:4 µi:1 amplifying:1 equilibrium:4 do:4 erasure:2 goes:1 get:1 familiar:1 zurek:11 simplest:1 overall:3 cannot:4 nonequilibrium:1 exchanges:1 report:1 during:5 quantifies:1 adiabatically:2 processes:1 precession:1 sources:2 fields:1 arxiv:1 investigate:3 though:1 through:3 gell:1 view:1 perpetual:1 res:1 reference:4 acquired:2 undergoes:1 lnp:1 operates:7 observed:1 edition:1 see:6 individual:1 result:4 w1:1 operated:3 bt1:1 aro:1 exploited:2 interacting:2 ways:2 nuclear:1 review:1 definite:1 dipole:2 demons:4 tend:1 originated:1 state:58 converted:1 szilard:3 µh:1 between:6 complications:1 neither:1 µb:5 available:2 terms:2 ability:1 nature:3 initially:4 darpa:1 cit:1 subject:1 however:2 ln2:13 efficiency:20 queensland:1 sleator:1 come:3 both:2 realizable:4 last:2 reverse:2 many:2 extracts:2 trades:1 equal:1 flipped:1 energies:1 logic:3 ernst:1 expense:1 experimental:1 detailed:2 σz2:1 point:1 reasons:1 cf:1 ii:3 initiative:1 throughout:2 erased:3 described:5 raise:1 engines:1 thermodynamics:12 addition:2 computing:1 three:3 been:4 extraction:1 spread:2 refrigeration:1 quic:1 basic:1 compensating:1 itano:1 ph:1 waste:1 containers:1 lett:4 engine:19 addison:1 direction:4 arises:1 controlled:5 maser:1 coherence:4 n00014:1 coherent:2 understand:1 coherently:9 decreased:1 spin:141 present:1 p2:7 p1:16 laser:1 external:1 tanh:4 tip:1 engineering:1 value:1 will:6 technical:1 while:6 suppose:5 viii:1 landauer:9 turchette:1 century:1 demon:34 violating:3 conditioned:3 equilibrate:3 converts:1 limit:1 rid:1 ignoring:1 technology:2 monroe:1 different:1 weinfurter:1 grant:2 perform:8 media:1 make:1 radiation:3 same:3 princeton:4 potentially:1 arguments:1 gets:5 higher:2 independent:1 used:5 bodenhausen:1 kelvin:1 effect:1 flows:7 fridge:2 ion:3 moment:2 uses:2 purpose:1 cycle:15 lower:5 weakly:1 off:3 whereby:1 studies:1 variety:3 seth:1 leff:2 non:1 thought:2 costs:2 mann:1 sets:1 entered:1 model:8 possesses:2 wc:1 exploits:1 less:2 being:3 generally:1 starting:1 proposes:2 underlying:1 using:4 rotates:4 previous:1 letting:1 adding:1 preprint:1 density:5 regarded:1 smith:1 source:1 qout:3 treatment:7 versa:1 5a:1 excited:1 5c:1 5b:1 increased:1 depends:2 possible:1 corresponds:1 entangled:1 acronyms:1 press:4 world:1 bit:9 formal:1 loss:2 rotate:2 necessary:1 like:2 follows:2 velocities:1 specific:2 steps:8 either:4 exploiting:2 simply:5 spins:19 because:1 classical:1 sequence:3 conditional:9 some:2 back:1 understood:1 erase:4 b1:2 insistence:1 extended:1 transversely:1 kimble:1 gradually:2 scale:2 dimensions:1 bottom:1 electromagnetic:5 measurements:2 wout:3 does:7 exposition:1 provides:1 allowing:1 trap:1 measuring:2 destroys:1 slight:1 2µb:3 peculiarly:1 processing:3 oscillating:2 conventional:1 quantified:1 wesley:1 step:4 although:1 emits:1 gained:2 about:10 actual:2 extension:2 getting:2 basis:1 introduces:5 o:2 sake:1 whence:1 larmor:1 mixed:1 introduced:4 op:1 undoing:1 cambridge:1 offdiagonal:1 wineland:1 maxwell:17 into:15 within:1 obtaining:1 bath:2 recognize:1 nothing:2 references:2 primarily:1 operator:1 additional:3 transfer:4 there:2 fast:1 start:2 conservation:2 low:3 way:4 ed:1 was:5 naturally:1 function:8 complete:1 form:1 enough:1 but:10 principles:2 pj:3 heat:29 gain:1 atom:1 photon:2 optical:3 considerable:1 coupling:2 pi:2 applying:4 consist:1 versions:2 whether:2 prevents:1 up:2 devices:2 until:1 placed:1 below:2 ρpi:1 exploration:1 pumped:2 ising:1 called:2 examples:1 mechanics:2 qin:5 constant:1 moore:1 classic:1 defined:1 inadequate:1 abstract:1 measure:3 am:1 general:2 single:1 reservoirs:4 our:1 accounting:1 regime:1 again:1 functions:2 no:6 ekert:1 edwards:1 when:8 detail:1 meekhof:1 field:27 other:3 role:1 department:1 realizability:1 conclusion:1 stat:1 repeat:2 generates:2 separate:1 models:3 gas:1 describe:1 rex:2 generated:1 massachusetts:1 included:1 incurred:1 gedankenexperiment:2 correlated:1 implies:3 shunt:1 vice:1 corresponding:1 physics:4 required:1 rather:1 mass:1 time:6 decoherence:15 requires:1 original:7 once:1
|
quant-ph9612035.txt |@word yamaguchi:1 secondly:1 concept:2 japan:1 consider:11 kensington:1 results:3 four:1 baby:1 proposition:8 entropy:59 grateful:3 go:1 expressions:1 trusts:1 cases:1 issues:3 gr:3 whose:3 certainly:1 maximally:1 depend:1 calculate:1 equivalence:5 tr:50 tp:2 tn:6 finally:1 asking:1 under:5 stochastic:1 characterised:2 worth:3 ingredient:2 p2:2 jensen:1 straightforward:2 returning:1 very:6 choice:1 every:2 p321:1 difference:1 matrices:4 generalised:14 dim:81 school:1 trn:1 did:1 issue:1 t2:5 applicable:2 t0:8 occurs:1 hartle:22 discrete:1 vector:3 math:7 recall:2 small:2 eigenvalues:3 noted:7 programme:2 upper:1 p1i:3 ρt0:1 dealing:1 consistent:51 fold:2 zero:6 evaluated:1 further:1 eigenspaces:1 canonical:8 spectral:4 ρq:1 what:2 plays:1 sub:1 giving:1 trivial:3 section:4 version:4 suspect:2 subspaces:1 new:8 pioneering:1 edited:6 princeton:2 simultaneously:1 gravitation:1 respectively:2 adrian:1 behaviour:1 refinement:10 asymmetry:1 les:1 ht2:2 ht1:2 address:1 represented:6 consideration:1 november:1 standard:21 respect:5 appears:1 change:1 obtained:2 popescu:1 allows:1 suggests:2 procedure:1 published:2 domains:1 suitable:1 changes:1 emerge:1 useful:1 projection:10 extra:1 summations:1 explained:3 attain:1 advocated:1 boolean:1 decrease:2 summation:1 resolutions:1 unit:4 readily:1 environment:2 use:13 quasi:1 projector:10 would:2 prove:2 probabilities:7 positive:9 negative:2 properties:7 comparing:1 noting:2 call:1 therefore:3 finest:1 associated:12 25th:1 type:4 theoretical:1 more:7 linden:4 preserving:1 clearly:4 operators:13 factor:1 λd1:3 ignorant:1 particular:9 localised:1 foundations:1 hole:1 iv:1 iii:2 emphasising:1 renormalising:1 must:2 logarithm:1 high:1 account:2 word:1 origins:1 tokyo:1 science:2 work:4 reproduce:3 minimum:11 values:3 minimisation:1 cam:1 following:6 making:1 dec:1 my:1 example:9 history:19 abcd:1 grained:6 give:1 calculation:1 sense:2 algebras:1 states:11 his:1 riedel:1 purity:1 degenerate:2 arise:2 subsystem:2 occur:1 simple:2 absolute:1 information:70 needs:1 varied:1 turn:3 rather:5 s2:3 s1:3 orthogonal:2 feature:1 s4:9 how:3 criterion:1 pure:19 symposium:1 coleman:1 priori:3 simplicity:2 product:7 description:1 algebra:1 may:24 max:1 earlier:3 derived:1 containing:1 independent:2 studies:1 repeat:1 attempt:1 third:1 facilitate:1 foulis:1 fine:1 cosmology:1 complexity:2 undo:1 so:18 expression:4 fundamental:2 decreasing:1 increase:1 words:1 order:4 operations:2 exclusive:3 acts:1 interpretation:2 dx:1 ith:1 produces:1 numbers:2 developed:2 over:13 choose:5 murray:1 interpreted:1 whilst:1 paper:7 london:1 looks:1 financial:1 mentioned:1 existence:1 satisfies:3 still:1 jaynes:2 its:2 before:2 group:1 thank:1 jeremy:1 chosen:2 interesting:4 temporal:1 jim:1 lj:3 decreases:6 li:3 window:18 offers:1 compelling:1 systems:1 quant:5 main:1 defining:2 finer:1 correspondence:1 non:4 motivated:1 greater:2 combination:1 trh:5 cover:1 framework:3 mxm:1 they:2 now:18 discuss:1 developments:1 represents:1 several:2 lies:1 always:1 university:2 hamiltonian:1 concave:1 identified:1 divides:1 orthonormal:1 theory:38 inequality:6 each:10 found:4 entirely:1 higher:2 traces:1 side:4 d44:1 homogeneous:9 development:1 ei:4 map:2 energy:1 reduce:1 idea:5 related:5 t3:1 inhomogeneous:3 sandu:1 weinberg:1 measurement:1 quantum:39 laboratory:1 operation:1 t1:5 greechie:1 es:7 out:2 projections:1 respects:1 shown:5 ezawa:1 matrix:6 space:39 furthermore:2 since:15 crucial:3 qc:3 denotes:1 content:2 replacing:1 kent:5 thermodynamic:1 medicine:1 constants:1 get:1 suffices:1 ri:7 rj:11 shows:3 decoherent:2 wiley:2 linear:1 written:7 diagonal:4 possibility:2 quite:2 bringing:1 approaches:1 statistics:2 advantages:2 york:3 members:1 imagine:1 put:2 van:1 9ew:1 additional:2 definition:16 pairs:2 qj:22 language:1 geometry:1 could:1 βx:1 times:4 ordering:1 impure:4 wright:1 u4:2 hence:8 dimv:1 trv:8 onto:7 assign:1 south:1 first:3 xj:2 initial:5 probability:12 feel:2 u1:4 number:4 xd:14 infinite:1 done:2 least:1 reached:1 precisely:2 illustrate:1 interchange:1 given:16 necessarily:2 checked:2 similarly:1 introduction:2 adjoint:8 system:11 construct:3 their:3 intermediate:1 draft:2 too:1 htn:2 just:1 ordered:4 scheme:4 bits:1 murayama:1 gives:1 option:1 relationship:1 recursively:1 latter:1 accurately:1 pni:3 motivates:1 part:1 somewhat:1 authors:2 x2:1 natural:3 x1:1 than:5 peaked:1 generalisations:1 split:2 require:2 namely:3 halliwell:3 project:1 classes:2 onedimensional:1 solely:1 minus:1 w2:4 motivation:2 persuasive:1 cn:2 takes:2 generality:2 ann:3 measure:12 discussions:1 say:2 ucsb:1 disjoint:5 seen:2 seem:1 seek:1 linked:1 genuine:1 min:4 convenient:2 self:8 rudolph:1 able:2 gravity:1 leverhulme:1 note:9 potential:1 take:3 finding:1 even:1 gleason:1 towards:1 unless:2 trace:3 shall:9 ıve:1 sets:17 nostrand:1 leave:1 most:6 said:4 but:6 sfi:1 pair:2 future:1 intrinsic:1 class:9 observation:1 considered:5 kj:2 clear:2 focussing:1 vertices:3 km:5 typeset:1 ways:1 kq:1 points:1 principle:1 refining:1 diag:1 left:1 physics:3 sum:6 fact:8 omnes:1 thomas:1 selection:2 particularly:1 show:13 spaces:1 relation:2 lloyd:1 analogue:2 d2:11 find:3 d1:7 2bz:1 eigenspace:1 situations:1 histories:43 should:9 penalty:1 only:10 explicitly:1 black:1 subsection:1 indeed:6 isham:6 pj:2 do:1 mixture:1 above:3 notation:1 means:2 familiar:1 zurek:3 between:2 cannot:5 closely:1 international:2 dw:2 symmetries:1 neither:1 pagels:1 evolution:7 reading:3 bar:1 course:3 approach:7 arxiv:1 dowker:2 investigate:1 stupid:1 contain:1 including:2 fixed:1 gell:8 anticipate:1 satisfy:2 coarsest:1 set:43 aspect:1 unpublished:1 maximum:5 relative:5 argued:1 see:11 college:2 result:2 w1:7 w0:7 fail:1 close:1 theoretic:1 ucsbth:1 invoked:1 tensor:7 αy:1 αx:1 positivity:1 state:9 proof:1 simplest:1 αi:72 drawn:1 boundary:2 αj:7 conditions:1 email:2 αn:2 attention:1 terms:3 august:1 missing:5 importance:1 p2i:3 notion:8 analogues:1 omn:7 however:16 reproduces:1 ji:6 key:4 problem:2 both:2 essentially:3 desired:1 many:6 taking:2 bution:1 according:1 called:2 context:8 logic:1 contribution:1 whole:2 finds:1 mann:8 piran:1 reside:1 u2:4 unclear:1 jj:10 point:4 reasons:3 had:1 others:1 penetrating:1 dimensional:18 fashion:1 simply:2 addisonwesley:1 normalisation:4 throughout:1 considers:1 second:1 considering:2 decohere:1 ensures:1 light:1 described:2 puts:1 basis:6 addition:1 strings:1 copies:2 been:8 int:2 much:1 grainings:1 coarse:5 minimise:2 expected:2 ph:5 pi:31 pn:2 define:12 corresponding:3 schreckenberg:4 propositions:14 subspace:2 understand:2 c2:1 houches:1 denote:2 those:1 quantisation:1 case:18 p1:4 unlike:1 contexts:2 might:9 ij:17 value:15 will:8 while:2 suppose:1 viii:1 situation:3 property:4 region:1 sw7:1 unitary:5 αt2:2 αt1:2 vol:1 von:2 damtp:1 thus:14 iw:3 equal:2 ii:6 need:5 itself:1 im:1 return:1 ic:1 technology:2 id:48 different:6 develop:1 thereby:1 trial:3 suggest:1 same:4 any:19 member:1 potentially:1 arguments:1 finite:2 events:1 difficult:2 hermiticity:1 fairly:1 used:6 singapore:3 again:1 i1:7 i2:6 upon:2 hand:7 v1:2 v2:2 uses:1 αtn:2 frequently:1 identity:5 recent:1 relies:1 lower:1 shortly:1 proceed:1 try:1 ingredients:1 well:2 without:3 mod:1 consistency:1 firstly:5 model:1 arising:1 dimension:15 usual:5 ny:1 world:2 proposed:2 less:1 being:2 topos:1 newton:2 ideas:4 questions:1 λd:1 ii1:1 alternative:1 griffiths:3 preprint:2 density:9 regarded:1 minimises:1 help:2 except:2 lattice:4 rˆole:4 attractive:2 easy:1 theorem:2 playing:1 reversal:1 ought:1 real:4 aspects:2 around:2 rev:5 easily:3 evaluate:1 showing:1 decomposed:1 possible:7 additivity:1 possibly:1 private:1 nor:1 press:1 using:2 like:1 minimised:3 helpful:2 follows:1 reduces:3 brun:1 either:1 evolutions:1 become:2 interestingly:1 mathematical:2 right:3 dordrecht:1 neumann:2 classical:1 sequence:1 butterfield:1 some:1 play:2 understood:2 elements:2 examples:5 b2:2 convex:10 universes:1 loss:2 happens:2 recently:1 dimensions:1 normal:1 id2:2 comments:1 id1:1 does:8 kobayashi:1 prob:8 refer:1 inserting:1 conference:1 measures:2 scientific:2 selecting:1 equivalent:3 step:4 revtex:1 although:3 pv:25 hilbert:19 bz:1 stage:2 comparison:1 about:2 central:2 nomura:1 extension:1 extending:1 discussed:1 meaning:1 o:1 sake:1 introduced:1 projectors:21 block:1 considerations:1 cambridge:3 communication:1 into:5 within:2 bound:3 three:1 nothing:1 appropriate:2 references:1 pi1:27 operator:35 negation:1 refined:2 next:2 acknowledgements:1 span:1 log:96 ρp2:2 extremely:1 support:1 there:16 question:1 u3:2 imperial:4 start:2 way:3 crucially:1 forward:2 was:2 naturally:2 function:35 form:20 offer:1 hw:1 encodes:2 hoped:1 taken:2 repeated:2 construction:2 subsidiary:1 true:2 exhaustive:3 partially:1 made:1 wise:1 society:1 up:13 us:6 windows:10 below:6 ρpi:7 uk:2 demonstrate:2 distribution:3 similar:1 calculated:1 blackett:1 mechanics:7 sort:1 ac:2 constant:3 choosing:1 pin:54 defined:15 certain:4 abstract:1 describe:5 proven:1 general:11 substantially:1 single:4 distinguished:1 postulating:1 our:12 partly:1 formalism:2 distributions:3 physical:3 ni:1 functions:32 compared:1 nl:1 no:12 na:1 when:3 proceedings:3 application:1 other:13 special:5 papers:1 envisages:1 theor:2 kullback:2 conclusion:1 stat:6 functorial:1 intend:1 varadarajan:1 remarked:1 bundle:1 stay:1 cb3:1 generated:1 important:6 previous:3 proceeding:1 pi2:5 needed:1 structure:5 implies:3 longer:1 requires:1 statistical:1 required:1 rule:1 graining:1 depth:1 ratios:1 time:40 far:3 n1:3 decoherence:72 resolution:3 having:3
|
quant-ph9612036.txt |@word lagrangian:2 four:8 entropy:8 consists:1 neglible:1 whose:3 calculate:1 under:4 worth:2 unrenormalized:1 every:1 vast:1 solution:6 convenience:3 cnea:1 wronskian:1 force:1 estimates:1 direct:1 approximation:1 likely:1 correlator:1 qualitatively:1 haake:1 even:3 selected:1 above:20 new:3 net:1 increasing:1 consisting:1 coefficient:4 evolving:2 aij:1 here:8 represented:1 path:11 κp:7 κr:7 obtained:11 glo:1 study:5 approaches:1 california:1 projection:2 elaborated:1 explained:2 plenum:1 total:3 derivatives:1 would:6 laflamme:1 negative:1 therefore:11 type:4 separated:2 relax:1 brings:1 odinger:8 hold:1 circumstances:1 springer:1 work:5 macroscopically:1 temperatures:6 root:1 example:7 renormalization:1 organized:1 feature:3 very:19 nontrivial:3 answer:2 ordinary:1 oscillatory:2 replacing:2 lae:1 oscillators:3 after:6 wrong:1 summarize:1 constants:4 effective:4 wint:2 environ:1 correlation:1 tantalizing:1 order:12 grabert:3 interpretation:4 zeh:1 vary:1 thesis:1 satisfies:1 before:4 difference:1 writing:2 fig:5 easier:2 overcome:1 maximal:1 them:3 combination:2 mixtures:1 effects:8 they:13 sixteen:3 represents:1 fringes:12 each:12 d40:1 d47:1 side:2 displacement:1 carry:1 literature:3 substantially:1 drude:10 superposing:1 restricted:1 diffusive:5 reader:1 ro:3 ri:14 rj:1 linear:15 associate:1 gardiner:1 midpoint:1 free:2 standard:3 davidovich:1 estimate:2 enormous:1 r0:7 r1:8 r2:1 created:1 iss:2 starts:1 tied:1 onto:3 already:1 features:3 restrict:1 another:1 eqs:1 approximately:2 master:35 too:1 leggett:2 ranging:1 a31:1 collapse:1 centered:3 distance:2 showed:2 second:4 preparation:13 classes:1 expo:1 tion:1 enables:1 fashion:1 rewrite:1 mind:1 manner:1 seen:4 seem:2 relatively:4 strength:2 convenient:3 responsible:5 oriented:1 effectiveness:6 broglie:1 though:3 involving:2 phase:1 don:1 observation:1 bracket:1 principle:1 sum:7 incorporate:1 labels:1 solutions:3 d2:7 d1:8 just:7 spite:1 ment:1 situations:2 integrate:1 do:4 df:1 de:4 dc:3 dx:1 dw:6 dt:7 du:5 ds:10 acknowledgments:1 analytical:1 habib:3 depends:4 w2:2 correlational:1 techniques:5 exponent:6 away:1 symmetric:1 simplest:1 approach:3 wd:1 terms:41 wb:1 wa:1 nature:5 weak:1 however:13 wi:1 vernon:2 ws:1 received:1 cos:6 ilo:2 raimond:1 contribution:1 argue:1 wider:2 σx2:4 basis:1 observing:1 three:1 been:16 phy94:1 iκ2:1 much:5 basic:2 quantities:1 concerning:2 coherent:3 fceyn:1 applied:3 originate:1 euclidean:6 applies:1 property:3 procedure:1 iv:2 ii:5 im:3 ic:2 interacts:1 containing:2 make:2 complex:2 quant:2 big:2 underdamped:1 grows:1 independent:6 peaks:31 trajectories:7 monotonic:1 hand:6 normalization:2 mentioning:1 joos:1 maxima:1 quoted:1 yet:1 previous:8 hao:1 deconstructing:1 weiss:1 spread:4 transformed:1 easy:3 apart:1 iτ:6 iφ:1 fundaci:1 possible:4 occurring:1 appearing:10 avila:2 specific:1 arbitrary:4 right:2 totals:1 contributing:1 plot:7 super:1 properties:5 anomalous:3 o:5 slightly:1 considerations:1 publishing:1 presence:2 down:2 pair:1 hanggi:1 wad:1 wac:1 wab:1 why:1 width:4 accordingly:1 way:8 triplets:1 was:7 form:19 idealized:2 especially:1 prevents:1 maximum:1 simplifying:1 proved:1 moore:1 computing:2 dξ:2 accounting:1 archive:1 interferences:1 regime:1 no:4 when:9 vanishes:2 interested:1 role:5 a15:1 a14:1 a17:1 a16:1 a11:1 a10:1 a13:1 a12:1 models:9 a19:1 a18:1 ξi:12 ξn:3 dissipation:1 ξf:2 dτ:2 packets:4 dσ:1 together:3 time:72 n2:2 concept:1 remarkable:1 brownian:6 remarkably:2 certainly:2 uneven:1 depend:4 environment:35 finally:5 monotonically:1 ρse:1 must:4 advantage:1 zhang:3 frequencies:2 maali:1 exact:11 presented:4 turns:4 solved:1 settle:1 prevent:3 mn:2 spectral:13 appear:4 satisfy:2 understanding:1 along:2 sieve:1 instituto:1 institute:1 studied:3 poisson:1 domains:1 hospitality:1 conveniently:2 studies:2 plotted:4 useful:7 extra:1 inducing:2 ipo:1 ipx:1 projector:2 predictability:1 memory:1 associated:5 msc:1 theoretical:2 today:1 validity:1 appendix:9 virtue:1 cases:2 effort:1 easiest:1 deformed:1 oscillator:2 modified:1 cat:7 values:6 following:19 making:1 claim:1 figure:9 performed:1 occur:1 verlag:1 ingold:1 write:5 criterion:1 pure:4 product:3 may:5 produce:5 data:2 2l0:2 stress:2 dynamical:1 ss:2 explicit:10 su:1 cosmology:2 so:6 deconstruction:1 representation:5 sg:2 lse:3 subsections:2 indeed:4 years:1 course:1 statistical:2 still:5 pointer:1 markovian:3 acknowledge:1 interesting:2 coordinates:10 giambiagi:1 main:2 non:10 evolution:40 introduce:2 identically:1 now:4 discuss:1 nor:1 term:17 realistic:4 entirely:4 ei:3 ed:2 gaussian:30 inhomogeneous:9 entering:2 ez:1 wavelength:6 shown:6 space:5 interference:24 investigation:1 formula:7 correct:2 shows:9 decoherent:2 theory:1 state:52 departamento:1 quite:2 matacz:1 complicated:3 e1:3 maˆıtre:1 derivation:3 motion:3 turn:1 first:15 origin:6 xi:14 variables:3 transform:3 xr:1 open:1 size:1 given:14 necessarily:1 unruh:1 c2n:1 types:1 speaking:1 x2:1 than:8 coefficients:45 wide:1 third:3 future:4 were:1 pre:1 ann:1 distorted:1 any:3 describe:7 aside:1 note:1 ideal:1 potential:2 take:1 coincide:1 trace:2 gunzig:1 formulae:9 multiply:1 analytically:1 wc4:1 considered:3 later:1 feynman:2 typically:2 quantity:1 tkb:1 show:13 friction:3 ground:2 ratio:2 histories:2 analytic:7 only:19 explicitly:5 over:9 rept:1 straightforwardly:1 cannot:1 2mn:1 boundary:9 regarding:1 intuitive:1 summary:1 kernel:8 burst:1 physically:1 wcd:1 uncorrelated:1 caldeira:2 satisfying:6 subsequent:1 outside:1 itp:1 between:22 notice:8 concentrate:1 analyzed:9 universitaria:1 suppressed:2 x2i:1 many:3 called:3 enabling:1 σx:7 σp:8 expression:7 comes:1 pabell:1 minima:1 121a:1 moreover:4 considering:1 dqdq:2 damping:2 νn2:4 davila:1 direction:1 enable:2 formed:2 observe:1 case:15 eis:1 squeezed:1 investigating:1 coupled:1 sudden:1 different:4 paz:9 same:5 arguments:1 physical:4 investigated:2 dreyer:1 locality:1 roughly:1 solve:3 coordinate:2 model:14 dimension:2 justify:2 being:9 captures:1 rest:2 zoller:1 remember:4 except:1 lett:2 momentum:11 real:3 b59:1 around:3 rules:1 ce:3 world:1 particle:3 reduces:2 velocities:1 wbd:1 grants:1 wbc:1 integrals:3 stationary:1 reduced:14 twelve:1 exposed:1 intact:1 superposition:4 nonzero:1 provided:1 extensively:1 expressing:2 propagating:1 equivalent:1 ez2:1 eiσ:1 discussed:3 practical:1 chou:1 mixed:1 cambridge:1 references:1 determine:3 operator:17 log:6 lok:1 there:3 dispersion:2 start:1 cats:1 low:3 delocalized:6 complete:3 attainable:1 dissipative:4 october:1 applying:1 ωs:4 liouville:1 reanalyze:1 ωo:12 ωn:2 detailed:2 ac:2 cirac:1 ad:1 aj:5 moved:1 general:8 examine:3 ar:1 moves:1 tedious:2 again:2 valid:4 forcing:1 unobservable:1 deviation:1 briefly:1 separate:1 includes:1 a1:4 a3:1 a2:4 a5:1 peak:6 a7:1 a6:1 a9:1 a8:1 2mkb:1 decoherence:36 starting:1 represent:1 consider:6 splitting:1 kicks:1 ciudad:1 generalize:2 expressions:11 research:1 nonlocal:2 present:8 presentation:1 iνn:3 straightforward:2 far:2 translations:3 denoted:1 dispersions:5 manageable:1 hamiltonian:2 t4:1 t2:3 applicable:3 large:1 small:10 renormalized:4 zero:18 further:1 calzetta:1 renormalizes:1 bilinear:1 what:3 sub:5 section:9 method:4 full:2 modify:1 provides:1 situation:3 nent:1 equations:11 amount:1 action:5 uniquely:1 via:1 followed:1 analyzing:6 ıa:1 takes:1 distinct:1 contains:6 more:9 operators:4 particular:7 known:5 producing:2 evolves:1 equation:68 remain:2 del:1 evolved:1 dec:2 history:2 neglected:1 states:27 numbers:1 sense:4 νn:5 information:1 goal:1 awkward:1 κr0:1 rather:13 buenos:3 ensemble:4 simplicity:2 algebra:1 wiley:1 derived:6 corrections:1 plane:1 fn:6 short:12 negligible:1 fundamental:1 κri:1 hierarchy:1 developed:1 distortion:2 thermal:11 paper:6 through:3 existence:6 its:17 roots:2 rapidly:1 scully:1 absence:5 ohmic:4 systems:5 argentina:3 evaluate:1 propose:1 noticing:1 reflected:1 yu:2 easily:4 2p:2 2q:3 always:4 factorizable:6 2g:1 2l:1 found:5 characterized:2 subsystem:1 weight:1 energy:1 hard:1 idea:1 extended:2 expect:2 measurement:8 quantum:13 since:7 denotes:2 acting:3 print:1 induced:2 difficulty:1 reason:1 asi:1 generate:1 definition:2 optics:1 exponentially:1 universidad:1 integrand:1 number:1 preservation:1 pablo:1 temperature:24 introduction:1 calculations:1 scheme:1 recovered:1 listed:1 behind:1 sizable:1 part:5 translation:1 believe:1 diffusion:10 determines:1 aac:2 double:1 ωo2:6 determined:12 contrary:3 remembers:1 paths:2 majority:1 internal:2 useless:1 finding:2 play:2 towards:3 measures:1 most:2 aires:3 kb:2 clear:4 physica:1 exp:14 physics:4 qbm:12 particularly:1 find:10 impact:1 parameters:9 subsection:2 factor:8 mazzitelli:1 notation:1 dependent:20 zurek:8 express:1 nonequilibrium:1 during:2 progressive:1 disregarding:1 unpublished:3 see:17 individual:1 conicet:1 degree:3 hagley:1 currently:1 conditions:17 knowing:2 2σx:4 initially:4 attention:1 2σp:3 vanishing:4 both:14 last:1 l20:7 wo1:1 wo2:1 context:1 forgotten:1 whole:2 experimental:1 point:7 simple:26 corresponds:2 simply:7 suppressing:2 kernels:7 ensures:1 described:3 pw:1 due:2 pj:1 ph:2 pi:3 po:8 important:5 generating:2 lived:2 overloading:1 understand:2 p2:7 p0:1 p1:2 exponential:3 pacs:1 while:5 behavior:9 vectors:2 espacio:1 reads:2 itself:1 rij:4 triple:2 jpp:1 vanish:1 grant:1 belong:1 2νn:1 ωn2:2 shorter:1 calculation:3 used:4 dξdξ:2 robust:1 recent:1 task:2 analysis:2 questions:1 using:17 λl:1 conclusions:3 antorchas:1 location:1 input:1 solvable:2 euler:1 generalized:6 louisell:1 showing:2 wij:2 appendices:1 follows:2 imposes:1 essential:1 some:8 b1:1 sight:3 oscillations:1 curious:1 ourselves:1 scale:22 describing:3 id2:1 integration:2 eliminate:1 tends:1 minimal:1 bd:1 santa:2 plots:1 relating:1 hilbert:3 bz:1 asymptotic:3 pβ:5 constraint:1 tracing:1 cutoff:8 into:5 integral:16 nsf:1 paradigmatic:1 proportional:2 σp2:3 interacted:1 long:2 analyze:11 propagator:6 elsewhere:1 delta:1 line:4 2πg:1 characteristic:3 up:1 us:11 2πn:2 un:6 uk:1 autocorrelation:10 fluctuations:1 matsubara:2 similar:1 laplace:3 constant:4 reconcile:1 defined:10 influence:10 single:5 pˆ:14 formalism:4 preventing:1 points:1 becomes:3 elements:3 problems:1 prepared:2 allowing:2 suppression:1 structure:4 correlated:2 implies:2 required:1 speculations:1 carrying:1 having:3 once:2 partial:1 results:8 gg:5 gf:3 gn:6 contributions:3 gi:1 wc:26 anglin:3 pˆs:5 squeezing:1 stable:2 include:1 ingredient:1 g3:3 g2:6 wave:5 matrices:2 entire:1 lombardo:1 integro:4 barbara:2 smaller:1 zi:1 uea:1 dynamics:1 index:1 giving:1 expressed:3 exercise:2 ibid:1 respectively:2 desired:1 separation:8 others:2 z1:4 z2:7 z3:11 remark:2 larger:3 resulting:1 makes:5 scales:1 integrations:2 apply:2 tools:1 manipulate:1 use:4 superpositions:2 remains:1 next:1 few:4 sort:1 initial:86 transient:2 normalized:1 iii:4 account:2 ρe:1 ρi:2 ρo:6 ρs:1 ρr:1 proof:1 process:8 haroche:1 pieces:4 high:8 assumptions:3 ρ2r:1 decaying:1 six:2 regions:1 frontiers:1 instead:2 sin:1 collection:1 realized:1 separations:1 allow:1 wigner:12 produces:2 2sg:1 meter:1 produced:2 including:1 mentioned:1 perfect:2 decay:8 lo:6 temporal:1 estimating:1 ls:2 derivative:3 defining:2 fourth:1 outlined:1 mention:3 transparent:2 university:2 astronom:1 l0:6 disregard:1 kpi:1 kpj:1 homogeneous:3 arxiv:1 doing:1 related:4 frequency:10 our:13 out:7 matrix:29 rep:1 rev:16 integrated:1 interactions:2 ısica:2 completely:2 york:2 ρij:1 interaction:6 determining:2 could:4 times:5 derivations:1 wunderlich:1 reached:1 precisely:2 system:40 relations:2 grow:2 their:3 intermediate:2 final:14 completed:1 exactly:4 environmental:2 manifestation:1 fuzzy:1 outline:1 bei:1 halliwell:2 inversely:1 providing:1 result:10 exhibit:1 lines:2 curves:1 enforces:1 need:2 clearly:4 xri:1 studying:2 able:2 mid:1 mix:1 gδ:1 gα:1 connected:1 class:7 dent:1 χn:4 fact:13 selection:1 text:1 supported:1 trivial:2 principal:2 q2:1 based:1 knowledge:1 should:3 inherited:1 local:8 equilibrium:17 means:2 ones:9 processes:1 densities:2 ubacyt:1 differential:4 contain:2 qi:20 view:1 2p2:1 computed:4 correlations:31 recently:1 acquires:1 interacting:1 tend:2 favor:1 written:9 closed:2 neither:1 brune:1 ends:1 importance:2 efficiency:2 observable:1 limits:1 taking:2 equal:3 equat:1 relevant:5 cn:1 cb:1 ca:1 harmonic:1 environments:1 cd:1 ab:7 respect:2 accomplishing:1 trajectory:2 romero:3 cauchy:1 define:2 arises:1 corresponding:1 scrutiny:1 c9:1 c8:1 c3:1 c2:3 c1:5 c7:1 c6:1 c5:1 c4:1 couple:1 splits:2 value:7 will:28 almost:2 vi:1 thus:22 examined:6 generic:3 juan:1 radiation:1 unity:3 units:1 gets:1 eds:1 parametrizes:1 upon:2 effect:8 v1:4 v2:4 qβ:6 never:1 frequently:1 schr:8 center:1 nevertheless:1 well:5 exceedingly:1 position:16 arising:4 usual:7 less:1 half:1 obtain:11 localize:1 macroscopic:1 rapid:1 density:40 nato:1 dqi:4 kick:1 identical:3 fate:1 know:2 press:1 displaced:2 like:7 qualitative:1 become:3 because:3 classical:5 polynomial:3 growth:3 happens:1 instantaneous:1 does:3 noise:14 2q2:4 selecting:1 how:8 simpler:1 about:3 actual:1 universe:1 dependence:6 recognized:1 krj:1 carries:1 kri:1 projectors:1 a4:1 equally:1 previously:2 functional:9 p2β:39 noticed:1 quadratic:2 function:47 hr:2 but:11 hu:5 squeeze:1 dξi:8 illustrative:1 coupling:3 compute:3 evident:4 smooth:1 below:12 decays:2 limit:4 demonstrate:2 problem:6 piece:2 pij:3 universal:1 linearity:4 denote:2 identities:1 functions:14 compared:1 variety:4 other:11 details:4 conclusion:1 uba:2 auxiliary:3
|
quant-ph9612037.txt |@word limited:1 measurements:1 consider:3 remarkable:2 caused:4 lack:1 focus:1 illustrated:3 roy:1 ciudad:1 entropy:20 follow:2 contributions:1 localized:5 whose:3 certainly:2 depend:2 alamos:2 april:1 tr:8 environment:18 quasi:2 critical:7 squeezing:1 preserved:1 th:5 under:5 analogous:1 dramatically:1 ingredient:4 case:6 zhang:1 very:10 continues:1 account:2 wave:3 lyapunov:5 every:1 orientations:1 fall:1 word:1 trouble:1 difference:3 logarithmically:2 condition:1 leads:1 indicate:1 hamiltonian:1 did:2 knight:1 solution:2 damped:1 large:7 vector:1 small:5 study:1 round:1 smaller:1 oscillation:1 folds:1 uncomfortably:1 direct:2 mantica:1 approximation:2 fold:1 second:3 proviso:1 timescales:2 notwithstanding:1 teq:7 dynamics:10 estimated:1 tempted:1 haake:1 even:6 what:3 nonlinear:1 plays:1 previously:1 apparatus:1 life:1 sum:4 selected:1 remain:3 find:1 reminiscent:1 above:7 scientists:1 obvious:1 principal:1 contrast:6 coefficient:2 edited:1 evolving:2 full:2 ibid:2 eliminated:1 respectively:1 presence:1 never:1 theorist:1 believed:1 pancake:5 relaxation:4 directions:8 along:8 sieve:1 equations:3 implicit:1 growing:1 tn:1 obtained:3 almost:1 balance:1 leaves:1 larger:6 reason:2 resulting:1 poisson:5 action:5 narrow:1 changes:1 involves:1 depart:1 scales:1 explicitely:1 plenum:2 highly:2 modulated:1 inequality:3 decrease:2 nonequilibrium:1 resolutions:1 planck:5 λdb:1 derivatives:2 use:1 superpositions:6 usa:1 positive:3 contains:1 predictions:2 hilbert:2 classically:11 approach:3 therefore:6 memory:1 taken:3 survive:1 stage:3 theoretical:1 today:3 more:3 separated:2 hu:1 becomes:1 apparent:3 odinger:1 validity:2 reversibly:1 interplay:1 final:1 reversible:3 basically:1 sharply:1 particular:1 known:2 cases:1 hold:1 producing:1 must:1 logarithm:2 evolves:3 keeping:1 defines:1 quantized:1 equation:14 oscillator:3 london:1 worth:1 immune:1 macroscopically:1 erg:1 values:2 rewritten:1 evolved:1 2λt:1 following:2 dec:1 example:4 purity:1 references:3 d24:1 predict:1 exactas:1 near:1 states:16 effectively:1 assumptions:2 numbers:2 arise:2 distinguishable:1 occur:3 verlag:2 information:4 monitoring:3 recovery:1 rather:6 discussion:1 get:1 feature:1 recovers:1 how:3 varies:1 buenos:1 familiar:1 answer:2 ordinary:1 isotropic:1 oscillatory:1 map:1 product:3 may:9 oscillators:1 after:9 collection:1 hence:4 studies:1 truly:1 grow:2 a91:1 short:5 natural:1 dynamical:4 effective:3 slightly:1 separations:1 correspond:1 fraction:1 complexity:1 negligible:4 allow:1 keeps:1 subsequently:1 increase:6 order:6 typical:2 wavelengths:1 least:3 wigner:17 help:1 indeed:4 over:13 displayed:1 satisfied:1 years:2 produced:1 course:3 thermal:3 paper:4 including:1 statistical:2 stretching:3 mentioned:2 existence:4 kinetic:1 still:3 pointer:2 its:17 derive:1 monitor:1 decay:2 ln:2 interesting:3 τd:2 solving:1 scully:2 forms:1 h2:1 detected:1 production:8 degrees:3 systems:30 tumbling:4 argentina:1 τr:3 h0:2 correspondence:26 eventually:1 them:2 good:1 motivated:1 halt:1 outlined:1 practice:1 sooner:1 units:1 effects:3 they:4 half:1 multidimensional:1 now:2 day:1 maintaining:1 easily:3 term:11 characterizes:1 traced:1 2d:1 sufficiently:4 magnitude:2 stopped:1 radian:1 each:1 found:2 entirely:1 quarter:1 summarily:1 side:1 characterized:1 asi:1 subset:1 voyager:1 everyone:1 directly:1 mesoscopic:1 energy:5 idea:1 used:1 contracting:3 frequency:1 obtains:1 measure:1 quantum:53 laboratory:1 happen:2 summary:1 nonlinearities:2 neighbourhood:1 out:5 emerges:1 space:21 rep:1 since:2 interference:5 chaos:12 research:1 looking:2 transforming:1 reader:1 induced:6 issue:2 occurs:2 shows:1 exactly:1 earlier:1 theory:1 assured:1 written:1 ascertain:1 ısica:1 little:2 departamento:1 quite:2 approaches:1 complicated:1 york:4 estimate:2 juan:1 interaction:3 cured:1 starts:1 could:1 transition:2 days:1 motion:4 turn:2 place:3 exponentially:4 signature:1 corrections:6 support:2 first:2 size:1 xk:1 major:1 initial:14 features:1 probability:2 striking:1 thereof:1 long:5 another:1 pablo:1 carry:1 precisely:3 open:7 spread:5 dispersion:4 given:8 salient:1 temperature:2 start:3 introduction:1 achieved:2 system:21 approximately:4 unruh:1 their:7 zaslavsky:2 master:1 too:2 consistent:2 compromise:1 perfectly:2 exponents:2 observations:1 shell:1 imperfect:1 lot:1 wavelength:1 continuous:1 eliminates:1 discover:1 environmental:1 part:3 predictable:1 hillery:1 somewhat:1 authors:2 x0:1 believe:3 than:14 preferential:1 peaked:1 distance:1 delocalized:1 habib:2 isolation:1 require:1 likely:1 ehrenfest:1 nevertheless:1 absence:1 represents:1 enables:3 buzek:1 springer:2 d40:1 dynamically:1 reduction:1 argument:1 invalidated:1 already:1 environments:2 width:6 manner:2 further:1 need:3 seem:2 obviously:1 clearly:1 chirikov:2 affairs:1 angle:1 form:3 zero:1 depending:1 convenient:1 self:1 responsible:1 able:1 isolated:2 b59:1 note:2 majority:1 potential:5 comment:1 take:2 forces:1 schematically:1 so:7 coincide:1 rate:8 heisenberg:2 begin:1 broglie:2 beyond:1 shall:2 object:1 joos:1 most:4 regular:4 aires:1 significant:1 phase:21 acquired:1 ford:1 measured:1 why:5 singled:1 forever:1 don:1 especially:1 consequences:1 fills:1 accord:1 calculated:1 devastating:1 flow:5 km:1 proceedings:1 bracket:9 principle:21 exp:1 mechanical:1 physics:3 assistance:1 fact:2 laws:1 planetary:1 hyper:4 particularly:1 show:2 violation:2 ny:1 anyway:1 rotating:2 purely:1 radii:1 rough:1 tend:6 fine:1 debate:1 occupation:1 o:4 squeeze:2 based:4 favor:1 situations:1 explain:1 enough:3 should:2 analytic:1 only:11 originally:1 summarizing:1 integrable:7 constant:7 local:2 zeh:1 equilibrium:6 diffusion:12 his:1 astute:1 di:1 vary:1 zurek:12 de:4 db:1 expectation:2 preferred:6 mission:1 joint:1 cannot:4 longest:1 new:4 during:1 saturn:4 nearly:2 evolution:11 substrate:1 textbooks:1 luminosity:1 arxiv:1 gutzwiller:1 yield:1 patch:2 limits:1 prevents:1 through:1 fixed:2 hyperion:12 valid:4 approaching:1 precluding:1 set:2 opposed:1 observer:2 our:5 physically:1 national:1 sian:1 packet:2 observed:1 opposite:1 see:7 result:7 close:1 ur:1 satisfies:1 considered:1 appear:4 lost:1 satisfying:1 exponent:4 review:1 below:3 diverge:2 symmetric:1 initially:3 state:15 various:2 discovers:1 closed:1 between:9 orbiting:1 simplifying:1 boundary:1 conditions:3 law:1 available:3 sections:1 comparable:2 terms:3 nature:2 originated:1 weak:1 however:2 moyal:4 casati:2 uniformized:1 extent:3 distinguish:1 universitaria:1 come:1 problem:6 both:1 cos:1 last:4 irregular:1 always:1 σc:4 many:2 taking:2 according:3 against:1 called:2 susceptible:2 generous:1 berry:2 context:3 proceed:3 reply:1 σp:2 pabell:1 strongly:1 presumably:1 relevant:2 timescale:15 point:4 simple:1 had:1 asymptotically:1 vast:1 corresponds:2 community:1 σc2:1 dimensional:1 represented:2 ii:1 121a:1 simply:5 stretched:2 polynomial:1 moreover:2 superselection:4 conference:1 decohere:1 pp:3 light:1 leggett:1 argued:2 basis:4 addition:1 trajectory:2 create:1 three:1 been:4 aspherical:1 int:1 faithfully:1 much:6 slowly:1 damping:1 interest:4 basic:1 expected:3 pk:1 ph:1 meeting:1 ann:1 define:1 direction:8 describe:1 corresponding:6 indeterminacy:1 observable:1 am:1 concerning:2 xxx:1 essentially:2 maps:1 coherent:6 dramatic:1 understand:2 coherently:1 folding:6 presented:1 importance:1 standard:1 applied:3 p0:1 look:1 exponential:7 contexts:1 defining:1 expanded:2 conserved:1 value:2 will:67 while:6 harmonic:2 behavior:6 squeezed:1 property:2 region:1 characterizing:2 unsatisfactory:1 would:4 orientation:1 coupled:3 chaotic:25 cerdeira:1 thus:10 non:2 hardware:1 reads:1 neurons:1 properties:1 everyday:1 diagnostic:1 orbital:2 different:6 recover:2 wiley:1 atmanspacher:1 etc:1 generic:1 paz:7 belong:1 radiation:1 same:3 any:3 shorter:2 quant:1 wavepacket:2 coworkers:1 mixtures:1 underdamped:1 physica:3 finite:1 consequence:1 difficult:1 breakdown:5 evolve:2 literature:1 eds:2 singapore:1 trajectories:3 effect:4 counterparts:3 hand:2 moving:1 potentials:1 moons:1 recent:2 argue:1 schr:1 center:1 minimize:1 makes:2 well:3 d47:1 bohr:1 exceedingly:1 without:1 solve:3 encounter:1 studying:1 position:6 model:1 dimension:2 bodies:1 left:1 distances:3 wavefunction:3 less:2 isolate:1 proximity:1 newton:1 aspect:1 followed:1 λi:2 rotates:1 macroscopic:11 letting:1 manuscript:1 superficial:1 poses:1 conclusions:3 conclude:1 seems:1 discuss:1 other:6 nato:1 lett:4 versa:1 theorem:1 stable:7 solvable:1 momentum:4 opt:1 explained:1 aspects:1 around:1 rev:8 susceptibility:1 rules:1 caldeira:1 period:2 increases:1 ciencias:1 wojciech:1 bit:1 unique:1 loss:1 appearing:1 like:1 particle:2 chaotically:2 translates:1 specific:2 yields:2 arbitrary:1 become:4 essential:5 accessible:2 sketch:1 right:2 often:1 classical:32 absolutely:1 some:7 back:1 competition:1 linearly:1 growth:2 examples:1 superposition:5 happens:1 provided:3 scale:5 tracked:1 lead:1 zeits:1 though:2 comments:1 moon:3 does:1 louisell:1 eliminate:1 tends:3 prog:2 unstable:6 fragments:1 proc:1 minimal:1 process:9 dittrich:3 scientific:1 power:3 reaching:1 equivalent:1 processing:1 uniform:2 expansion:1 although:1 instability:6 2n:6 takes:2 gained:1 polynomially:1 carried:2 impenetrable:1 freedom:2 dependence:1 recognized:1 reduced:1 range:2 d45:1 consequently:4 therein:2 soc:1 own:1 markovian:1 accompanied:1 orders:2 into:6 within:2 negative:1 remarks:2 appropriate:1 because:3 ppw:1 hubert:1 operator:1 proportional:1 σp2:1 classicality:2 behaving:1 connell:1 fill:2 heq:5 suffice:1 there:4 question:4 approximate:1 fast:1 overestimate:1 los:2 influencing:1 facultad:1 low:1 way:3 series:1 astrophysics:1 yrs:1 was:4 naturally:1 function:21 elsewhere:2 newtonian:1 fundamentals:1 becoming:1 but:11 gaussian:2 volume:8 failure:2 properly:1 trying:1 true:3 naturales:1 longer:1 wisdom:1 leaky:1 frontiers:1 whether:1 characteristic:3 smooth:7 up:1 us:4 until:1 assume:1 liouville:6 limit:7 distribution:11 similar:2 agree:1 expect:2 mechanics:5 b62:1 associated:2 moore:1 defined:5 steady:1 abstract:1 measurement:2 influence:2 generating:1 general:2 single:1 fringes:1 ensuing:1 periods:1 formulation:1 gradients:2 graham:4 internal:1 regime:5 predictability:1 compared:3 paradox:3 nm:1 no:5 mathematica:1 when:9 continually:1 reality:1 preventing:1 field:1 interested:2 role:2 approximated:1 theor:1 2di:1 shrink:2 reaches:1 icarus:1 picture:1 introductory:1 coherence:4 generates:1 preceding:1 berman:2 nonclassical:1 a0:6 generated:2 important:2 studied:1 b256:1 structure:2 coupling:2 vice:1 2mkb:1 typically:2 age:1 required:1 interacting:1 d26:1 conjectured:1 ensuring:1 compete:1 presenting:1 time:15 far:1 σci:1 decoherence:38 starting:1 external:1
|
quant-ph9612038.txt |@word dewitt:1 consider:1 ali:1 lack:1 kanai:4 leads:4 known:2 whose:3 depend:3 equivalence:1 preserved:2 under:3 alberta:2 case:3 choice:3 emphasized:1 exact:2 condition:1 hamiltonian:10 turns:1 solution:3 recall:1 small:1 dutra:1 direct:2 greenberger:1 dynamics:3 canonical:20 what:1 stands:1 above:1 satisfy:1 ualberta:1 respectively:2 here:2 explore:1 const:1 equations:1 change:1 dec:1 institute:1 study:3 studied:1 usually:1 complicated:1 uniquely:2 requiring:1 use:1 levine:1 positive:2 brittin:1 next:4 m0:7 theoretical:1 operators:5 odinger:8 eλ:4 particular:3 killam:1 must:2 kumar:1 valued:1 razavi:1 equation:10 oscillator:9 canonically:1 trans:1 f1:7 f2:11 f3:2 calculation:1 december:1 νe:1 sense:1 fortunately:1 maps:1 nontrivial:3 ordinary:1 map:1 riesenfeld:1 de:3 transforming:1 oscillators:7 constants:1 man:2 correspond:1 rather:1 so:1 order:1 dx:6 kinetic:1 thank:1 acknowledge:1 ln:2 interesting:1 solving:1 choose:1 derivative:1 might:1 theo:1 non:1 they:3 souza:2 now:2 easily:2 university:2 presented:1 2m:5 higher:1 differential:1 financial:1 energy:1 ea:1 frequency:6 measure:1 quantum:14 eq:3 out:1 canada:2 shown:3 space:2 nuovo:3 since:1 rev:9 research:1 re:1 induced:2 integrated:1 math:6 shows:1 foundation:1 linear:1 mω:1 albuquerque:1 free:9 standard:2 formation:1 put:1 derivation:1 exponentially:1 δij:1 hence:4 first:2 eǫ:8 precisely:1 given:2 unknown:1 eqs:4 relations:1 their:2 listed:1 statement:1 supermanifolds:1 exactly:3 part:1 x2:7 eγt:2 determines:2 unfortunately:1 require:1 bea:1 cimento:3 depends:1 determined:1 arun:1 argument:1 generalization:1 manner:1 seen:2 clearly:1 self:1 note:4 finding:1 play:2 most:1 formulae:2 acknowledgements:1 class:9 consequences:1 considered:1 calculated:1 implications:1 exp:3 physics:1 fact:2 precise:1 2m0:1 show:1 lewis:1 iǫ:2 solutions:1 trivial:1 caldirola:4 knowledge:1 ment:1 should:2 lemma:1 only:1 cheng:1 means:2 dependent:12 express:1 2mg:1 words:1 2me:1 dt:2 dr:1 gen:3 evolution:2 textbooks:1 arxiv:1 yield:1 dodonov:1 mapped:1 fixed:1 view:2 requirement:3 set:1 schreiber:1 undergoes:1 namely:2 discussions:1 subject:1 αt:1 identification:1 closed:2 terms:1 however:2 jr:1 concentrate:1 ji:1 article:1 according:1 context:1 eiǫ:1 expression:1 finds:1 affine:1 ca:1 harmonic:10 dimensional:2 respect:1 considers:1 transformations:14 been:2 much:1 treat:1 ph:1 corresponding:3 spectrum:1 fung:1 mail:1 denote:1 p2:7 unlike:1 choices:2 korsch:1 ǫx:1 unitary:3 metric:6 ir:2 thus:1 quantize:1 agarwal:1 lengthy:1 perform:1 make:1 unity:1 quant:1 infer:1 difficult:1 hermiticity:1 independent:3 used:1 effect:5 action:2 moving:2 purpose:1 kim:2 schr:8 well:1 analysis:2 solve:2 position:7 latter:1 manifold:1 gdx:1 edmonton:1 campbell:1 yet:1 belongs:2 transformed:2 lett:3 solvable:2 transformation:12 momentum:4 real:1 2j1:1 results:1 corresponds:1 press:1 using:2 particle:9 alternatively:1 abdalla:5 arbitrary:5 classical:3 some:1 back:1 examples:1 happens:1 provided:1 dimensions:1 lead:2 subclass:1 does:1 prog:1 rescale:1 equivalent:1 hilbert:1 about:1 discussed:1 o:1 cambridge:2 previously:1 within:1 adjointness:1 references:1 operator:3 utility:1 support:1 there:1 hasse:1 gij:1 function:1 form:8 reduce:1 converse:1 but:1 berg:1 hc:1 line:1 true:1 made:1 compute:1 wish:1 us:6 demonstrate:1 problem:2 mechanics:4 constant:5 defined:2 ko:2 abstract:1 general:1 identities:1 functions:2 mostafazadeh:1 when:1 other:2 role:2 may:2 hausdorff:1 important:1 t6g:1 anticommutator:1 baker:1 pseudo:1 mass:12 dot:1 time:20 original:1
|
quant-ph9612039.txt |@word inverse:1 represent:1 concept:2 allowed:2 consider:4 remarkable:1 directions:1 lack:1 brownian:1 focus:1 leads:1 grateful:1 consists:1 na:1 contributions:3 reasoning:3 polinomials:1 reluctant:1 particles:14 preserves:1 careful:1 referring:1 re:1 concerned:1 equivalence:14 braginsky:1 passage:1 predicting:1 finally:2 investigation:1 preserved:1 under:3 stochastic:7 analogous:2 pˆz:10 worth:1 interacting:1 kπ:1 spreading:6 far:5 zˆ2:2 2re:4 rise:1 account:4 helpful:1 choice:3 print:2 manipulated:1 every:1 additional:3 sensitivity:1 fall:17 choosen:1 difference:2 bringing:1 condition:2 school:1 dominate:1 reciprocal:1 level:6 positions:1 notes:1 proposals:2 solution:3 correct:1 winter:1 admissible:1 vector:1 progress:1 dealt:2 small:2 inspection:1 equation:8 configurations:2 upper:1 smaller:1 force:3 coordinate:2 lecture:1 consistent:3 coefficient:1 maintain:1 feasibility:1 second:3 lines:1 value:6 equal:1 rigorous:1 further:2 dynamics:3 salvio:1 odd:4 rough:1 even:6 established:1 what:1 apparatus:2 deeply:1 section:9 selected:2 remain:1 uniform:4 looking:1 experiment:7 above:4 lifshitz:1 new:5 falling:5 contributes:1 consisting:1 contrast:1 body:3 edited:8 evolving:1 full:1 simultaneously:1 evaluating:1 prescriptions:1 respectively:7 eif:1 here:3 atoms:3 reported:3 asymmetry:1 objects:9 focused:1 possibility:6 separation:4 others:2 represented:4 path:1 along:2 strong:1 z0:11 appears:2 galilei:2 calculate:1 obtained:6 scienze:1 male:5 suitably:1 institute:1 involved:4 study:3 vectors:1 allows:3 vibrating:1 leaving:2 resulting:2 karim:1 action:2 conveniently:1 fourier:4 subjected:1 genuinely:1 row:1 emerge:2 via:3 regardless:2 although:2 family:1 explicitely:2 vin:1 magnitude:1 stochasticity:2 addressed:1 apply:1 resolutions:1 should:5 cloud:2 vienna:1 permitted:1 putting:1 additive:1 zρ:1 would:1 former:1 recalling:1 give:1 ψt:1 hilbert:4 distinct:2 definiteness:1 kinematics:3 therefore:3 totality:1 ψm:1 taken:1 care:2 type:1 until:1 reflects:2 more:9 israel:1 formally:1 becomes:1 operators:3 factor:6 odinger:10 validity:3 needed:1 appendix:5 rigid:1 normalized:1 sharply:1 particular:6 known:2 hold:1 iii:3 must:2 maz:2 comoving:1 mg:8 include:1 riis:1 mm:2 recall:1 inertial:14 work:2 mi:29 modified:1 london:1 cat:17 trajectories:1 dˆ:4 macroscopically:3 minimum:1 values:13 rewritten:2 ms:2 concepts:2 following:7 vt:8 dec:1 stimulating:1 history:1 modulation:1 indicated:2 solved:1 calculation:2 introduces:1 arise:2 organized:1 complications:1 accept:1 states:36 weighting:1 assumptions:1 performed:3 sense:3 distinguishable:2 species:1 english:1 counterpart:2 monitoring:1 straightforward:1 σz2:6 interacts:1 discussion:3 means:3 feature:2 write:1 very:2 resolution:1 pure:3 b5:2 instead:3 ordinary:1 conceptual:3 parameter:1 sin:3 hundreds:1 simplicity:1 pleasure:1 description:3 information:3 may:6 december:1 after:2 derived:1 mapping:1 straightforwardly:2 independent:2 produce:1 designed:2 waves:2 end:1 compatibility:1 grot:1 man:2 opto:1 natural:3 dynamical:2 imply:1 light:1 quoted:3 dissertation:1 explicit:1 lost:1 thorne:1 stimulate:1 generic:3 accelerated:6 molasses:1 so:6 fundamental:1 verify:1 representation:3 king:1 increase:1 order:8 turns:2 typical:1 imagining:1 holds:3 interpretation:2 laboratory:6 indeed:2 over:2 entries:1 constrained:1 satisfied:2 meter:6 interpreted:2 top:1 course:1 paper:1 through:5 statistical:1 signs:1 still:4 its:6 operative:1 before:1 mathematics:1 du:1 thank:1 img:1 recover:1 chosen:1 interesting:1 masses:7 relativity:2 troubles:2 khalili:1 coordinates:1 actually:1 better:1 previously:1 detected:2 microscopic:1 systems:3 pergamon:1 decreased:1 main:1 xxix:1 setting:1 ideal:2 correspondence:2 non:8 crucial:1 motivated:1 university:5 than:2 was:5 ya:1 universality:1 outlined:1 gauging:1 processes:1 investigated:1 tonin:1 framework:2 steane:2 letting:1 hamilton:1 effects:4 univocally:1 now:3 discuss:2 dielectric:1 fields:2 represents:2 february:1 equality:2 hereafter:1 off:2 reasonably:1 presented:2 b3:4 malkin:1 merge:1 gt2:1 accomplishments:1 2a:1 each:7 found:5 universit:1 interfering:1 characterized:2 mean:6 ann:1 domain:2 schemes:2 just:3 cohen:1 evolve:1 mesoscopic:2 mv:3 gaussian:15 related:4 t3:3 operator:2 owing:1 interplay:2 measurement:11 quantum:64 our:7 eq:10 repulsive:1 special:4 out:4 batchelor:1 given:9 hughes:1 matrix:5 simplifies:1 space:11 restricted:1 furthermore:1 since:5 interference:2 qc:1 denotes:1 content:1 transforming:1 pˆ2:1 at2:1 rb:1 denoted:1 formula:1 clarify:1 induced:2 viable:1 math:2 shows:1 bouyer:1 numerical:3 reformulation:1 theory:4 interactions:1 wineland:1 mechanisms:1 fisica:1 free:19 standard:3 difficulty:1 completely:1 perturbation:1 complicated:2 term:4 besides:3 imagine:1 ask:1 marzlin:1 estimate:2 phd:1 cornerstone:1 milburn:1 widespread:1 definition:5 derivation:1 language:1 ion:1 determining:1 collapsing:1 times:4 motion:12 turn:1 place:1 assumed:1 consequence:1 lia:1 think:1 first:6 origin:3 accounting:1 already:4 probability:6 striking:1 sentence:1 third:1 possessing:2 coming:1 geodesic:2 transform:3 adopted:1 another:1 diagonal:6 pˆ:3 precisely:1 aharonov:1 york:3 b9:1 little:1 necessarily:2 analitically:1 exists:1 table:2 strict:1 introduction:2 leading:2 dipartimento:1 system:6 least:1 parallel:1 their:2 intermediate:1 master:4 tune:1 scheme:2 fuzziness:1 ehrenfest:3 recovered:3 gives:2 correlations:1 abovementioned:1 trapped:2 bouncing:1 explanation:1 exactly:1 released:1 assumption:1 optical:1 nieto:2 manifestation:1 attempt:2 translation:1 macmillan:1 peculiar:1 specify:1 diffusion:1 distance:2 kind:1 variational:1 last:3 penrose:2 isolation:1 distinguishes:1 roberto:1 namely:2 final:1 preparation:8 matter:2 classes:1 contrary:2 supposed:2 were:1 zanello:1 rate:1 treated:1 distinguished:1 function:3 symmetries:1 behavior:3 bounces:1 unchanged:1 msec:1 curves:1 manuscript:1 width:2 variable:1 unlikely:1 archive:2 curved:1 null:1 any:5 elsewhere:1 acceleration:5 forced:1 strength:1 realm:1 form:9 zero:1 academic:1 check:1 latter:2 responsible:1 gravity:6 instance:6 emphasis:1 internal:1 square:1 analogy:2 negligible:1 subject:1 require:1 registered:1 m2:1 allerton:1 heisenberg:2 spectral:1 continuous:5 a3:2 allow:2 opposite:2 impulsively:1 goldman:2 qadir:1 object:2 most:1 invoked:1 ensure:1 bmi:1 definitions:2 remarks:2 probabilistic:3 class:5 three:1 probes:1 deviations:1 consequences:1 crew:1 considered:4 average:24 ko:2 physica:1 principle:22 exp:15 mechanical:4 velocity:4 left:1 physics:7 sum:1 fact:5 science:1 show:1 detection:1 probe:1 recipe:2 appearing:1 implying:1 attempts:2 yurke:2 carefully:1 routinely:1 analogue:3 determined:1 ground:2 ratio:4 knowledge:2 parameters:1 tof:8 rovelli:3 situations:1 writes:1 less:2 written:2 supported:1 operational:2 entities:1 only:8 going:1 intrinsically:3 postulated:1 various:3 constant:5 padova:4 local:3 accurate:1 achieve:1 do:1 mixture:1 µk:1 viewpoint:1 di:3 dependent:4 familiar:1 felice:1 between:16 overall:2 expectation:3 preferred:1 famous:1 ones:4 dz:2 despite:4 combinations:1 during:3 dt:5 2mi:3 net:1 evolution:15 de:3 approach:1 translating:1 arxiv:1 fixes:1 grav:1 summary:1 investigate:1 experiments:4 roger:1 predicted:3 dodonov:1 mapped:2 including:2 fixed:3 inside:1 view:2 available:3 set:2 motions:1 reference:10 achieved:3 imposing:1 frame:4 testing:2 maximum:1 relative:5 gr:1 see:7 individual:1 result:1 successive:1 discussions:2 close:1 best:1 wonder:2 closer:1 recording:1 gravitation:9 extend:1 speed:1 definite:1 pisa:2 naturwissenschaften:1 initially:3 state:31 difficulties:1 identification:4 closed:1 hopefully:1 affecting:1 accustomed:1 geometric:1 reading:1 conditions:4 arrival:3 preexisting:1 audretsch:2 terms:4 vertical:1 nature:6 importance:1 attention:1 weak:5 ascribed:2 4m2i:1 however:3 deterministic:2 vanishing:4 vt2:1 matos:1 distinguish:1 understanding:1 distribution:3 observer:1 both:5 cos:4 toward:1 prescription:5 observing:1 freely:5 taking:1 uncertainty:3 according:3 demanded:1 quantization:1 fulfilled:2 sensitive:1 merging:1 selective:1 purely:7 bristol:1 filho:1 variance:8 contribution:3 summarizing:1 expression:4 zˆ:13 experimental:6 ansatz:1 among:1 relevant:2 cn:4 cm:1 nonrelativistic:4 simple:2 effective:1 inc:1 corresponds:3 whatever:1 height:5 dimensional:2 galileo:5 maintained:1 simply:1 hope:1 consideration:1 cs:1 moreover:3 rep:1 throughout:1 torsion:1 considering:3 pp:1 configuration:2 described:1 transformations:2 cavities:1 basis:2 equations:3 create:1 due:8 been:16 z1:3 hitting:1 t2:3 z2:3 hawking:1 expected:4 ph:2 universal:1 define:2 madey:1 direction:2 arises:1 flight:24 unavoidable:1 observable:3 preliminary:1 quantities:3 offered:2 formed:1 precision:1 geodesics:1 coherent:1 ensuring:1 representative:1 rephrased:1 denote:4 irrelevant:1 obtainable:2 present:3 case:24 extracted:1 p0:2 wiseman:1 unlike:1 structures:1 davies:1 evaluated:3 will:9 while:3 suppose:3 match:1 cannot:3 applies:1 stopping:1 situation:1 revisited:1 2k:1 procedure:3 stoler:2 nikitin:1 versus:1 detailed:2 studied:1 satisfying:1 vogel:1 phenomenological:1 vi:2 presilla:1 2iµ:1 thus:2 them:1 surface:1 iv:2 ii:2 itself:2 im:3 im2:1 seen:1 affected:2 vz:2 property:1 alone:2 monroe:1 increased:1 acknowledgments:1 different:16 perhaps:1 italy:2 combination:1 σz:4 perform:1 arguments:2 make:1 same:10 clearly:3 princeton:2 complex:2 quant:2 wavepacket:1 viola:5 revival:1 helium:1 several:1 composition:1 evidence:1 exhaust:1 used:3 peaks:2 singapore:1 b10:1 conceived:1 upon:1 effect:10 hand:3 cesium:1 running:1 szriftgiser:1 introduce:1 unpublished:1 potentials:1 infinite:1 invariance:1 landau:1 normalization:2 recent:4 lower:1 schr:10 center:1 lockhart:1 whole:1 floor:1 well:5 analysis:1 patterns:1 observations:1 without:6 solve:1 temperature:1 mod:1 easily:1 firstly:1 position:29 bodies:6 usual:2 ny:1 evanescent:1 proposed:2 onofrio:5 being:8 generally:1 observed:1 obtain:1 rest:3 aside:2 assigned:1 press:8 manipulation:1 underlying:1 atomic:6 world:2 years:1 uller:1 momenta:3 envisaged:1 macroscopic:2 eigenstates:1 previous:4 κz:16 sampled:1 signal:1 density:8 surprises:1 noted:1 point:4 dalibard:2 except:1 conclusions:1 potential:2 transformed:1 lett:9 theorem:2 thoughts:1 possess:1 transformation:6 momentum:11 centrifugal:1 identical:5 tests:3 vii:1 iν:1 around:2 rev:16 demands:1 conclude:1 phenomenology:1 showing:1 results:1 possible:5 propelled:1 unmeasured:4 vacuum:1 confined:1 using:4 emergence:1 variables:1 marzolo:1 meaning:1 semiclassical:2 modifications:1 necessary:1 like:8 particle:13 therein:1 exploiting:4 reduces:1 velocities:2 disentanglement:1 exploit:1 accelerating:1 manifest:1 consensus:1 collect:1 pendula:1 imposes:1 either:3 sezione:1 follows:3 degree:1 become:4 tower:1 stationary:1 essential:1 cooled:2 italian:1 mathematical:1 parity:3 sketch:1 performing:2 wavepackets:1 classical:38 people:1 some:10 back:1 b4:2 calculated:3 b6:2 mat:2 b1:3 sight:1 respect:5 proper:1 extended:1 bord:1 sufficient:1 ourselves:2 happens:1 provided:3 vol:1 total:1 recently:1 measurements:2 antimatter:1 comments:1 get:1 rewarding:1 does:2 decomposition:1 expressing:1 assuming:1 speak:1 analyzed:1 philadelphia:1 refer:1 measuring:1 process:3 noise:1 scientific:1 power:1 slight:1 equivalent:2 wavefunctions:2 agreement:2 tannoudji:1 step:2 upward:1 2m:7 properties:2 bz:1 stage:1 zur:1 limitation:1 kinematical:2 actual:1 carried:1 constraint:1 column:1 kasevich:2 discussed:4 dependence:8 o:6 reduced:2 deserves:1 involving:1 nothing:1 trajectory:1 mixed:1 bertotti:1 introduced:4 a4:2 considerations:4 cambridge:5 real:1 publishing:1 presence:1 h2:8 material:1 into:6 within:6 obtaining:2 balances:1 phase:9 hermitian:1 weighted:1 references:1 female:5 einstein:2 frames:7 proportional:2 methods:1 relativistic:3 schrodinger:1 deal:1 few:1 measured:3 springer:3 initial:23 question:4 approximate:1 long:1 start:1 cats:1 structure:1 way:6 letter:1 ψn:6 analyze:1 sections:1 chu:2 lowest:1 survives:1 complete:4 newtonian:1 enough:2 something:1 leiden:1 adjusting:1 differences:3 denoting:3 but:5 tate:1 fairbank:2 repeated:1 properly:3 gain:1 hz:1 atom:3 remote:1 line:2 inverted:1 he:2 directed:1 infn:2 made:4 coefficients:3 surprising:1 understood:1 prevents:1 gravitational:17 up:2 us:10 theoretical:1 placed:1 b7:2 limit:8 critical:1 continuously:1 fluctuations:3 problem:5 similar:2 called:4 accelerate:1 mechanics:11 toller:1 associated:3 b2:3 zeno:1 defined:6 reproducing:1 configurational:2 mirror:3 linearity:1 deep:1 general:7 single:4 karpacz:1 exist:1 postulating:1 operatorial:1 orders:1 corresponding:8 hamiltonian:3 distributions:12 simplest:2 physical:2 tedious:1 again:2 nj:1 compared:1 nm:2 no:7 b8:1 whereas:2 wavefunction:7 when:7 detail:3 meekhof:1 reality:2 field:6 conceptions:1 other:8 role:1 details:2 holding:1 test:12 weights:1 concerning:2 nice:1 deviation:1 picture:5 apparent:1 superposition:7 separate:1 models:1 remarked:2 reached:1 ultimately:2 prepared:7 a1:1 commutator:1 generated:2 a2:2 a5:2 allowing:4 a7:1 a6:1 influence:1 reanalyzed:1 decoherence:1 shown:1 gedankenexperiment:3 metastable:1 regime:2 coupling:6 starting:4 required:2 berlin:1 ammerzahl:1 equivalently:1 impossibility:1 observe:3 mass:17 nelson:2 time:42 observables:2 overturned:1 requires:2 having:9 once:2
|
quant-ph9612040.txt |@word ginzburg:1 sch:1 whose:2 const:1 calculate:2 truong:1 under:14 chirally:1 rise:3 every:1 experimentally:1 school:4 cause:1 solution:4 vector:12 indices:10 levicivita:1 ǫh:2 consistent:1 disclination:2 second:8 even:3 established:1 errors:1 while:1 above:2 new:10 ever:1 coefficient:1 simultaneously:1 behavior:1 here:4 atoms:2 active:3 path:42 quite:2 contraction:2 obtained:7 endpoints:4 study:1 permit:1 advantages:1 changes:3 projection:1 explained:1 plenum:1 sliced:12 marchetti:1 total:1 univ:1 derivatives:17 would:4 therefore:4 type:1 until:1 separated:1 naive:3 odinger:9 curvature:30 phone:1 berlin:15 gλν:2 must:5 springer:6 mo:1 work:1 theories:3 root:1 example:3 indicated:1 give:1 relativistic:1 cartan:2 end:1 turn:3 provide:1 feature:2 how:3 nontrivial:2 significance:1 answer:1 ordinary:4 massive:1 description:2 transforming:3 earlier:3 minimized:1 demanding:1 wrong:2 parallel:1 types:4 effective:3 hasty:1 appreciate:1 algorithms:1 keeps:1 order:7 over:13 vary:4 xi:32 london:1 japan:1 before:1 fiz:2 writing:3 nonholonomic:41 fig:9 versus:2 them:5 combination:1 slicing:4 they:11 singularity:1 gλµ:1 each:10 side:4 successively:4 series:2 principles:2 literature:3 dewitt:11 crucial:2 particles:6 eprint:1 reader:2 linear:2 midpoint:6 free:3 standard:4 reparametrizations:1 wanted:1 aj0:2 correctness:3 corrections:1 onto:1 rank:1 restrict:2 spinning:5 another:3 cartesian:11 rewritten:2 similarly:1 eqs:2 xin:7 too:2 burgess:2 inconvenient:1 variational:4 somewhat:2 distance:2 matter:7 publ:1 powers:3 rewrite:4 spectrum:2 seen:3 seem:1 academic:1 latter:1 responsible:1 oriented:1 forces:1 shall:3 sσµν:1 object:1 extending:1 germany:1 phase:1 observation:1 definitely:1 principle:30 saying:1 soluble:1 iǫ:1 gauge:1 solutions:2 d2:7 just:2 geodesics:6 integrate:1 rice:1 do:3 seifert:1 cheng:1 dd:24 de:6 preferred:4 dx:1 dt:32 ds:2 dq:18 runs:1 bar:1 textbooks:2 fields:8 pioneering:1 reference:2 observed:2 depends:1 result:7 dµ:3 best:1 clarifies:1 tensor:26 symmetric:4 simplest:1 approach:3 discovery:1 terms:11 nature:2 however:10 hashitsume:1 receives:2 contribution:4 adapted:1 2nd:1 basis:9 three:1 been:12 interest:1 basic:2 expected:1 stresses:1 j0n:2 pnµ:2 mandelstam:1 manifolds:3 applied:5 reciprocal:1 employ:1 euclidean:5 property:2 procedure:11 played:1 ii:2 ij:1 disappear:1 containing:3 perform:1 make:2 freie:1 quant:2 avoids:1 several:1 independent:4 elworthy:2 trajectories:7 differing:1 hand:8 spacetime:1 burgers:5 materials:1 possesses:1 quoted:1 dyads:1 transforms:1 yet:2 stratonovich:3 previous:1 enters:1 bullough:1 infinitely:1 had:1 passive:1 transformed:7 easy:2 iλ:4 breaks:1 possible:8 spanned:1 rµν:3 unique:3 brought:1 performing:1 specific:5 abdalla:2 schwarz:1 arbitrary:6 nonintegrability:1 www:5 right:5 people:2 successfully:1 somehow:1 pelster:1 dropping:2 contributing:1 predicting:1 shifting:1 properties:4 chapter:1 stokes:3 raised:1 presence:9 puzzle:1 down:3 lies:1 sov:1 amsterdam:1 often:2 indispensable:1 initial:4 transform:1 way:4 was:10 lowest:2 form:19 epsilon:1 differences:7 failure:5 scholtz:1 removed:1 true:4 absent:1 gorkov:1 versions:3 crystal:6 fermi:3 nµ:3 textbook:3 evidence:2 postscript:1 dν:1 exist:2 commuting:3 archive:1 physical:4 no:15 na:1 whereas:1 when:9 vanishes:2 setting:1 role:6 sponding:1 superposition:1 describe:2 variable:2 longer:6 coulomb:1 dφ:1 proposed:1 interval:3 time:56 quantity:3 particular:1 leads:3 certainly:2 inverse:2 analogous:2 advantage:1 choice:2 advised:1 emphasized:1 riemann:8 presented:5 upper:2 pnν:1 prediction:1 sign:1 adds:1 appear:1 contracted:4 goes:1 lifshitz:1 kleinert:21 satisfy:3 prescriptions:1 understanding:1 tangent:1 along:7 appears:3 exemplified:1 institute:1 petersen:1 usually:1 conveniently:1 studies:1 emerge:2 useful:6 raise:1 extra:4 planck:2 additive:2 working:2 covariant:7 sµ:1 live:1 theoretical:2 introducing:1 clue:1 appendix:1 rigid:1 valued:6 avoiding:1 following:4 arrive:2 stream:2 sample:2 dxn:3 performed:3 dxi:9 allowed:1 hydrogen:3 occur:2 fortunately:1 discussion:4 orthogonality:1 write:3 fourth:1 coleman:1 parameter:2 map:1 product:3 mat:1 may:12 produce:1 natural:1 explicit:1 sniatycki:1 so:10 definitions:1 clarke:1 prefactor:1 indeed:3 soc:1 zichichi:1 course:2 motions:1 omitting:3 differs:2 still:1 derive:3 group:4 curly:3 coordinates:22 forms:2 offers:1 main:1 introduce:4 records:1 hamilton:6 identically:1 now:6 discuss:1 possess:4 term:15 equality:1 name:1 square:3 ei:93 arbitrariness:1 ej:8 ed:1 conventions:1 mapping:24 eq:12 shown:1 space:69 gonzales:1 lagrangian:1 cancels:1 looking:1 contained:2 formula:7 correct:16 shows:2 after:5 theory:14 quark:3 complicated:1 dpn:2 e1:2 carg:1 e2:3 derivation:2 selections:1 impose:1 motion:25 thing:1 place:2 undesirable:1 think:1 first:13 origin:3 simplifies:1 xn:35 symmetry:4 omitted:1 variables:4 directly:5 array:1 given:7 theoretische:1 plastic:2 indicate:3 brevity:1 veff:1 structures:1 gives:7 progr:1 asymmetric:1 continuous:1 x0:1 x1:1 than:6 coefficients:1 unfortunately:1 accordance:1 require:1 were:1 angel:1 ann:1 turned:2 argument:2 generalization:3 contortion:3 exchanging:1 any:7 downwards:1 note:2 ideal:6 potential:4 take:1 forming:1 coincide:5 begin:1 sure:1 multiple:1 opposite:1 enter:1 surprising:2 considered:1 average:1 feynman:2 laws:3 precise:1 show:3 spaces:20 inconsistent:2 varenna:2 only:18 explicitly:1 extremum:1 correctly:2 dekker:1 expectation:1 schotte:2 aλ:1 aκ:1 closure:4 podolsky:1 yield:1 predicted:1 mapped:2 ricci:3 physically:1 violated:1 j0:8 namely:1 corre:1 commutation:1 ways:2 subsequent:1 review:1 definite:1 outside:1 between:6 geometric:12 damgaard:2 jn:1 como:1 jetp:1 parentheses:1 many:4 region:1 according:3 laplace:4 expression:7 comes:2 among:2 dislocations:1 lagrange:3 cancel:1 moreover:1 dislocation:4 kµν:2 kµλ:2 capable:2 locally:1 nakazato:1 wants:1 direction:1 offered:1 formed:3 6m:1 fortschr:2 observe:1 external:1 tokio:1 irrelevant:1 former:1 those:3 case:7 rawnsley:1 intimately:1 polymer:1 metric:18 redlich:1 different:11 eiµ:15 same:8 html:4 arguments:1 extended:1 singapore:2 trivially:2 kubo:1 changing:1 bryce:1 minimize:2 without:10 components:3 coordinate:23 model:3 kawai:2 summer:5 being:3 generally:1 aǫ:10 actions:5 summed:1 seems:1 priori:1 lett:12 mottelson:1 momentum:3 aspects:1 around:6 rules:4 world:2 accepted:1 mod:3 particle:18 collective:2 velocities:1 either:2 integrals:11 mentum:1 differentially:1 beltrami:4 specifies:1 reidel:1 deduce:2 specified:1 images:6 nonzero:1 provided:1 slice:1 dimensions:4 eiλ:6 eiκ:1 eiν:3 mesons:1 decomposition:3 provides:1 propagating:2 scientific:2 power:1 intimate:1 equivalent:2 notable:1 eiσ:1 inherent:1 comparison:1 fiziev:2 discussed:2 act:2 cambridge:1 image:4 references:4 inverting:1 determine:1 einstein:12 elementary:2 rossi:1 hep:6 log:1 area:1 assumed:2 there:13 extremizing:1 low:1 resolvent:1 assumes:1 aµ:1 trying:1 gστ:1 detailed:1 taylor:1 certain:1 aj:2 general:9 formulation:1 reexpress:1 completeness:1 field:14 valid:1 spatial:1 schaposnik:1 briefly:1 symbol:10 deriving:2 commutator:1 important:6 sνµ:1 calls:1 perturbatively:1 curve:1 mass:1 starting:5 itˆo:1 consider:4 caused:2 scalar:8 commute:3 generalize:1 expressions:4 referring:1 equivalence:11 tr:2 nonlocal:1 tn:21 th:6 stochastic:6 tb:14 kν:1 ta:17 fax:1 amplitudes:1 mpc:1 multi:3 witten:1 difference:5 deformations:1 condition:3 hamiltonian:4 applicable:1 t0:4 kondo:1 small:3 integrability:3 bilocal:1 further:2 canonical:5 subscripts:1 what:2 brackets:3 section:4 thickness:1 version:1 contrast:2 condensed:1 component:1 fluctuating:1 equations:24 antisymmetric:5 allows:1 amount:1 action:49 successors:1 uniquely:3 via:4 followed:2 conventional:1 r1212:3 contains:6 nucl:5 taken:1 more:7 flat:18 operators:1 varying:1 known:7 producing:1 quantized:2 recall:1 equation:27 det:12 remain:2 evolved:1 triads:5 memoirs:1 neglected:1 states:1 sphere:2 sense:1 robinson:1 axis:1 information:1 goal:1 rather:4 xxxv:1 acts:1 simplicity:1 fr:1 fu:7 derived:2 orbits:6 plane:1 verified:1 short:13 fundamental:7 ito:2 help:2 developed:2 paper:1 quevedo:2 kinetic:4 excitations:1 its:10 affine:13 absence:4 systems:7 might:1 good:3 easily:2 2s:4 always:1 level:1 noneuclidean:1 found:8 universit:1 characterized:2 referred:1 generation:2 energy:3 reduce:1 bosonization:4 toda:1 expect:1 quantum:17 beyond:1 rosenblum:1 nuovo:1 since:20 denotes:2 induced:2 reformulated:1 favored:1 reason:3 imagine:1 generate:2 american:2 circuit:1 consequence:2 top:4 geodesic:1 done:2 defects:8 differ:1 temperature:1 introduction:2 leading:3 expand:3 statement:1 kµ:2 part:7 differentiate:1 consult:1 postulate:5 kind:2 leggett:1 determines:4 dtl:1 double:2 determined:2 treated:1 canceling:1 defect:2 conjugate:1 lie:2 generalized:1 analogy:1 jacobian:14 finding:3 sherrington:1 play:4 measures:1 most:6 clear:3 coincides:2 physica:1 kr:1 exp:19 posses:1 physics:11 naively:1 ambiguities:2 marinov:1 celebrated:1 authors:1 relation:10 find:9 generators:2 factor:1 integrable:5 huygens:1 his:5 notation:2 express:2 famous:2 rest:1 combinations:1 him:1 arxiv:1 see:16 contour:1 gravitation:3 mechanically:1 various:2 eksp:1 subscript:2 conditions:1 available:1 recently:3 missing:2 vanishing:1 both:7 last:6 relabel:1 quantization:8 connection:15 les:1 context:3 experimental:3 point:16 simple:6 corresponds:3 semiclassical:2 bλ:1 pp:3 described:5 transformations:19 tomonaga:1 due:6 describes:2 ensured:1 ph:2 pn:2 treatment:1 generating:2 nonabelian:1 transferring:1 fokker:2 qaµ:1 replaces:1 resulting:3 solid:1 straight:1 expanded:1 evaluated:4 ǫq:1 replaced:1 evaluating:2 schouten:1 vol:3 encountered:1 reads:2 itself:2 ready:1 vanish:1 nielsen:1 italy:1 emphasize:1 widely:1 modification:1 survey:1 development:1 used:3 paths:12 uses:1 purpose:2 predecessors:1 recent:3 lower:4 pµ:1 gνµ:1 obviously:2 consistency:1 abbreviation:1 bµ:11 intervals:1 atomic:3 using:16 alternative:3 source:1 theorem:3 transformation:18 euler:6 follows:5 yields:1 reduces:1 mathematical:6 methods:3 some:3 understood:2 examples:1 sight:1 ourselves:1 delivered:1 describing:1 though:2 integration:14 providence:1 connecting:1 prog:1 proc:2 inserting:6 run:1 s12:1 bi:3 step:1 verifications:1 gνλ:1 durhuus:1 consequently:1 therein:1 christoffel:9 into:19 within:3 integral:31 encircling:1 appropriate:1 proportional:7 autoparallel:5 statistics:1 institut:1 question:2 long:2 propagator:1 governs:1 anywhere:1 atom:3 line:2 gravitating:1 2πi:4 erice:2 up:1 us:11 ur:1 similar:4 called:13 associated:5 defined:1 geyer:1 single:3 curl:1 graham:2 defines:2 amounts:1 schroer:1 rewriting:2 application:1 points:3 nat:1 elements:1 semiclassically:1 problems:2 generated:3 sides:1 ago:1 orbit:6 weights:1 requires:1 having:1 once:1 partial:3 gr:1 results:1 illustrated:2 eds:1 houches:1 go:1 superspace:1 concerned:1 excluded:1 indicating:1 expressing:1 wave:3 matrices:2 entire:3 implying:2 attempts:1 optics:1 arnimallee:1 enclosed:1 index:2 gavazzi:1 plays:1 giving:2 expressed:2 access:1 experiment:1 body:3 gµ:2 led:3 respectively:2 objects:1 others:1 extrema:1 cern:1 pˆµ:1 makes:3 involves:2 formulated:2 integrations:3 apply:1 orderings:1 use:3 feb:1 commun:1 recalling:1 okano:1 themselves:2 formally:1 becomes:5 integrating:1 infinitesimal:7 obvious:2 broglia:2 drops:2 process:1 high:1 holds:1 cancelation:1 sij:2 physik:8 advocated:1 counter:1 lines:9 correspond:2 element:1 gµν:31 yamanaka:1 produces:2 move:2 discretization:3 interpreted:1 symbols:2 comma:1 mentioned:2 chosen:1 masses:1 choose:1 derivative:7 wellknown:1 symmetrization:6 operator:11 landau:2 front:3 rotation:2 realize:1 weyl:1 related:4 constitute:1 society:2 measure:22 separating:1 our:8 special:1 out:7 matrix:4 rep:1 rev:11 woodhouse:1 ref:1 math:5 completely:2 york:2 usual:2 shortest:5 backwards:1 geometry:6 could:2 times:1 length:4 teor:2 metaplectic:1 congr:1 reached:1 precisely:2 ordering:2 behaves:1 system:4 relations:2 their:8 final:6 nobody:1 frishman:1 cimento:1 amplitude:9 bes:2 distinguished:1 hagen:1 curves:4 extremals:1 su:2 need:2 curved:14 viewed:3 angle:1 mappings:6 ohlich:1 able:1 gravity:3 curvilinear:9 instance:1 subject:2 calculus:3 lectures:9 techniques:1 representation:1 intrinsic:2 consequences:3 url:1 neighboring:1 construction:1 mechanical:2 typical:1 pˆν:1 fact:6 violation:2 rotating:1 purely:1 postulates:1 based:1 should:7 candidates:1 constituents:1 employed:1 local:1 achieve:1 δxi:6 means:1 familiar:2 oner:1 ones:2 words:1 procedures:2 evolution:2 differential:12 expansions:1 calling:1 qc:1 contain:1 including:1 fixed:5 hadronization:2 qn:52 statistical:1 exists:3 variations:15 frame:2 differentials:4 edition:2 geometrically:5 quantizing:1 qµ:1 nuclear:2 favor:1 written:7 closed:7 ulke:1 invariant:4 boundary:1 email:1 reinhardt:1 importance:1 key:1 tensors:4 freely:1 taking:1 equal:4 figures:1 holonomic:9 otherwise:1 relevant:2 conclude:1 harmonic:1 respect:4 torsion:63 reexamine:1 geometries:2 addition:1 trajectory:2 sµν:7 sµλ:1 determinant:3 arises:2 corresponding:2 prescription:2 present:1 noncommuting:1 novel:1 defining:1 appearance:1 will:10 layer:2 thus:15 surprisingly:1 surface:4 hubbard:1 finite:5 difficult:1 incorrect:1 http:5 upon:3 effect:3 parametrized:4 identity:3 schr:9 center:1 nevertheless:1 well:11 position:4 latest:1 spherical:1 obtain:7 morette:1 liotta:1 preprint:8 nonrelativistic:1 smith:1 mathematically:2 reasons:1 dqn:1 rectilinear:1 identical:2 spinless:1 increased:1 historic:1 know:2 press:2 immediately:1 vλ:2 vν:4 like:2 δx:3 δq:32 vortex:1 superflow:1 δi:1 become:1 δa:2 accessible:1 because:1 qed:1 classical:20 searching:1 qep:1 choosing:1 proper:3 lead:3 kleiner:4 ese:1 does:5 11b:1 expansion:9 hǫ:4 simpler:1 extension:3 freedom:1 introduces:2 dependence:2 recognized:1 langer:1 carries:3 introduced:2 equally:3 contractions:1 letters:2 previously:1 pergamon:1 functional:3 additional:8 quadratic:1 2m:2 function:7 but:3 repeated:3 lowered:1 manifests:1 hg:1 he:2 made:1 whether:1 gravitational:4 smooth:1 demonstrate:1 problem:4 piece:1 mechanics:9 contribute:1 denote:2 crystals:4 duru:1 functions:3 variety:1 qν:1 detail:1 arctan:1 other:11 details:1 quantities:3 theor:2 conclusion:3 variation:8 qσ:1 risken:1 auxiliary:2 resolution:1 emery:1 rule:2 original:1 northholland:1 volumes:1 richardson:1 vaµ:3
|
quant-ph9612041.txt |@word represent:3 consider:14 directions:2 out:1 results:14 laura:4 eds:1 bergmann:1 follow:1 expressions:10 research:2 inverse:2 spin:1 deterministic:1 acting:1 γu:3 ıa:2 indicate:1 stochastic:1 analogous:1 norm:12 γd:3 applied:1 belonging:2 global:6 advantage:1 zhang:1 very:7 kψ:2 springer:2 wave:7 kϕ:2 experimentally:2 trouble:1 difference:5 exact:1 condition:3 paz:1 leads:1 level:2 lombardo:2 turns:1 solution:3 large:5 solved:1 vector:11 minimal:10 small:3 eigenvalues:2 added:2 possibility:1 upper:9 zo:1 dealing:2 aip:1 approximation:2 zero:5 rigorous:4 further:1 chem:1 linear:4 spectral:27 established:4 what:6 projectors:2 appear:3 chicago:2 giving:1 section:16 interactions:1 analogously:1 experiment:1 poles:5 subspaces:1 new:12 3a:2 method:2 satisfy:1 full:2 chose:3 aω1:1 never:1 component:5 friedrichs:8 asymmetry:10 objects:6 free:2 represented:3 path:1 strong:1 equations:8 appears:3 change:10 deduced:1 obtained:14 instituto:1 division:1 singapore:1 study:1 vectors:24 completely:2 amount:1 simultaneous:1 survey:1 usually:6 advantages:1 fourier:1 changes:3 york:2 criticism:1 f0:112 formulated:1 useful:1 rodrigues:1 explained:3 limv:1 psychological:1 hardy:6 centenary:1 names:2 apply:1 total:2 univ:6 bra:1 use:6 dωω:1 would:5 prove:5 remains:1 contains:4 ψt:1 properties:4 process:2 call:3 therefore:15 nardone:1 theoretical:2 possible:2 more:12 israel:1 formally:1 said:1 successful:1 becomes:1 operators:1 berlin:3 reversible:7 breach:1 known:1 foundations:1 δcd:2 iii:1 eiht:6 must:10 high:1 account:4 word:2 dzg:1 correos:1 deformed:1 fadeev:1 equation:11 work:3 theories:6 remain:3 del:1 pioneered:1 making:3 dec:1 my:1 example:3 control:1 claim:1 compare:1 impose:2 dual:2 figure:5 stated:1 calculation:1 grav:2 exactas:1 organized:1 chiu:2 states:35 performed:1 want:6 sense:4 handle:1 times:1 action:1 axis:1 huge:1 requirements:1 decaying:7 thing:1 provide:1 ifs:1 orthogonality:6 write:2 how:3 paley:1 pure:4 answer:1 instead:1 ordinary:2 verlag:2 explains:1 gordon:1 simplicity:1 product:2 singular:1 may:2 thermodynamic:1 fz:24 after:1 singularities:1 diagram:1 applications:1 plane:12 cambridge:5 representations:1 choice:8 data:1 physic:1 realized:1 short:1 dynamical:1 biorthogonal:1 computations:1 light:1 noises:1 explicit:2 correspond:2 think:1 perhaps:1 cannot:5 so:16 fundamental:1 representation:3 order:5 forced:2 logunov:1 wigner:1 words:1 produces:1 essence:2 over:8 choose:3 course:3 wiener:1 paper:9 london:1 statistical:2 left:4 satisfies:1 still:1 castagnino:9 before:1 group:1 decay:4 chosen:3 interesting:3 fix:1 relativity:1 conjugation:1 better:2 continuations:2 microscopic:1 fig:14 mail:1 argentina:3 main:3 defining:1 into:5 texas:1 arguments:1 them:1 someone:1 buenos:2 combination:1 propose:1 impossible:3 processes:1 introduce:1 bang:1 they:5 half:9 singularity:1 now:9 vm2:1 discuss:3 bigger:1 ift:2 growing:2 february:1 gamov:11 always:3 university:1 hamiltonian:11 arrows:3 establishing:2 orthonormal:1 astronom:1 filling:1 2a:2 arrow:11 fω:64 repeating:1 european:1 traces:2 mean:5 domain:5 square:1 just:10 directly:2 dωe:2 energy:10 dωa:1 related:1 inverted:2 literature:3 ex:1 measure:2 quantum:33 our:16 ghosts:2 eq:25 special:2 really:4 try:1 shown:3 meijer:1 matrix:2 space:37 restricted:1 furthermore:1 since:11 rev:4 chaos:1 denotes:1 particles:1 replacing:1 contained:4 izt:3 rel:2 reader:1 parravicini:1 correct:1 math:6 shows:3 benjamin:1 foundation:1 temporal:1 theory:30 exterior:1 associate:1 ısica:2 diagonal:2 departamento:1 quite:1 approaches:3 complicated:1 term:5 elsewhere:1 enhance:1 beginning:3 definition:2 interaction:3 could:2 omit:1 feasible:2 iz0:5 ordering:1 int:1 exponentially:1 universidad:1 consequence:2 austin:1 neglect:1 first:6 origin:3 already:2 features:1 probability:4 variables:3 powerful:1 number:4 iht:22 approximate:2 restrict:1 done:6 relations:3 another:1 pellegrini:1 iafe:1 precisely:5 open:1 take:1 given:13 necessarily:1 exists:4 their:4 introduction:3 eqs:23 system:4 least:2 semiaxis:1 assumption:1 california:1 observations:1 postulate:2 scheme:1 final:1 rosario:2 microscopical:1 asymmetric:7 explanation:2 continuous:5 outcome:1 part:1 manipulation:1 believe:2 representing:1 than:9 begins:1 iωt:5 kind:3 roles:1 penrose:1 was:4 roberto:1 second:7 submitted:1 halliwell:2 preparation:2 future:7 were:2 mackey:2 3b:3 perturbative:1 rewrite:1 mind:1 spectrum:2 curves:4 say:4 substantial:3 close:2 need:1 seen:1 cosmology:2 demonstration:1 clearly:3 irreversibility:6 bohm:8 sandwiched:1 jour:1 lim:13 dωdω:2 note:1 internal:2 generalized:22 bogolubov:1 davies:1 coincide:4 acquires:1 tool:1 unperturbed:1 oscillators:1 even:4 sure:1 antoniou:3 trace:1 shall:12 gunzig:3 sets:1 reach:1 systems:4 mario:1 regular:6 aires:2 comparing:1 nothing:1 analytically:2 measured:1 class:8 give:1 considered:5 clear:3 physica:2 doe:1 feynman:1 proceedings:1 points:4 exp:5 mechanical:1 petrosky:2 usual:14 physics:6 notion:2 fact:18 laws:2 precise:1 show:7 past:6 able:1 namiki:1 spaces:15 solutions:3 decompositions:8 interpretation:1 trivial:2 find:6 promote:1 based:3 knowledge:1 aω:9 explain:2 state:20 supported:1 analytic:24 only:22 going:1 corresponds:1 subsection:1 integrable:1 adequate:1 he:1 local:4 zeh:1 equilibrium:1 do:7 ingredient:4 above:3 notation:1 means:1 ϕt:1 zurek:1 de:5 reichenbach:2 unimportant:1 ones:4 dz:34 dx:1 probably:1 during:1 gen:2 gel:4 following:4 evolution:20 heaviside:1 conditions:2 arxiv:1 expansions:4 2b:3 yield:3 book:1 bad:1 analytical:1 aesthetic:1 meromorphic:1 set:11 computed:4 reference:4 physically:2 national:1 namely:7 result:2 conicet:1 recently:1 forthcoming:1 best:1 subject:1 vω2:8 satisfying:6 fand:4 prigogine:3 review:1 functionals:11 its:2 symmetric:4 written:3 closed:1 between:9 progress:1 boundary:1 approach:3 preserve:1 triplet:4 terms:6 extend:1 nature:5 originated:1 indirectly:1 adjoint:2 weak:4 however:3 interpolate:2 council:1 vanishing:2 cut:1 fluctuations:1 preprint:2 reappears:2 ket:1 both:5 essentially:4 toward:1 last:5 limits:1 many:1 region:4 according:4 etc:4 grain:1 gibbsian:1 contribution:2 oct:1 expression:3 schroedinger:1 experimental:1 relevant:1 necessary:4 point:1 reasons:1 continuation:2 cf:2 community:1 cd:17 alone:1 pole:3 grants:1 simply:1 comprehension:1 constant:2 ae:2 cu:12 semigroups:1 described:1 basis:2 z0:56 invert:1 three:1 been:2 ai:3 much:2 coarse:3 interest:1 basic:2 ph:1 define:6 life:2 hawking:1 corresponding:6 reasonings:1 cosmological:4 restrictions:1 quantities:1 coherence:1 precision:1 maps:1 observe:1 understand:1 derivative:1 nrs:1 xxi:1 presented:1 irrelevant:2 present:1 case:19 exponential:7 pacs:1 appearance:1 conserved:1 value:2 deformation:2 will:18 information:1 while:2 ar:1 suppose:1 viii:1 behavior:5 freely:1 rigged:3 property:1 taking:3 procedure:1 iy:2 identical:5 larger:1 gorini:2 espacio:1 almost:2 endowed:2 formulation:2 thus:12 non:1 equal:1 ii:7 reads:1 good:2 im:1 cone:1 io:15 limit:1 vz:2 vanish:5 different:9 classified:1 verified:1 perform:2 make:2 belong:1 radiation:6 cross:1 same:10 any:4 complex:14 quant:1 emphasize:1 modification:4 colloquium:1 finite:6 coarsegraining:1 difficult:1 development:1 used:8 zwanzig:2 see:5 trivially:1 i0:6 sudarshan:4 subsystems:1 hand:3 doublets:1 domains:3 moment:1 purpose:1 caption:1 antorchas:1 eigenvectors:8 lower:9 task:1 nevertheless:2 whole:1 ingredients:1 well:7 springerverlag:1 know:7 obviously:1 thought:1 todorov:1 solve:1 consistency:1 model:26 stating:1 shadowed:4 quoted:1 golden:1 being:6 ress:8 invariant:1 obtain:32 rest:2 identify:2 farther:1 predicts:1 world:2 alternative:1 schwinger:3 macroscopic:2 previous:3 speculate:1 bibliography:1 vω:12 seems:3 nacional:1 iω:1 simple:2 belongs:2 developments:1 easy:1 theorem:2 reversal:1 remaining:1 scientific:1 useless:1 real:7 fundaci:1 big:1 showing:2 decomposed:1 measurement:1 inversion:4 period:4 matters:1 ciencias:1 press:5 using:18 formal:6 imposed:2 like:8 follows:1 popov:1 unstable:15 schwarz:3 integrals:2 alternatively:1 evolutions:2 conclusion:1 essential:3 asymptotic:1 mathematical:5 sketch:1 because:4 methods:1 deal:3 some:2 deduce:4 towards:2 moreover:1 extended:2 peter:1 happens:1 embodied:1 dense:2 axiomatic:1 lead:1 decision:1 measurements:2 overlap:2 coupled:1 does:1 decomposition:12 economical:2 assuming:1 proc:1 demonstrated:4 either:1 decide:1 reasonable:6 poincar:1 equivalent:2 conventional:5 expansion:6 step:1 casilla:1 found:5 tasaki:3 hilbert:4 bz:1 simpler:1 about:2 simplest:1 dze:1 extension:8 lasota:1 universe:12 am:1 theorems:1 discussed:1 δc:1 compatible:1 dzs:1 a2:1 extensions:7 mixed:3 introduced:8 consequently:2 other:1 exactly:1 primitive:1 ingenier:1 presence:2 h0:26 within:2 integral:4 functional:3 sachs:1 included:1 right:4 references:3 einstein:1 operator:10 ei:3 symbolizes:1 statistics:1 classical:1 area:2 probabilistic:1 there:3 transform:1 long:2 why:1 start:1 ci1:1 conservation:1 facultad:1 way:12 ed:5 analyze:1 sections:1 naturally:1 function:16 himself:1 complete:4 form:3 but:14 hu:1 gadella:4 properly:1 gain:1 line:1 removed:1 irreversible:13 proposal:1 partially:2 made:1 compute:5 intuitive:1 2πi:11 wish:1 up:4 us:12 tell:1 origins:1 below:3 decays:3 fermi:1 today:1 sum:1 demonstrate:1 problem:6 called:1 stirring:1 mechanics:17 approximated:1 proved:3 af:8 defined:21 certain:1 abstract:1 describe:1 pid:1 direction:3 deep:1 general:7 substantially:2 single:4 khk:1 rule:2 av:1 lifetime:1 formalism:6 distributions:2 check:2 computational:1 physical:40 again:4 functions:13 compared:1 analyticity:3 no:4 cos:1 when:11 vanishes:1 reality:2 field:4 valid:7 details:1 branch:1 papers:2 test:6 mathematics:1 dωs:2 observable:3 deviation:1 picture:1 draw:1 elements:1 provided:2 models:1 problems:2 prepared:1 a1:3 cpp:1 meaning:3 important:3 uba:1 observables:3 variable:4 sides:1 structure:2 acknowledgment:1 ghost:1 dω:49 assume:4 values:8 proposed:4 factors:1 curve:14 together:2 graining:1 mimic:2 time:64 far:1 antilinear:3 starting:1 having:1 once:2
|
quant-ph9612042.txt |@word represent:1 since:1 consider:2 switched:1 magnetic:4 desirable:1 results:1 computation:1 gj:11 whose:1 depend:1 young:1 finally:2 critical:1 include:1 dramatically:1 applied:2 premium:1 frequencies:3 wave:1 summarized:1 resonant:1 difference:3 magic:3 vibrational:5 level:9 knight:1 standards:1 deutsch:2 pulse:8 l3:1 approximation:1 surrounding:1 second:1 will:2 selected:1 axial:1 experiment:1 net:2 satisfy:3 condensed:2 nonlinearly:1 promising:1 component:1 here:1 plenio:1 groups:1 along:1 coupling:2 z0:5 extreme:1 parameters:1 institute:1 amount:2 resulting:1 published:2 suitable:1 appropriately:1 extra:1 transit:1 frame:1 total:1 army:1 positive:1 laflamme:1 tabulated:1 leaks:2 therefore:1 today:1 more:2 lowering:2 virtue:1 particular:3 cases:1 must:2 science:1 work:3 modified:1 remain:1 values:4 splittings:1 ms:1 following:1 dec:1 example:1 ions:13 neglected:1 states:23 numbers:1 µj:3 lamb:8 information:1 requirements:2 ie:2 feature:1 species:1 how:5 gate:20 parameter:8 map:1 de:1 may:4 ladder:1 mapping:1 collection:4 applications:3 geometrical:1 realized:3 third:4 negligible:1 expression:1 fundamental:2 order:2 operations:2 office:2 pointed:1 flips:2 stability:3 paper:1 through:3 existence:1 thank:1 acknowledge:1 ln:1 picard:1 swapped:1 pulses:6 absence:1 itano:7 rabi:5 setting:4 focussed:1 thereby:1 heinzen:2 steane:1 effects:2 instead:1 rotation:3 realize:1 2u:1 hamiltonian:1 radians:1 l2:1 trap:5 truth:1 each:2 2m:7 2k:7 schemes:1 ei:1 generation:1 series:1 energy:2 reduce:1 frequency:11 static:1 quantum:28 transitions:1 eq:5 out:1 divincenzo:3 shown:1 driving:1 factors:1 surrounded:1 rev:19 research:2 increase:1 replacing:1 rf:2 mediated:1 dominated:1 denoted:1 ref:2 correct:1 linear:1 formation:1 jozsa:3 e0:1 r2493:1 interaction:3 exposing:1 transition:2 success:1 motion:5 american:1 place:1 hemmer:1 onto:1 eqs:2 first:3 simplifies:1 manuscript:1 laguerre:1 possessing:1 number:2 simplified:3 least:1 another:2 impossible:1 electronic:6 glauber:1 interact:1 system:1 construct:1 their:3 scheme:7 bits:2 national:2 trapped:7 optical:2 eliminated:2 than:1 population:1 king:4 showed:2 zero:2 individual:1 correction:4 7l:5 miquel:1 need:1 unaffected:1 any:2 strength:1 built:1 depending:1 agency:1 isolated:1 k2:1 k1:1 potential:1 so:1 hyperfine:1 electric:1 who:1 phase:5 nonlinearity:1 drive:1 feynman:1 subsequent:1 physics:1 shor:2 show:2 dipole:1 rotating:1 lloyd:2 degraded:1 find:1 ground:4 slov:1 based:1 copyright:1 implementation:1 entangling:1 controls:1 should:1 only:5 candidates:1 boulder:1 do:1 beams:4 zurek:2 between:7 october:2 report:1 roles:1 settings:1 fields:2 tuned:3 including:1 available:1 requirement:1 achieved:1 sensitivity:1 travis:1 computer:1 result:2 eliminating:1 micromotion:1 subject:1 satisfying:1 resonantly:1 nuclear:1 motional:6 state:12 jth:1 simplest:1 reading:1 preserve:1 barenco:2 terms:1 gould:1 however:2 news:1 configuration:1 both:1 zoller:5 zeeman:1 flipped:1 logic:18 adapted:1 otherwise:1 comment:1 relevant:1 co:1 separation:1 point:1 simple:1 harmonic:2 maintained:1 polynomial:1 table:3 schleich:1 specializing:1 described:1 tuning:1 basis:1 three:4 been:2 detuning:1 much:1 pj:1 jefferts:1 ph:1 lett:11 controlled:2 coherence:1 photon:2 6n:1 confinement:2 external:1 wavevectors:1 spin:1 present:1 naval:1 case:1 multi:2 laser:10 pacs:1 transformation:2 employ:1 invoking:1 while:3 replaced:3 error:2 mitchell:1 procedure:1 unitary:1 vogel:1 coupled:2 thus:1 couples:1 technology:1 monroe:4 bollinger:2 pseudopotential:1 paz:1 radiation:1 same:1 stimulated:1 quant:1 several:4 difficult:1 filho:1 ion:19 moment:1 levels:7 wired:1 center:1 pellizzari:1 com:6 no:2 well:1 thought:1 spectator:2 coordinate:1 gates:2 matos:1 when:4 accurate:2 rotated:2 atomic:5 paul:1 speed:1 cn:15 candidate:1 dicke:8 wavevector:2 reasons:1 spread:1 transformed:1 attractive:1 apart:1 excited:2 opt:1 insensitive:2 government:1 possible:1 spanned:1 entangled:2 confined:2 bit:5 mod:4 appearing:1 like:1 particle:1 collective:4 alkali:1 popular:1 security:1 accuracy:1 reduced:7 cooled:2 because:1 exposed:1 some:1 duration:3 there:1 willis:1 does:1 connecting:1 assuming:1 mode:5 scientific:1 equivalent:1 l1:1 oscillating:1 although:1 exciting:1 bz:1 simpler:1 integers:1 thomas:1 carrier:4 repulsion:1 act:2 discusses:1 wineland:7 appropriate:1 references:1 operator:4 proportional:1 additional:1 few:1 u7:1 support:1 reduction:1 was:2 9be:1 raman:3 form:1 metastable:2 simplifications:1 removes:1 brana:1 elimination:2 raising:2 auxiliary:8 reset:1 made:1 applying:1 places:1 circuits:1 below:1 spectroscopy:1 fluctuations:1 strongly:1 cirac:5 associated:1 computing:1 universal:1 describe:1 general:3 single:10 internal:14 meekhof:4 amounts:1 allow:1 ekert:3 generally:1 virtual:3 lately:1 nx:1 field:5 other:1 matt:1 important:2 allowing:1 structure:1 building:1 faster:1 coulomb:1 assume:1 required:2 together:1 equivalently:1 leibfried:1 mass:2 time:1 n1:2 decoherence:2 requires:1 having:1
|
quant-ph9612043.txt |@word limited:1 four:1 entropy:52 consists:5 whose:2 calculate:1 aug:1 ohya:1 under:7 dukes:1 worth:1 conjecture:1 risk:7 intriguing:1 ζn2:1 ζn1:1 bringing:1 maxθ:2 suffices:3 z12:1 solution:2 convenience:2 vector:11 indices:1 commented:1 concise:1 second:4 rigorous:1 eigenspaces:4 even:1 above:13 new:6 increasing:1 consisting:1 coefficient:10 notions:2 never:2 equals:19 here:16 reported:1 represented:2 path:23 logarithmic:9 obtained:7 suitably:1 study:4 approaches:3 ignoring:2 suitable:1 appropriately:2 projection:1 explained:1 highly:1 sloane:1 viennot:1 total:5 unit:15 aitchison:3 would:16 subpath:1 negative:1 substitutions:1 definiteness:2 call:1 therefore:23 von:11 composite:1 berlin:1 hold:1 must:13 springer:1 setup:1 work:6 concepts:2 root:2 example:6 indicated:2 give:2 cited:1 bennett:4 involve:2 indicates:1 degenerate:1 guarantee:1 end:2 provide:2 enn:1 recovers:1 how:3 nontrivial:1 description:3 replacing:2 earlier:4 symmetrisation:1 unentangled:1 parallel:4 attempt:2 third:1 noncommutativity:1 summing:1 complexity:3 interior:5 correlation:1 order:20 over:35 london:1 diagonally:1 before:6 monotonicity:3 fit:1 fix:3 xm:1 writing:4 ims:1 complex:5 differently:1 maximal:1 eventually:1 them:2 combination:5 they:11 eigenvalue:4 each:9 side:15 nonessential:1 series:11 principles:2 literature:1 combining:1 laboratory:1 conjectures:1 divincenzo:1 restricted:2 crucial:2 particles:1 combinatorial:2 conjectured:1 rm:1 ri:1 linear:6 associate:1 standard:6 stochasticity:1 estimate:4 r2:3 starts:1 multiparameter:1 onto:3 already:9 features:2 coding:17 restrict:5 another:1 cartesian:1 similarly:4 eqs:1 deutsch:1 needed:1 serve:1 somewhat:1 distance:2 msri:1 rate:1 normalizing:1 project:1 enables:1 quebec:1 seminal:1 fashion:2 behavior:3 rewrite:2 boston:1 mind:1 manner:4 seen:4 seek:1 tells:3 seminar:1 realm:2 latter:1 maxw:1 subjects:1 transactions:1 metrics:4 extending:3 codeword:1 min0:1 nagaoka:1 treats:1 points:4 tech:1 principle:2 sum:36 channels:1 nonpositive:1 random:1 hasegawa:1 substituting:2 analogue:6 larson:1 proposed:2 paralleling:1 summarizing:1 matters:1 constant:2 oct:5 do:13 mixture:1 succinct:1 cryptography:2 de:1 dz:8 dx:9 dy:8 report:1 reconstruct:1 dr:5 runs:1 acknowledgments:1 analytical:2 riemannian:2 reference:4 imitate:1 observed:5 depends:3 result:24 schick:1 λi:2 best:3 subject:1 said:4 capacity:1 tensor:7 symmetric:15 ira:1 caves:1 approach:3 grabner:2 petz:6 gauß:7 embeddings:1 extend:2 nature:6 wn:2 restricting:1 however:10 residual:1 extent:1 bose:1 improve:1 essentially:3 jeffreys:20 une:1 receiver:2 qubit:1 los:1 presumably:1 very:1 wider:1 commutative:1 puts:1 basis:15 three:4 been:8 extraction:1 much:2 interest:4 basic:6 expected:2 families:4 quantities:3 concerning:1 spin:6 encyclopaedia:1 applied:4 reciprocal:2 transformation:2 employ:2 suppose:4 property:5 procedure:2 iy:7 played:2 kohn:1 iv:1 ii:2 disjoint:5 ij:2 containing:2 perform:1 suggest:2 make:1 concavity:2 quant:1 split:4 mixtures:2 several:1 independent:11 i1:3 i2:3 counterparts:1 hand:23 normalization:1 subspaces:1 cardinalities:1 epr:1 academic:4 contact:1 studying:1 left:11 just:1 assigned:1 spherically:3 facts:2 yet:2 adding:1 unique:1 candidate:6 5u:2 similarities:1 belongs:1 transformed:1 easy:2 opt:2 neglecting:1 possible:21 spanned:1 possibly:2 rahman:1 replace:4 occurring:1 specific:3 steps:25 arbitrary:3 www:1 right:3 people:1 successfully:1 alamos:1 proceeding:1 bottom:1 comments:2 everything:2 ucsb:1 linearly:7 chentsov:5 algorithmic:1 derivatives:4 statistician:2 binomial:11 substitution:1 properties:4 proceed:4 o:22 slightly:1 automatically:3 22n:2 soc:3 presence:1 obtaining:2 bound:1 chooses:1 down:19 lies:3 hermitian:2 neumann:11 rely:1 compression:12 comparing:1 combinatorics:2 support:2 initial:1 transform:1 cassinelli:1 way:3 was:16 form:30 denoting:5 failure:1 true:2 portions:1 maximum:6 discarding:1 simplifying:1 strengthening:1 proved:5 computing:2 abstract:1 tria:1 proven:1 evidence:1 peres:1 proves:1 exist:1 dθ:17 distributions:13 archive:1 nj:1 no:27 ekert:1 when:5 vanishes:4 ny:1 setting:10 role:2 sponding:1 papers:1 test:1 ns:1 kullback:3 intend:1 superposition:1 initio:1 preceding:2 jones:1 nonnormalizable:1 assume:2 interval:1 together:2 remarked:1 n1:2 n2:19 dϕ:3 decision:3 dϑ:8 remarkable:1 global:2 focus:1 leads:2 roy:2 computation:4 remarkably:3 devoted:1 dimensionality:1 clarification:1 malley:1 finally:4 monotonically:1 stabilizing:1 analogous:1 string:2 orthogonal:1 geometrical:1 anonymous:2 entries:7 exact:3 solves:1 level:19 did:7 turns:3 noiseless:4 coincidences:1 upper:1 says:4 findings:1 det:10 maximization:1 prediction:2 substitute:3 appear:2 axes:1 uniform:9 goes:2 groups:2 address:2 appears:1 institute:3 popescu:1 studied:3 trial:3 louck:1 usually:1 digamma:1 studies:1 montreal:1 useful:1 raise:1 compare:3 additive:1 working:1 prove:13 sake:1 positive:3 finetti:1 going:1 opposed:3 theoretical:1 today:1 improper:1 validity:1 appendix:3 cases:6 cardinality:13 logarithm:6 parameterize:1 originally:1 oscillator:1 radon:1 values:6 hope:1 following:8 making:2 trans:8 social:1 claim:4 want:1 figure:10 expanding:1 mohanty:1 topic:1 counting:1 occur:1 verlag:1 redundancy:32 s2:7 discussion:2 write:12 pure:3 syst:1 optimal:2 parameter:17 product:10 mar:2 mat:1 may:7 max:5 helmut:1 designed:1 data:10 natural:1 succeeded:1 lemmas:6 explicit:4 yielding:1 su:2 st:1 inform:6 so:24 omes:1 representation:3 typical:2 matsushima:1 considerations:4 indeed:4 pointed:1 displayed:1 years:3 course:10 statistical:7 argued:1 still:2 ieee:11 equalling:2 tending:1 derive:4 group:1 summands:4 interesting:3 coordinates:5 forms:3 mail:2 main:1 non:1 barron:37 identically:1 bogoliubov:7 now:30 discuss:1 developments:1 tropy:1 term:18 equality:1 possibilities:2 el:1 domain:8 weighted:2 ei:2 ed:1 hypergeometric:10 quaternionic:1 approximates:1 ex:2 eq:3 es:8 shown:5 space:19 furthermore:4 barnum:1 interference:1 contained:8 investigation:2 internet:1 formula:15 shows:3 after:6 theory:30 ascertain:2 divergence:3 possibility:8 quite:6 statistics:3 california:1 bayes:15 besides:1 milburn:1 care:1 impose:1 turn:3 qn:12 first:22 origin:1 xi:1 xn:3 striking:1 variables:1 approximate:1 xz:2 xy:2 simplified:1 specifically:1 directly:2 carry:3 xs:1 angular:1 size:1 interchange:4 given:39 checked:1 meaningful:1 indicate:1 1b:1 bits:3 gives:13 wellbehaved:1 continuous:1 accurately:1 undertaken:1 x2:28 x1:3 representing:1 than:18 coefficients:4 accordance:1 future:1 represents:1 san:1 generality:1 ann:1 generalization:1 say:8 recover:1 saw:1 any:21 gasper:1 note:8 sciences:1 take:2 objective:1 coincide:2 channel:1 formulas:13 multiple:1 trace:7 beta:1 rationale:1 pair:1 analytically:1 considered:5 average:12 later:4 implications:1 typically:2 precise:4 shor:3 infinitude:1 show:9 delta:1 fifty:2 spaces:1 ensembles:1 state:11 only:20 explicitly:5 quantph:1 get:3 expectation:1 cannot:1 progress:1 gen:1 differentiating:1 reveal:1 regarding:2 podolsky:2 yield:3 summary:1 relative:34 namely:2 biedenharn:1 fidelity:3 concern:2 krattenthaler:19 satisfying:2 review:1 definite:2 label:2 between:2 reading:1 qubits:2 jr:1 concentrate:2 comm:1 analyzed:1 concentrated:3 tractable:1 many:4 pertain:1 according:3 leibler:3 expression:30 among:1 characterization:1 werner:1 cancel:3 moreover:4 considering:2 capable:1 wien:1 workshop:1 combined:1 prodinger:1 bures:2 6a:2 6b:1 6c:3 6d:2 6e:3 observable:2 photon:1 observe:5 bayesian:20 those:12 case:40 trick:1 shall:3 squeezed:1 situation:8 orientation:1 characteristics:1 metric:21 return:1 worry:1 pap:1 binary:2 different:7 twoparameter:1 april:1 same:13 inquiry:1 arguments:2 investigated:1 singapore:1 trivially:1 kubo:6 running:1 codes:5 entanglement:2 gallager:2 relies:1 minimize:1 roughly:1 without:1 solve:1 coordinate:1 model:1 dimension:3 comment:1 manifold:1 being:13 ci:2 rest:1 relevant:3 summed:6 differentiation:1 eorie:1 photons:1 seems:2 except:6 treatment:1 versa:1 complements:1 extensive:1 momentum:1 real:2 bernardo:3 2u:10 rules:3 sums:7 admitting:1 harmonic:1 using:16 correcting:1 mod:2 reduces:6 serves:1 discarded:2 either:3 integrals:1 reduced:3 grouping:1 conditional:2 matching:1 nonzero:5 provided:2 toth:1 models:2 lexicographically:1 refer:2 scientific:1 equivalent:1 notably:1 pθn:14 found:4 svozil:1 comparison:3 theorems:1 generated:1 whence:3 estimator:3 mixed:3 acz:1 mean:5 cambridge:4 unbounded:1 image:1 numerically:3 references:1 determine:18 einstein:3 operator:4 log:143 removing:1 strictly:2 there:13 start:3 assumes:2 complete:4 regard:5 posterior:1 applying:3 embedded:1 multiplicity:2 agree:1 eigenvector:3 obtains:2 detailed:1 ac:2 taylor:1 certain:4 describe:2 general:10 ap:26 examine:3 enable:1 bishop:1 tedious:1 again:16 completeness:1 ideally:1 mathematik:1 mathematica:3 storage:1 terminating:4 mathematics:1 massless:1 polar:2 briefly:1 symbol:1 time:1 representable:2 a1:2 important:4 bounded:1 massachusetts:1 observables:1 tricky:1 hirasawa:1 noncommutative:1 behavioral:1 starting:4 original:2 sci:1 consider:11 splitting:3 mnw:7 generalize:1 follow:1 expressions:1 research:8 rd:1 re:1 tt:2 tr:14 program:1 th:21 tf:2 stochastic:4 presentation:1 belonging:2 straightforward:2 far:2 reader:5 corollary:2 verd:1 difference:3 condition:1 applicable:1 large:3 maximin:17 employing:1 grateful:1 zero:5 displays:1 further:3 canonical:2 what:14 sud:2 diag:1 section:2 brief:1 version:2 intersect:1 method:2 contrast:5 christian:19 component:2 compressed:1 berkeley:2 cos2n:5 strong:1 equations:1 sender:1 allows:1 prior:36 amount:1 schumacher:9 action:4 via:2 family:24 requiring:1 vis:2 establish:3 conventional:1 takes:3 massar:1 distinct:3 contains:1 vh:38 mori:6 taken:9 achieving:1 more:12 operators:1 surprisingly:1 particular:15 known:2 producing:1 presumed:2 keeping:2 recall:5 equation:3 des:1 protons:1 dec:1 f1:23 f2:8 challenging:1 states:11 sphere:12 minimum:4 numbers:3 sense:4 axis:1 insignificantly:1 information:41 respective:4 goal:1 rather:5 clarke:38 acts:2 ensemble:4 fp:13 fs:1 fu:1 algebra:3 wiley:1 derived:7 ζn:66 tries:1 plane:1 rissanen:2 choice:4 chiefly:1 resemble:1 grandy:1 parameterized:3 perhaps:1 fundamental:2 help:1 developed:1 mixing:1 thermal:1 paper:6 through:2 berthiaume:1 y2:1 its:13 itp:1 solving:1 actually:1 microscopic:1 systems:22 might:5 good:6 motivated:3 propose:2 yf:1 framework:4 yz:2 oxford:1 easily:4 2r:10 2s:1 fully:5 presented:1 2z:1 2c:1 2l:7 2m:5 2n:45 2h:53 2j:5 2k:9 weight:1 reduce:2 expect:1 undertake:1 measurement:1 quantum:116 http:1 beyond:1 really:1 since:14 projected:2 denotes:3 acting:1 equate:1 induced:1 issue:3 occurs:2 monotone:12 enforcing:1 guess:1 difficulty:2 members:2 put:2 beginning:3 generate:2 definition:11 pairs:2 retained:1 plot:1 nonnegative:8 conducted:1 wehrl:1 probability:47 number:22 utilized:1 done:3 maple:3 equating:2 passes:1 differ:3 minimality:1 introduction:7 leading:2 least:9 assumption:1 identity:1 statement:4 cosn:2 scheme:3 shifted:1 relationship:1 appreciation:1 part:8 favorable:4 authors:1 kind:1 polarized:1 kindly:1 fuchs:1 double:1 determined:2 risks:1 treated:1 comput:1 outstanding:2 footnote:1 summable:1 vilenkin:1 paths:11 generalized:4 analogy:3 finding:2 commentary:1 inference:6 measures:2 most:1 assoc:2 comparisons:1 nothing:1 measured:2 cover:1 physica:1 kl:2 braunstein:2 electrons:1 ρvi:1 physics:3 naively:3 differentiate:2 particularly:1 multiplicities:4 thomae:1 find:14 dividing:3 distributed:1 assertion:1 surveyed:1 factor:1 columns:1 his:1 dominant:5 invoke:1 dependent:4 express:3 methods:3 famous:1 closely:1 competing:1 during:1 him:1 resolve:1 arxiv:1 stirling:3 garcia:2 investigate:2 common:12 dyck:2 approaching:1 set:39 achieved:4 achieves:2 see:32 individual:2 sec:21 close:3 theoretic:3 analog:1 positivity:1 various:2 probably:1 available:1 recently:1 complement:2 attention:3 analogues:1 vanishing:1 distinguish:1 both:9 last:2 reverse:1 connection:1 context:1 whole:2 finds:1 arbitrarily:1 noninformative:1 point:5 simple:1 asymptotically:8 corresponds:2 leon:2 dimensional:8 simply:4 likes:1 consideration:1 throughout:3 pp:42 described:9 transformations:1 due:8 strategy:4 describes:1 asymptotics:20 kronecker:1 ph:1 pi:1 empty:1 pm:1 addison:2 referee:1 else:1 p2:1 pierce:1 p1:1 look:1 exponential:1 estimations:1 evaluated:3 while:6 replaced:4 evaluating:1 error:9 unitary:1 vol:40 averaging:1 overlooked:1 orthogonaux:1 itself:2 rij:9 triple:1 lengths:1 resulting:6 univie:2 used:8 lie:2 comprehensive:1 moment:4 uses:1 recent:4 eigenvectors:15 task:1 analysis:7 picks:1 landmark:1 entry:2 parametric:2 hypothesized:1 abbreviation:1 world:1 reviewer:1 alternative:4 λh:35 λn:2 letting:1 kluwer:3 informal:1 guaranteed:2 signals:5 source:6 theorem:50 remaining:1 march:2 evaluate:5 kass:1 catalan:2 integer:5 bit:2 formal:1 follows:4 signal:7 ignore:4 yields:7 essential:2 terminology:1 mathematical:3 sketch:2 often:2 some:21 back:2 bach:1 understood:1 economic:1 b1:2 ourselves:3 investigating:1 describing:2 combinatoire:1 minimax:26 though:3 per:1 piscataway:1 providence:1 tends:3 proc:1 minimal:4 bf:12 run:1 step:16 bp:22 redundancies:23 santa:1 bs:2 hilbert:3 integers:5 pθ:18 remains:2 range:3 extensions:1 adami:1 consequently:3 bloch:4 gamma:1 computational:1 into:9 within:4 integral:6 locus:1 polynˆ:1 appropriate:1 proportional:2 rows:1 span:2 probabilistic:1 question:4 lond:1 long:3 vienna:1 considerably:1 elsewhere:1 atom:1 line:3 considerable:1 2πe:2 up:20 us:27 similar:3 called:2 entropies:8 associated:3 defined:6 coincides:1 globally:1 single:1 proofs:2 priors:3 application:2 priori:1 wasserman:1 arithmetic:1 elements:21 generates:1 nonclassical:2 beltrametti:1 meaning:1 vectors:14 fisher:14 sides:2 ago:1 correlated:1 implies:6 vice:1 required:1 equivalently:2 95k:1 requires:2 having:1 partial:1 results:23 eds:1 edu:1 contributions:1 compact:1 disposal:1 concerned:1 include:1 labels:5 continues:4 bounding:1 2ru:1 matrices:46 morozova:2 eigenvalues:14 barbara:1 noted:3 smaller:4 zi:7 sin2:3 fold:3 dordrecht:3 dynamics:1 index:5 expressed:1 referees:1 exercise:1 fujiwara:1 multivariate:1 led:1 sept:4 degree:1 exchange:1 respectively:4 sinn:1 slater:25 z2:5 cerf:1 remark:5 parameters:2 clarendon:1 technical:1 larger:2 products:4 implement:1 relation:1 examining:1 apr:1 summation:7 apply:6 use:11 feb:2 asymptotic:50 commun:1 recalling:1 next:3 classically:2 totality:1 themselves:1 zij:8 subsection:1 formally:2 becomes:3 normalized:2 iii:1 hints:1 sample:1 haussler:1 infinitesimal:1 obvious:2 averages:1 proof:26 calculation:2 purposes:1 assumptions:1 notation:8 uqam:1 holds:3 varies:3 instead:2 sin:10 blocks:1 collection:1 demonstrating:1 computations:5 correspond:1 redundant:1 element:20 lβ:2 realizes:1 lα:1 subsequently:2 s1:7 furnish:1 move:1 symbols:1 including:3 mentioned:3 hornstein:1 chosen:1 lo:1 choose:7 communication:1 derivative:8 lz:1 lx:1 ly:1 factorial:1 innermost:2 attains:2 mention:1 dar:1 front:17 establishes:3 dirac:1 university:3 sufficiently:1 universita:1 magnitude:4 transmitted:2 truth:1 disregard:1 traces:1 subset:5 doing:2 stabilisation:1 related:3 our:33 special:3 out:7 matrix:30 rev:8 induction:4 math:9 statist:5 approached:2 diagonal:6 completely:1 york:4 jozsa:3 shortest:1 applications:3 geometry:1 determining:1 could:2 times:3 counterpart:9 length:4 assumed:2 hence:9 facilitate:1 respond:1 equates:1 klimyk:1 precisely:4 quality:1 strict:2 unknown:2 behaves:1 system:6 their:8 siam:1 final:1 ζˆn:3 exactly:14 july:1 completes:3 characterizations:1 limiting:1 exhibit:2 unlikely:1 need:4 clearly:10 hessian:1 mappings:1 min:5 pursued:1 able:4 instance:1 concerns:1 encyclopedia:1 lγ:2 unless:2 class:2 volume:6 sin2n:1 absurd:1 mechanical:1 fact:16 selection:1 supported:2 bring:1 planning:1 q0:11 based:3 eigenspace:4 should:6 jan:1 lemma:25 attained:3 employed:3 he:1 achieve:1 handle:2 means:12 familiar:1 overall:1 joint:1 ones:1 legitimate:1 evolution:1 qu:33 densities:17 contain:2 qi:1 fixed:14 view:2 exists:3 correlations:1 computer:3 terms:13 welsh:1 nuclear:1 tend:1 written:2 invariant:6 boundary:7 barenco:1 importance:1 hypothesis:2 amer:3 distribution:11 restrictions:1 limits:2 equal:11 etc:1 estimation:2 otherwise:3 unitarily:2 adjusted:1 ch:1 co:1 conclude:3 ca:1 cf:8 ab:1 maximize:1 sequences:1 respect:26 cp:11 geometries:1 addition:3 copies:1 treat:1 utilizing:1 define:4 determinant:3 arises:1 corresponding:25 subspace:6 cos:4 bulk:1 subsets:6 value:10 will:14 ar:4 almost:1 vi:5 vj:1 thus:19 vm:1 surface:1 helped:1 examined:1 claimed:2 generic:1 lett:4 member:3 parts:7 gibbs:1 largest:12 units:1 finite:4 privileged:1 difficult:1 ball:8 infinity:3 logic:1 upon:3 mutual:1 v1:1 v2:4 frequently:1 expand:2 nevertheless:2 well:6 sets:11 position:1 usual:1 spherical:3 less:3 rosen:2 obtain:12 biometrika:1 clocks:1 paul:19 nov:1 preprint:1 density:55 nats:3 bell:1 smith:1 lattice:7 add:1 identical:6 definitive:1 were:1 know:6 press:6 immediately:1 loss:1 like:6 success:1 alternatively:1 δs:1 δn:9 δi:3 works:1 replacement:1 parity:2 exceed:1 because:4 classical:30 sequence:2 choosing:2 convex:2 proper:1 peter:2 ballot:27 lead:1 does:6 summand:2 assuming:2 demonstrated:1 expansion:4 wesley:2 conveyed:1 although:4 analyses:4 stage:1 deriving:1 about:3 trivariate:1 actual:1 carried:1 extension:3 macchiavello:1 compatible:1 introduced:1 faithfulness:1 previously:3 functional:1 square:2 utility:3 transfer:1 inner:5 terminates:1 function:10 gessel:1 triangular:1 but:11 hj:1 construction:4 convergence:1 partially:1 made:2 compute:11 places:1 instructive:1 whether:4 wish:1 below:2 limit:5 problem:1 walter:1 lvi:1 display:1 mechanics:6 bearing:1 universal:12 contribute:1 denote:1 goodness:1 relates:1 inf:2 identities:1 nongeneric:1 diego:1 functions:4 other:16 shannon:8 conclusion:1 repeat:1 expressible:1 june:2 4r:1 rule:4 strings:4 4n:1 portion:17 cleve:1 validation:1
|
quant-ph9612045.txt |@word ny:1 concept:2 sci:2 consider:1 proposed:4 show:1 indeed:1 particular:1 results:1 leads:2 using:1 alternative:1 yamamoto:7 eigenstates:1 before:1 massar:1 rapid:3 based:1 knowledge:1 parameters:1 conclusions:1 ment:1 ingredient:1 seems:1 enough:1 than:2 aviv:2 only:3 other:1 device:2 lett:3 weakening:1 alter:7 adiabaticity:1 carolina:2 do:5 non:2 protective:22 weakness:1 regarding:1 wave:5 finding:1 vorontsov:1 know:2 they:1 new:1 press:1 during:1 difference:1 exact:1 unfounded:1 school:1 necessary:1 level:1 university:3 arxiv:1 applicable:1 expectation:1 jersey:1 beverly:1 found:2 signal:3 mathematical:1 ann:1 adiabatic:2 tel:2 neumann:3 disentanglement:1 energy:10 some:2 back:2 approximation:1 second:1 result:1 measurement:15 quantum:9 our:3 naming:1 out:1 category:1 what:1 potential:3 driving:2 nondegenerate:2 measurements:26 rev:6 its:1 state:13 does:4 aharonov:5 a50:1 between:3 reply:1 contrast:1 shows:1 measuring:2 foundation:2 process:1 full:2 recently:2 theory:1 nature:1 weak:3 lead:1 clarify:1 completely:1 slow:1 although:1 systems:2 post:1 strong:2 observing:1 change:3 calculate:1 observable:3 about:4 dec:1 central:1 leaves:1 infinitely:1 discussed:2 location:1 o:1 ignoring:1 rovelli:1 protection:2 neighbor:1 introduced:1 south:2 first:2 comment:2 there:2 probability:1 point:1 communication:3 into:1 disentangled:1 harmonic:5 braginsky:1 entanglement:3 acad:1 been:1 another:1 sequences:1 moreover:1 research:2 bound:1 significantly:1 given:1 described:2 usa:1 needed:3 unknown:1 initial:5 sackler:1 system:8 fast:1 unruh:1 their:4 popescu:1 therefore:3 statement:1 basic:3 ph:1 was:1 tell:1 observations:1 function:5 israel:2 ghose:1 corresponding:1 complete:1 definition:1 metastable:1 academy:1 corrected:1 took:1 but:2 gap:4 larger:1 interaction:3 authors:1 known:2 foundations:1 anandan:2 irrelevant:1 former:1 observed:2 grant:2 science:1 work:1 oscillator:5 value:2 eigenstate:8 probe:1 while:1 protected:4 hope:1 princeton:1 squeezed:3 property:6 called:1 procedure:2 pre:1 claim:1 selected:1 changed:1 entail:1 zeno:2 give:1 almost:1 certain:1 von:3 generalization:1 need:2 single:2 way:1 thorne:1 want:2 home:1 claimed:2 demolition:2 any:6 humanities:1 incorrect:1 information:6 strength:1 end:1 us:2 national:1 no:2 supported:1 fixing:1 make:1 note:2 sciences:2 ideal:8 priori:2 quant:1 significance:1 department:1 finite:1 misinterpreted:1 columbia:1 raymond:1 excitation:1 after:1 effect:2 falls:1 phy:1 faculty:1 variable:1 frequently:1 astronomy:1 measured:1 recent:2 coupling:4 considered:2 physics:2 ingredients:1 together:2 vaidman:5 more:1 part:1 negligible:1 frequent:1 administered:1 observables:1 requires:1 latter:1 outcome:1 left:1
|
quant-ph9612046.txt |@word limited:1 consider:2 remarkable:1 rev:12 varying:1 desirable:1 results:1 fluids:1 four:3 roy:1 controversial:1 consists:1 putterman:6 expressions:1 2r2:1 whose:1 certainly:1 bremsstrahlung:1 technique:1 young:1 finally:1 those:1 th:2 under:1 te:1 case:25 supported:1 very:3 account:1 wave:4 ultraviolet:1 chodos:1 1ps:1 emphasized:1 categories:1 d37:1 shock:3 t2:1 science:1 small:1 optics:2 smaller:4 eberlein:1 broader:1 pulse:3 filled:2 further:1 dynamics:4 seth:1 shining:1 blue:1 established:1 plays:1 trapping:1 d2:1 pandey:2 near:3 current:1 experiment:2 above:3 values:2 method:2 contrast:1 body:1 edited:1 simultaneously:1 lee:1 mechanisms:5 heller:1 here:2 pratt:1 others:1 represented:1 strong:1 respect:1 extreme:1 obtained:1 instituto:3 involved:1 study:1 vectors:1 completely:1 example:4 sofar:1 gaitan:3 usually:1 hbt:11 fourier:1 plotted:2 uniquely:1 ase:3 scales:1 visible:1 apply:1 estimate:1 standing:1 plot:1 conventional:1 takes:1 would:9 remains:1 give:1 emits:1 scenarios:2 few:1 a53:1 therefore:2 attribute:1 taken:3 type:1 today:1 more:2 becomes:2 apparent:1 emission:18 curvature:1 particular:3 known:2 cases:6 1µm:1 keeping:1 sphere:5 electrodynamic:1 lapse:1 work:1 itself:1 obvious:1 following:1 dec:1 collapsing:2 stimulating:1 compare:1 renormalization:1 figure:3 brown:2 process:16 relativistic:1 neglected:1 high:5 collision:1 b180:1 emitting:7 magnitudes:1 information:6 rather:1 discussion:1 get:1 feature:1 regions:1 fourth:1 reject:1 erfc:1 parameter:7 sin:3 simplicity:1 may:3 mag:1 geometrical:2 revealed:1 parallel:3 stress:2 short:3 natural:1 caixa:1 effective:1 light:19 spectra:1 lines:10 derivatives:1 provide:1 so:4 allow:2 correlation:21 e54:1 order:3 typical:2 pointed:2 produced:1 thermal:5 already:1 scott:2 mentioned:2 captions:1 still:1 its:5 before:1 interesting:1 d33:1 production:2 fig:5 might:2 versus:1 non:3 good:1 greater:1 lentz:1 janeiro:2 practice:1 introduce:1 anticipated:1 obeyed:1 closer:1 front:1 now:1 nor:1 easily:2 classified:1 sufficiently:1 magnitude:2 each:1 acoustic:3 entirely:1 mean:1 heavy:2 domain:2 another:1 ed:1 energy:13 gaussian:9 related:3 manifests:1 static:2 expect:1 measurement:5 quantum:3 eq:2 really:2 shown:1 goldhaber:2 space:5 since:4 crucial:1 particles:1 collisions:1 wilson:1 squares:2 ref:1 theory:1 ısica:3 given:2 quite:1 extraordinary:1 reason:1 kodama:1 formation:1 besides:2 imagine:1 hep:2 detecting:1 beginning:1 generate:1 log:1 definition:1 pairs:1 r2:5 geometry:5 could:6 motion:3 american:1 place:1 consequence:3 quadratically:1 first:5 origin:7 behaves:2 probability:2 striking:1 heinz:2 directly:1 angular:1 size:3 guess:1 necessarily:1 temperature:1 introduction:1 data:2 achieved:1 approximately:1 glauber:1 1e:5 encouragements:1 white:1 shifted:1 shell:6 relationship:1 explanation:1 continuous:1 serve:1 immediate:1 reflecting:2 differentiate:1 authors:2 x2:1 eliminated:1 than:4 dynamical:6 expanding:1 wide:2 pamplona:1 was:2 see:1 submitted:1 roberts:2 determined:1 amplitude:2 were:1 toward:1 sp:1 shrinks:1 acknowledged:1 spectrum:2 curves:5 correspond:1 gyulassy:2 need:1 seen:2 concentration:1 apparently:1 clearly:2 conversion:1 convenient:1 latter:1 mie:1 mechanism:4 note:4 k2:16 k1:16 interior:1 circles:4 even:3 play:1 though:1 most:2 moss:1 sandra:1 phase:1 pais:1 kay:1 measured:2 radiating:1 considered:2 ki:1 later:1 drive:1 proceedings:1 points:1 principle:1 exp:1 lays:1 velocity:4 physics:2 fact:1 applied:1 precise:4 phenomenon:1 show:2 random:1 scattered:1 dependences:1 range:2 chaoticity:2 trivial:1 cnpq:1 slow:1 based:2 just:3 parameters:2 sphericity:1 situations:1 written:1 should:8 analytic:1 only:2 black:1 factor:4 employed:1 milton:1 nucl:1 equilibrium:3 varios:1 do:1 his:1 means:1 beams:1 de:6 fluid:3 ones:1 expresses:1 during:2 respectively:1 collisional:1 differentiating:1 dq:1 processes:1 qr:6 pimentel:1 arxiv:1 investigate:1 hydrodynamic:2 fixed:1 sep:1 shedding:1 set:1 ser:1 burst:1 sensitivity:1 observed:1 opposite:1 namely:1 radius:2 result:2 discussions:1 brazil:3 instance:1 phases:1 µz:2 federal:1 speed:2 currently:1 symmetric:1 behind:1 correctly:1 between:4 geometric:1 conditions:1 discovery:1 available:1 initially:1 emitted:7 however:5 gratefully:1 wu:2 distinguish:2 bose:2 come:1 suggested:1 both:1 cos:1 acoust:3 prescription:1 many:1 region:5 contract:1 padula:1 faperj:1 casimir:4 argue:1 experimental:2 among:3 period:1 coincidence:1 analyzed:1 simply:1 wider:1 constant:1 throughout:1 gratitude:1 ps:1 b182:1 implosion:1 due:5 been:3 int:1 much:1 treat:1 basic:1 expected:1 ph:3 corresponding:2 formed:1 gas:8 precision:1 coherent:5 spin:1 former:1 present:1 p2:1 intriguing:2 p1:1 laser:3 exponential:6 solid:3 defining:1 straight:2 value:2 sonoluminescence:11 while:2 behavior:3 orica:1 property:1 iz:1 chaotic:4 characteristics:1 hama:1 thus:1 them:1 surface:1 iv:1 rio:2 vs:1 converts:1 neuhauser:1 crum:3 different:6 suggest:1 corresponds:4 radiation:3 same:1 any:4 paulo:3 complex:1 quant:1 widely:1 several:2 composition:1 difficult:1 development:1 independent:1 used:1 effect:6 hand:1 ion:1 barber:5 necessity:1 dielectric:1 center:1 scenario:1 nevertheless:2 well:3 analysis:3 phil:1 academic:1 model:1 kauffmann:1 spherical:5 blackbody:1 world:2 unesp:1 being:2 sound:1 obtain:1 sources:2 shape:5 atomic:3 aspect:1 spherically:1 scattering:1 intersection:1 candidate:1 density:3 photons:3 extra:1 seems:1 parametrization:2 source:29 lett:9 rafelski:2 identical:2 around:1 possible:3 elapsed:1 smallness:1 know:1 vacuum:1 press:1 using:1 postal:1 like:1 particle:2 sizes:1 workshop:1 signal:1 velocities:1 shapes:1 multiplicative:1 weiner:1 essential:1 poor:3 because:1 some:6 examples:3 table:2 happens:1 vol:1 scale:5 lead:2 cavity:1 measurements:2 camp:1 fapesp:1 does:1 meaningful:1 distinguishing:1 refer:3 measuring:4 scientific:2 power:1 slight:1 rua:1 expansion:1 stellar:2 pressure:1 wong:1 found:1 plots:2 relating:1 properties:2 about:3 extension:1 extending:1 discussed:3 dependence:3 hanbury:2 consequently:1 homogeneous:1 soc:3 locally:1 chu:1 orders:1 into:4 within:5 three:1 appropriate:1 references:1 determine:7 einstein:2 nowadays:1 fev:1 statistics:2 span:4 additional:1 constantly:1 transform:1 conservation:1 quanta:3 slopes:1 bubble:14 knowledge:2 interferometry:6 function:15 aguiar:1 medium:1 form:4 enough:2 phenomena:1 differences:2 but:3 elze:2 line:1 partially:1 inside:4 systematics:1 us:3 emissions:1 d20:1 distribution:6 4r2:1 similar:3 clarke:1 required:1 associated:1 defined:3 abstract:1 am:3 ao:3 general:1 multiparticle:1 single:3 twiss:2 distributions:1 universidade:2 triangles:2 physical:1 functions:5 compared:1 dotted:2 no:5 a211:1 whereas:2 when:1 application:2 other:3 role:2 spatial:5 out:2 deviation:1 coherence:1 photon:8 important:3 a5:1 studied:1 variable:1 independently:1 factorized:7 pion:1 abscissa:1 assume:2 resolution:6 proposed:2 interval:1 curve:1 time:19 requires:1 having:1 once:1
|
quant-ph9612047.txt |@word limited:1 desirable:1 four:1 parameterization:1 const:1 4ns:1 presents:1 worth:1 summarized:1 experimentally:2 solution:4 convenience:2 vector:5 consistent:6 direct:7 approximation:6 likely:5 implemented:5 even:6 errors:20 ˆx:2 ˆy:3 ˆz:5 b03:2 decoding:33 above:2 ˆi:1 ˆj:10 consisting:1 seeks:2 κn:32 mec:13 interrupting:1 here:4 plenio:1 active:1 obtained:8 elaborate:1 complicated:6 changes:1 numerical:25 projection:1 unitary:6 sloane:1 achievable:1 glance:1 total:6 unit:4 plot:1 would:14 dnk:1 dnj:5 noting:1 therefore:8 type:5 successful:2 odinger:1 berlin:1 interaction:7 excellent:1 hold:2 circumstances:1 springer:1 ma:1 work:5 iheff:7 concepts:1 root:1 example:4 renormalization:1 indicated:2 ingenuity:1 bennett:2 organized:1 involve:1 indicates:3 feasible:1 absolute:1 provide:3 machine:1 how:5 symposium:1 preferable:1 ψin:1 description:5 undergoing:1 replacing:1 earlier:2 gottesman:1 minimizes:1 types:1 third:2 algorithms:5 operate:2 order:16 operations:1 over:5 london:4 satisfies:2 before:2 fit:1 exhibits:2 destroyed:1 noninteracting:1 fig:13 quant:6 overcome:2 them:2 amenable:1 steane:4 effects:9 they:11 represents:5 reasonable:3 each:10 side:2 mean:3 schemes:5 financial:2 fairly:1 t2:4 literature:2 laboratory:1 divincenzo:3 network:12 crucial:2 gov:1 foundation:1 topt:7 turning:2 linear:1 gardiner:1 given:24 free:4 corrects:1 estimate:1 depolarizing:1 starts:2 tolerant:4 δij:1 corrections:7 moving:1 onto:1 already:1 another:2 thick:1 timothy:1 similarly:3 approximately:1 needed:1 master:25 too:2 egham:1 geneva:2 realization:2 incur:1 somewhat:1 zero:7 matter:1 solely:1 bridge:1 modern:1 seen:3 seem:2 picks:1 dozen:1 estimated:1 convenient:2 latter:3 isolated:1 oriented:1 transmit:1 effectiveness:1 decoheres:2 ih1:3 though:2 object:1 swiss:1 involving:1 decohered:1 phase:14 don:1 observation:1 calculated:1 sum:5 dot:2 random:5 resemblance:1 proposed:6 spite:1 implementation:4 adequate:1 hamiltonians:6 do:1 mixture:1 di:1 κ2n:1 dt:18 represented:7 carmichael:1 runs:1 acknowledgments:1 analytical:8 nδ:4 reference:1 δjk:1 margolus:1 resist:1 depends:2 result:5 fail:1 optimum:10 techniques:7 simplest:3 conceptual:1 approach:5 discovery:2 preserve:1 terms:10 weak:2 however:14 modeling:1 protect:5 fault:4 against:4 faces:1 exceeds:1 distinction:1 qubit:62 argue:1 com:1 asked:1 appeared:1 royal:1 κt:4 puts:1 basis:7 three:14 been:15 quickly:1 commission:1 much:3 interest:4 basic:1 expected:2 dots:1 graphical:1 families:1 xxx:1 coherent:1 2n2:1 applied:6 publicly:1 aim:5 near:3 abrupt:1 35th:1 procedure:7 ih:3 id:4 containing:1 weinfurter:1 make:2 complex:2 potentially:1 dimensionless:1 several:3 grows:1 european:1 independent:3 i2:2 i5:2 hand:5 normalization:1 kept:1 maximizing:1 scenario:2 contact:3 greatest:1 simulated:1 paradigm:1 left:2 just:4 via:1 identify:4 yamamoto:2 previous:4 character:1 weiss:1 elt:1 designate:1 survival:1 disagreement:1 possible:9 whichever:1 performance:1 occurring:7 appearing:1 performing:1 steps:7 arbitrary:6 evolutions:3 beneficial:7 right:2 successfully:1 undisturbed:1 opposite:2 illustration:1 pr4:2 o:5 plus:1 considerations:1 soc:1 markovian:2 presence:5 down:3 hermitian:3 often:3 support:2 initial:14 approximate:1 fraction:2 was:6 lowest:2 decoded:2 form:7 becoming:1 differences:1 encodes:1 decodes:1 encoded:9 versions:1 maximum:4 stages:4 b1:3 zeno:1 abstract:1 evidence:1 exist:1 simulations:10 archive:1 physical:2 nn:2 no:12 ekert:1 wavefunction:1 generally:1 vanishes:1 reality:1 setting:2 papers:2 picture:3 superposition:3 models:5 dissipation:2 stoke:1 longer:4 dψ:2 assume:8 time:68 concept:1 particular:5 focus:1 osi:1 roy:1 computation:9 devoted:1 certainly:1 inverse:1 depend:1 eˆ:2 environment:32 finally:1 advantage:1 orthogonal:2 choice:2 stays:1 exact:1 presented:4 turns:1 proposals:1 noiseless:1 substitute:1 adds:1 appear:4 sequential:2 satisfy:2 realizations:1 understanding:1 along:1 change:4 studied:1 commonly:1 ineffective:1 schack:3 useful:7 merely:2 flexibility:1 alamitos:1 projector:1 working:1 prove:3 positive:3 give:5 scenarios:1 memory:4 encode:2 introducing:1 ua:17 validity:1 cases:7 effort:1 reviews:1 values:8 arrive:1 4κt:1 figure:11 performed:3 allowed:1 occur:3 verlag:1 monitoring:1 discussion:2 pure:4 optimal:5 parameter:1 product:3 may:8 max:2 applications:3 produce:2 date:1 grow:1 times:5 natural:1 so:21 sn:2 sc:5 subsections:1 22n:1 experiments:1 statistical:1 still:5 ieee:1 tending:1 group:1 acknowledge:2 interesting:2 non:6 conversations:1 gate:12 now:3 discuss:1 term:5 possibilities:1 realistic:4 square:1 significantly:1 ed:1 gaussian:1 conventions:1 ey:2 ex:1 ez:2 eq:6 shown:5 space:6 interference:1 looking:2 correct:4 shows:2 plotting:1 after:4 theory:2 possibility:4 unwanted:2 e1:2 milburn:1 impose:1 programming:1 first:13 surviving:2 omitted:1 variables:2 fast:1 directly:2 open:1 angular:1 size:1 little:2 necessarily:2 checked:2 unitarity:1 indicate:3 convention:2 white:1 gives:5 way:5 continuous:8 representing:2 than:11 impractical:2 unfortunately:2 require:3 future:2 were:4 outcome:1 remained:1 correction:71 generalization:3 crossover:3 say:1 recover:1 saw:1 any:5 efficient:1 note:5 take:3 destroy:2 channel:4 multiple:2 trace:1 normal:1 algebraic:1 pr0:2 acknowledges:1 surprising:1 considered:1 average:3 later:2 typically:1 quantity:1 shor:10 spaced:3 show:1 spaces:1 fifth:1 ground:1 ratio:2 proportion:1 written:4 analytic:4 only:10 explicitly:2 black:2 get:4 expectation:2 cannot:2 nearly:1 ssc:5 prime:1 parkins:1 bounds:1 relative:1 college:2 differentiable:2 fails:1 satisfying:1 ways:1 review:1 outside:1 between:20 qubits:36 comp:1 analyzed:1 many:10 region:2 according:1 σz:6 σy:1 σx:2 expression:1 among:3 effective:4 period:1 moreover:1 mary:1 wants:1 direction:1 qsd:9 external:2 former:2 those:4 case:25 unravelings:1 situation:2 discrepancy:2 different:6 develop:1 paz:1 same:11 shifts:1 html:1 arguments:2 runge:1 regime:2 kutta:1 investigated:1 constraining:1 severe:1 without:1 solve:3 very:7 model:5 laboratories:1 dimension:2 justify:1 gates:18 nc:1 transmitting:1 when:14 ne:6 ch:1 summed:1 ψini:4 zoller:3 seems:2 except:1 lett:7 wiseman:1 real:3 around:1 read:1 psc:7 decomposed:1 early:1 using:10 execution:1 correcting:12 particle:1 reduces:2 benefit:5 either:2 reduced:4 unraveling:5 provided:2 confirm:1 process:2 scientific:1 power:1 equivalent:5 wavefunctions:1 evolve:3 rearranging:1 ρˆl:2 comparison:4 discussed:2 generated:4 practical:7 act:3 road:1 numerically:1 references:1 operator:29 watchdog:1 log:7 area:2 assumed:1 there:22 los:1 low:2 lot:1 series:1 complete:2 enough:2 smolin:2 dissipative:2 applying:2 adriano:1 regimes:1 ac:4 cirac:2 certain:4 describe:2 moved:1 general:5 tˆ:7 examine:3 again:7 unwelcome:1 storage:15 field:2 mathematics:1 drift:1 includes:1 a1:1 a0:2 a3:1 a2:3 a4:2 m18:1 decoherence:12 cpu:1 represent:6 monte:1 consider:5 expressions:1 denotes:2 causes:1 tr:1 ts:1 tn:3 preserved:1 stochastic:6 td:1 worse:1 straightforward:2 far:3 denoted:2 hewlett:2 difference:4 treating:1 hamiltonian:11 t4:3 t5:3 list:2 t3:3 t1:4 large:5 small:6 programme:1 grateful:1 b24:1 qmw:1 rate:13 further:2 canonical:2 what:4 nonlinear:1 brackets:1 section:12 version:2 method:3 condensed:1 full:2 component:1 ranges:1 equations:3 allows:1 delocalizing:1 amount:3 action:1 technique:1 followed:1 takes:2 probabilities:3 comparing:1 taken:5 more:16 lowering:1 operators:13 corrected:7 emission:2 varying:1 known:1 evolves:2 keeping:1 science:2 equation:36 remain:1 dec:1 spontaneous:2 compare:1 states:13 sphere:2 minimum:3 numbers:1 sense:2 axis:2 information:1 needs:1 goal:1 rather:5 acts:2 ensemble:11 simplicity:1 suppose:1 derived:1 plane:2 workstation:2 short:1 negligible:1 sect:6 fundamental:1 help:1 reservoir:3 developed:1 soon:2 thermal:1 paper:8 through:2 suffer:1 excitations:1 its:5 rapidly:1 tˆe:7 tˆd:7 solving:2 actually:2 microscopic:1 systems:13 might:6 good:6 return:1 framework:1 oxford:4 easily:1 always:2 iff:1 found:3 2n:5 weight:1 reduce:1 gifford:1 extended:2 todd:1 quantum:68 operation:10 beyond:1 leave:1 itˆo:1 since:7 research:1 acting:2 print:1 induced:1 issue:4 occurs:1 difficulty:1 members:1 definition:1 retained:1 3pu:1 computers:7 exponentially:1 probability:18 encoding:38 number:8 done:5 calculational:1 equating:3 differ:2 temperature:1 introduction:1 leading:1 interact:2 construct:1 identity:1 calculations:5 scheme:4 store:1 imperfect:10 relationship:1 required:3 optical:3 authors:3 schr:1 diffusion:4 albeit:1 determined:3 treated:1 randomly:2 vulnerable:1 depending:2 build:1 analogy:1 eff:8 measures:1 effecting:1 most:10 significant:1 measured:3 stands:1 ke:1 clear:1 braunstein:1 part:1 exp:1 superoperator:1 physics:12 surrey:1 particularly:1 relation:1 carefully:1 find:3 indicator:2 simulating:4 parameters:4 ox1:1 being:1 subsection:1 factor:1 intractable:1 dependent:1 zurek:1 udiger:1 during:19 arxiv:1 factorization:2 common:2 switzerland:1 set:9 see:8 individual:1 close:1 contour:1 please:1 smallest:1 various:1 probably:2 subscript:1 conditions:3 available:3 recently:2 initially:3 complement:1 attention:1 untouched:1 vanishing:1 both:13 improved:1 reverse:2 annual:1 correctable:2 context:2 whole:1 experimental:2 point:2 simple:14 corresponds:1 whatever:1 dimensional:2 dephase:1 described:5 publishing:1 due:4 faithfully:1 ph:6 pn:1 treatment:2 great:2 gap:1 fund:1 exponential:1 b01:1 while:5 optimization:2 b04:3 behavior:2 error:85 resolved:1 goldwasser:1 laflamme:2 vol:1 itself:3 belong:1 shorter:1 stimulated:1 relatively:1 conflict:1 higher:5 development:1 used:15 strength:3 uses:1 recent:2 spent:1 analysis:2 obviously:2 exponentials:1 calderbank:2 atomic:2 world:1 regardless:1 alternative:2 conclusions:1 relevance:1 excited:1 evaluate:1 entangled:3 bit:16 0ex:1 success:5 follows:4 yields:2 mathematical:1 methods:2 some:9 back:1 b4:1 b5:1 b6:1 b7:1 b0:2 examples:1 b2:1 b3:1 b8:1 scale:2 integration:5 proc:1 minimal:1 run:2 reach:1 jumps:8 agreement:2 step:3 plots:1 hilbert:7 handled:1 completing:1 simulation:7 range:1 bloch:1 computational:1 into:8 within:2 appropriate:2 proportional:5 statistics:2 tw20:1 long:1 brun:3 analyze:2 sections:2 properly:1 line:4 raising:1 uy:9 consist:1 circuits:2 up:2 us:1 uk:5 fluctuations:1 similar:6 called:1 gisin:3 storing:1 worthwhile:4 defined:6 influence:3 single:28 defines:1 codes:19 rains:1 dashed:2 application:1 b14:1 department:3 mismatch:18 problems:3 sx2:2 correlated:1 algorithm:3 practically:1 lanl:1 requires:2 once:1 code:13 illustrates:1 results:9 illustrated:3 go:1 compact:1 deterministic:3 include:2 resources:1 queen:1 continues:1 sensitivity:1 matrices:5 transmission:14 notes:1 2κt:1 optics:1 noted:1 lˆ:1 smaller:1 jump:1 carlo:1 giving:1 networks:2 experiment:1 degree:1 desired:1 others:1 convert:1 involved:1 larger:6 resulting:2 implement:1 shaded:2 makes:1 involves:1 addresses:1 castin:1 addressed:2 apply:3 use:10 superpositions:2 commun:2 remains:3 next:4 few:3 themselves:1 noisy:4 sort:1 optimizing:2 formally:1 becomes:2 benchmark:2 normalized:1 control:4 calculation:1 effectively:1 varied:1 decaying:1 occuring:1 instead:3 hurdles:1 collection:1 efficiently:1 realized:2 correspond:4 allow:2 produces:1 despite:1 looks:1 perfect:6 chosen:5 lj:3 tsc:2 degrees:2 choose:4 derivative:1 defining:1 fourth:1 rotation:1 february:1 university:4 identified:1 l2:1 l3:1 l1:1 constraints:1 doing:1 density:16 society:1 measure:3 our:13 out:3 maximizes:1 matrix:5 rev:12 lecture:1 ref:5 math:1 interactions:3 completely:1 epsrc:1 backwards:1 geometry:1 could:4 keep:1 length:1 isotropic:12 hence:3 iht:1 intuitively:1 ihn:1 precisely:1 unknown:1 system:20 realistically:1 their:1 πp:1 perfectly:1 final:2 ih2:3 ih3:2 exactly:2 environmental:6 reflecting:1 simulate:2 observed:1 isolation:1 providing:1 miquel:1 unlikely:2 need:2 clearly:3 viewed:2 studying:1 able:1 heff:1 subject:1 accuracy:1 combat:1 propagate:1 face:1 proceedings:1 normally:1 fact:1 chances:1 text:1 supported:1 purely:1 chuang:2 based:1 controls:1 should:9 dalibard:1 partially:2 local:1 achieve:2 handle:1 ones:1 sz2:2 sz0:2 procedures:4 holloway:1 evolution:17 numerous:1 differential:4 fixed:1 requirement:1 constructing:1 notational:1 national:1 correlations:1 computer:12 closer:2 phases:1 interacting:2 tend:1 state:64 progress:1 email:4 barenco:3 efficiency:3 sleator:1 problem:6 taking:1 equal:2 ln:1 figures:1 bristol:2 trajectories:9 relevant:1 ca:1 cf:3 maximize:1 respect:1 selfadjoint:1 second:3 trajectory:8 treat:1 define:2 arises:2 controlled:1 sufficient:2 essentially:1 last:1 c1:7 c0:7 present:5 unlike:1 value:10 will:24 dephasing:8 examines:1 thus:5 surface:2 sqrt:1 unity:3 pauli:4 mølmer:1 units:7 finite:6 difficult:1 http:2 effect:8 ion:1 expand:2 off:1 center:1 adapted:1 modeled:2 well:9 arising:1 usual:1 less:1 obtain:3 stored:1 imparts:1 drawback:2 add:1 match:1 identical:1 elapsed:1 five:11 press:1 variants:1 loss:1 lincoln:1 necessary:2 like:7 lost:1 alternatively:2 qualitative:1 wooters:1 become:4 exceed:1 because:5 classical:5 sequence:2 library:2 growth:1 tmr:1 demonstrates:1 instantaneous:3 does:6 assuming:3 whereas:1 trap:1 noise:40 expansion:5 clarendon:1 although:1 stage:3 about:3 actual:1 commutator:1 freedom:5 dependence:1 important:3 spiller:1 projectors:1 software:3 equally:3 own:1 year:1 additional:3 crucially:1 notices:1 function:3 hy:1 hp:1 but:14 construction:1 lindblad:13 ha:1 eat:1 dξj:4 made:3 compute:1 packard:2 instructive:1 wish:1 below:2 limit:1 percival:3 int:1 contribute:1 denote:2 effected:6 compared:3 variety:1 percent:1 other:3 hpl:1 conclusion:2 kinds:1 variation:1 else:1 coupling:4 factors:1 persistent:1 cleve:1 westfield:1
|
quant-ph9612048.txt |@word represent:1 positions:6 code:73 gs:3 consider:4 maximum:1 global:2 results:4 existing:2 gf:2 commute:3 entropy:1 grateful:2 consists:2 saturating:1 gm:5 research:1 reasoning:1 row:4 relationships:1 whose:4 c0:6 knill:2 subjected:3 similarity:1 environment:1 finally:1 program:1 those:1 th:4 under:1 alberta:1 applied:1 string:1 advantage:1 orthogonal:3 very:3 reader:1 print:9 stabilized:1 affect:2 matrices:2 paz:2 transmission:2 turns:1 plotting:1 vector:4 recall:2 barbara:2 noted:1 upper:20 mceliece:1 translating:1 second:5 further:1 eigenspaces:2 linear:20 established:3 what:1 errors:12 appear:1 richard:1 t2n:1 section:7 selected:1 brief:1 negates:1 errorcorrecting:1 above:8 entanglement:1 new:8 acknowledgments:1 satisfy:1 simultaneously:1 respectively:2 applies:6 modify:1 here:2 packing:3 others:1 along:2 quite:1 change:1 trans:1 institute:2 leaves:1 studied:1 allows:1 commonly:1 leaving:2 accomplished:1 resulting:2 complicated:1 involves:2 plotted:1 via:2 useful:3 explained:1 private:1 unitary:4 analyzing:1 welch:1 apply:5 establish:1 unit:1 asymptotic:7 would:1 codewords:6 remains:1 next:4 vol:10 anticommutes:1 call:7 therefore:7 memory:1 calgary:2 e2:1 theoretical:2 more:2 formally:1 successful:3 submatrix:7 operators:8 corrected:2 aware:2 particular:1 known:2 iii:2 must:1 states:3 springer:1 isomorphism:3 r2:5 science:2 past:1 work:1 mk:4 values:3 stabilizer:33 following:2 dec:1 example:6 proof:1 claim:1 weaker:2 abelian:1 december:1 bennett:1 involve:1 sphere:3 degenerate:3 sense:1 tolerant:1 occur:2 absolute:1 information:5 respective:1 recovery:1 provide:1 verify:1 holds:2 how:4 criterion:1 instead:1 guarantee:1 parameter:4 inputs:1 product:4 replacing:1 earlier:1 mapping:3 restrict:1 demonstrating:1 gottesman:2 date:2 representations:1 data:4 types:3 syndrome:1 transposed:2 natural:3 third:2 computations:1 lines:5 yielding:1 element:1 emanuel:1 rather:1 switch:2 so:1 specifying:1 asserts:1 definitions:1 order:2 operations:4 delsarte:1 submatrices:1 ith:15 noteworthy:1 over:3 flips:1 years:2 enumerators:2 paper:3 through:7 y1:15 converting:1 fidelity:4 benjamin:1 its:3 before:1 perfect:1 recalling:1 group:1 maps:2 interesting:4 lj:2 lk:7 better:1 fig:5 alter:1 them:1 good:1 stabilizers:1 thereby:2 was:3 matches:1 propose:1 attains:2 steane:2 they:1 oxford:1 now:1 structural:1 easily:2 intuitively:1 always:2 university:3 b3:2 transmitted:1 each:28 2n:4 macchiavello:1 mean:2 subset:1 en:5 weight:2 series:1 gaussian:2 related:1 bijective:1 encodings:1 quantum:70 our:7 operation:2 special:2 nonexistence:2 canada:2 divincenzo:3 shown:3 matrix:17 space:3 restricted:3 furthermore:1 2s:1 rev:8 denotes:2 may:2 contained:1 transposing:1 at1:2 denoted:1 2k:2 correct:3 announced:1 1n4:1 foundation:1 log2:6 theory:9 standard:8 completely:1 california:2 corrects:2 e4:3 e1:6 generate:1 e3:1 encode:1 definition:4 depolarizing:7 r1:7 language:1 geometry:1 computers:1 david:1 first:14 xk:10 features:1 probability:8 bijection:3 u1:1 coding:4 number:1 rank:2 channels:4 instances:1 improvements:1 construct:7 another:2 precisely:2 open:1 passes:4 given:3 introduction:2 least:4 draft:1 perfectly:1 bits:4 recovered:1 commutativity:2 way:1 explanation:1 braun:1 part:1 x1:6 representing:1 than:3 specify:2 achieves:2 scheme:1 holland:1 fundamental:1 imply:1 providing:1 generality:1 unchanged:1 miquel:1 close:1 need:3 apparently:4 any:17 conversion:1 constructions:2 zero:1 efficient:2 convenient:1 latter:2 note:2 instance:4 concerns:1 best:4 transmit:1 techniques:1 completed:1 channel:23 begin:2 towards:1 altered:1 allow:1 though:3 anticommute:1 most:2 eight:1 codeword:11 phase:6 probabilistic:1 class:2 inequalities:1 consequences:1 considered:1 stronger:7 typeset:1 points:1 verlag:1 hamming:1 physics:2 sum:1 fact:3 shor:7 show:8 supported:1 fifty:1 spaces:1 threshold:1 analogue:2 help:1 based:4 simulating:1 eigenspace:1 state:4 should:2 only:2 version:3 generators:11 factor:4 do:3 notation:1 means:3 zurek:1 cannot:2 macwilliams:3 aforementioned:1 during:1 reveal:1 outperform:1 transposition:1 arxiv:1 alteration:1 yield:1 fixed:2 set:13 modulo:4 constructing:1 exists:6 transpositions:1 national:1 sharpens:1 bounds:11 connections:2 see:5 computer:1 result:3 existence:2 discussions:2 recently:1 forthcoming:1 satisfies:3 analog:1 subject:3 capacity:15 tensor:1 c2t:2 nondegenerate:8 ieee:1 symmetric:4 written:2 converted:1 closed:1 between:6 ui:4 conditions:2 b2t:1 terms:3 extend:1 qubits:7 attention:2 york:2 received:1 last:3 limits:1 many:2 nserc:1 flipped:1 σz:18 σy:10 σx:10 figures:1 qubit:17 among:6 bell:1 appeared:1 overview:1 ca:2 asymptotically:1 corresponds:5 dimensional:1 respect:3 considering:3 pp:10 described:3 transformations:2 basis:4 addition:3 three:4 been:5 phy94:1 ai:1 much:2 basic:2 applying:4 ph:10 correction:7 define:4 cx1:4 corresponding:2 commutes:2 sufficient:1 coherence:1 subspace:1 assert:1 external:1 c2:2 c1:2 general:1 spin:1 present:2 case:3 since:1 developing:1 solid:2 value:1 will:5 while:2 behavior:1 error:49 property:7 procedure:1 larger:1 laflamme:3 almost:1 characteristics:4 thus:6 iv:3 ii:2 claimed:1 binary:18 different:1 intact:2 combination:1 grant:1 identities:1 juan:1 yn:15 connection:1 same:1 quant:10 pauli:1 several:1 rumsey:1 independent:2 infinity:1 effect:3 sys:1 nk:2 hospitality:1 hans:1 changing:2 lower:6 suffices:1 well:4 analysis:1 without:1 position:4 model:5 g1:8 stating:1 calderbank:3 proposed:1 being:1 obtain:2 immediately:1 shadow:1 previous:2 generator:12 capabilities:6 simple:1 setting:1 extends:1 lett:4 theorem:2 transformation:3 take:4 identical:1 represents:1 couple:1 possible:1 using:4 bit:11 unique:1 correcting:36 loss:1 necessary:2 like:2 performing:3 specific:4 wooters:1 yields:2 arbitrary:1 translated:1 sloane:3 fault:1 terminology:1 mathematical:1 exceed:2 because:1 often:1 classical:34 sequence:1 successfully:2 some:10 understood:1 added:2 examples:1 b2:2 specified:5 proofs:2 δn:3 shall:7 extensively:1 comments:1 does:1 tends:1 ucalgary:1 straightforward:1 equivalent:4 l1:7 bi:1 broken:1 revtex:1 santa:2 properties:11 bz:1 noisy:5 about:3 column:12 theorems:1 distinct:2 mixed:1 referred:1 slightly:6 automatically:2 previously:4 communication:3 into:6 within:4 bound:26 due:1 references:2 operator:2 amsterdam:1 additions:1 reducing:1 rows:3 van:1 additional:2 there:9 question:2 transform:2 u2:1 inner:1 fraction:2 m1:4 sections:1 naturally:1 function:2 north:1 form:11 smolin:2 lint:1 independently:3 but:2 taken:2 construction:4 elimination:2 attainable:2 line:2 considerable:1 info:1 wise:1 improved:1 whether:1 rate:1 up:2 below:1 un:1 limit:1 demonstrate:1 similar:4 b1:2 detailed:1 twirling:1 defined:4 certain:4 abstract:1 describe:1 am:2 proven:1 denote:2 proves:1 exist:3 commuting:2 ni:2 functions:1 codes:59 no:10 rains:5 dashed:2 ekert:1 when:2 other:2 shannon:1 becomes:1 department:1 tech:1 out:1 arithmetic:3 kinds:1 generates:2 why:1 a1:2 generated:1 a2:2 bounded:4 younger:1 required:4 implied:1 time:1 cleve:3 n1:2 decoherence:2 original:3
|
quant-ph9612049.txt |@word gd:1 concept:4 consider:4 rev:1 dynamic:1 primed:1 leads:1 commute:1 savel:1 grateful:1 δcd:2 naukova:2 dimentional:1 devoted:1 blm:2 gad:1 gab:5 under:3 td:1 sound:1 belonging:1 φnr:2 far:2 frequencies:1 conditions:1 induce:1 wave:13 sbornik:1 lrs:1 putting:1 fall:1 exact:1 condition:7 kovalev:1 discrets:1 integrating:7 t2:1 solution:17 integro:1 vector:1 guiding:1 markov:4 βx2:1 equation:63 smaller:1 rrc:1 onecomponent:1 approximation:2 second:7 theory:3 established:1 nonlinear:3 deeply:1 section:2 uniform:2 3i:1 version:1 new:3 method:2 that2:1 movement:3 satisfy:4 edited:3 degree:1 whose:1 respectively:3 realizations:1 component:3 here:14 understanding:4 φr2:10 φr1:10 objects:1 possibility:4 groups:5 equations:34 nachr:1 galilei:14 obtained:5 search:1 glm:2 institute:1 study:3 studied:1 allows:2 reason:1 ξ2k:4 ξ2j:1 resulting:1 rosenau:1 action:1 symmetrical:2 ξ2a:3 narrow:1 makes:1 divide:1 lkin:1 elaborated:1 complying:1 h3:4 private:1 e5:1 summation:3 total:1 establish:2 unit:2 derivatives:3 use:2 takes:3 would:1 contains:4 permitted:1 choosen:1 call:3 therefore:1 m3:1 m2:1 associated:1 type:8 theoretical:9 more:4 nauka:8 becomes:1 operators:21 odinger:47 reversible:1 particular:5 known:5 cases:1 must:2 account:4 continuos:1 mc:1 permits:4 science:2 inertial:1 work:5 modified:3 mv:5 values:3 following:4 dec:1 conformity:1 example:6 dxj:2 lφ:11 impose:1 indicated:1 stated:3 relativistic:27 allowed:1 states:1 lorentz:6 dxk:4 numbers:2 sense:10 dxa:1 information:5 h4:1 gcb:1 gcd:1 shirkov:2 write:1 how:1 instead:3 parameter:1 sin:2 algebra:26 may:17 after:2 derived:1 dx0:1 hence:3 rations:1 dokl:2 representations:2 law:5 compatibility:3 constants:1 man:9 supersonic:1 realized:1 natural:1 third:2 light:7 author:1 correspond:2 su:1 δma:1 δmb:1 δmc:1 so:2 allow:1 representation:3 cherenkov:1 order:6 cumulative:1 interpretation:2 help:1 over:3 mx2:1 iae:2 paper:1 differs:1 existence:5 satisfies:2 its:3 leznov:1 group:35 symmetry:65 δg:1 solving:2 symptoms:1 choose:2 ξ1k:1 mail:1 main:1 maximal:9 non:13 h1:2 combination:1 ya:1 tpk:1 introduce:3 xg:14 framework:3 mxk:1 acta:1 rotation:1 sixteen:1 yu:1 structural:1 2v:2 2w:4 2p:1 alembert:9 davydov:1 ussr:2 each:1 found:8 repeating:3 characterized:1 mean:2 em:1 differential:3 weight:12 energy:7 hls:1 principles:2 engaging:2 unprimed:2 investigated:1 poincare:1 quantum:6 ev:2 eq:12 special:1 out:2 mv2:1 matrix:1 space:17 since:2 induces:1 research:3 particles:2 transforming:1 investigation:1 formula:3 rn:1 induced:1 lag:1 linear:11 circumstance:1 free:10 standard:7 admits:1 approaches:1 base:2 york:1 besides:1 vorob:1 put:2 subalgebras:1 dubna:2 r4:4 definition:7 applications:2 determining:3 could:1 transition:1 βx:3 turn:2 maximality:2 place:1 consequence:1 moving:3 fian:1 speeds:3 first:6 xj:8 xk:17 xh:5 already:1 features:1 malkin:2 shapiro:1 xb:27 xc:20 variables:8 xa:32 number:2 xd:19 δjb:2 nova:1 another:2 xs:1 xp:4 xq:1 xv:1 illustrate:1 given:6 similarly:1 introduction:3 unknown:2 system:4 relations:4 their:1 too:4 hypothetical:2 structures:1 final:1 completed:1 akad:2 proving:1 formulate:1 x0:19 than:7 coefficients:2 showed:1 accordance:4 depends:2 determined:1 were:2 enables:1 abstracts:1 distinguished:1 bination:1 w2:1 symmetries:12 hagen:2 electrodynamics:1 turned:1 matem:1 generalization:1 take:2 onigl:1 any:2 seminar:4 lie:34 academic:2 studying:4 latter:2 indexes:1 note:1 potential:1 generalized:2 analogy:4 equaling:2 mir:2 moscow:15 formulas:1 begin:1 serov:1 index:3 object:1 systems:1 algebraic:3 vnu:1 formulae:3 phase:5 fand:1 kc:2 kb:3 give:1 kd:4 considered:1 ko:10 minlos:1 dimension:1 proceedings:6 exp:16 omit:1 velocity:13 physics:11 2m0:1 ibragimov:1 show:2 izdat:2 multicomponent:1 relativization:1 xl:1 helv:1 relation:1 solutions:13 analogue:1 find:3 q1:3 ratio:2 parameters:2 aφ:5 soliton:1 behind:2 θjk:5 should:1 only:3 generators:9 ges:1 do:1 dk:2 klein:2 means:2 ones:3 valuable:1 invariant:3 combinations:1 gel:1 gbc:1 g0k:2 fields:7 arxiv:1 summary:2 twice:3 nauk:3 dodonov:3 contain:1 discussing:1 valid:1 view:1 δja:2 conform:1 δjc:2 set:26 reference:1 frame:1 differentials:1 relative:2 namely:2 result:5 w1:1 satisfying:2 commutation:1 distinctive:1 definite:1 wiss:1 written:2 various:1 between:2 consecutive:1 approach:5 available:1 publishers:1 2m:8 however:2 δad:3 wv:1 δaf:1 wt:1 δaa:1 δab:5 jk:3 distinguish:1 raczka:1 δak:1 both:3 cos:2 providing:1 many:1 taking:3 equal:4 russia:1 enabling:1 propagation:10 colloquium:1 exceeds:1 expression:2 shabad:2 aa:1 relativity:2 point:1 δac:2 dimensional:4 interrelations:1 respect:3 cp:5 mc2:2 ct:1 forms:2 transformations:15 basis:1 addition:3 px:4 py:1 due:2 been:2 pb:1 pc:1 describes:1 basic:1 pk:4 ph:1 algebras:5 ak:4 ls:49 dots:1 direction:2 corresponding:9 nikov:8 6i:2 coherent:1 ensuring:1 chur:2 olver:2 c2:16 general:6 former:1 present:5 case:11 p0:4 uncertain:1 value:3 will:3 property:3 real:3 thus:5 them:1 iv:1 itself:2 vt:1 vw:1 vx:6 ic:1 nikitin:3 movements:2 0b:1 different:4 etc:1 acknowledgments:1 belong:2 radiation:1 same:2 poincar:2 quant:1 higher:4 extended:3 v2:3 transformational:2 purpose:1 infinite:5 propagated:1 invariance:11 subgroups:1 task:1 schr:47 com:1 well:3 analysis:1 thought:1 barut:1 utrecht:1 sets:1 possesses:1 left:2 ny:1 proposed:3 less:1 being:1 when:10 obtain:1 rest:3 seen:2 transforms:1 speed:12 4m2:3 preprint:3 generator:1 application:4 pa:6 interprete:1 niederer:1 source:1 k0:1 transformed:1 lett:1 theorem:5 trifonov:1 transformation:5 momentum:8 designate:1 identical:2 conformed:1 results:3 possible:3 finding:3 netherlands:1 voigt:1 using:1 accepted:1 igl:7 necessary:3 particle:19 follows:4 velocities:3 dumka:2 δh:1 arbitrary:5 become:1 works:1 reduced:2 terminology:2 mathematical:5 exceed:1 right:2 old:3 methods:5 classical:4 conditional:1 some:4 permitting:1 examples:1 δbc:4 δbd:2 δbg:1 δbf:1 dimensions:2 shall:15 cv:1 aab:2 prof:2 fragments:1 propagating:2 conventional:1 illustration:1 bk:2 display:1 ratios:6 accompanied:1 properties:10 earlier:1 about:1 carried:2 o:1 pz:1 2x0:3 b0k:2 ξ1a:1 h2:8 maxwell:6 into:17 within:2 h6:1 m0k:4 qjk:3 h5:1 remarks:1 appropriate:1 because:2 references:1 einstein:1 operator:10 unambiguous:1 schrodinger:1 additional:3 area:3 transfer:1 initial:3 question:1 transform:1 kurchatov:1 start:1 accordingly:2 much:1 way:1 jinr:2 resulted:1 was:1 m0:5 function:15 δkb:5 δkc:5 form:6 δka:4 usp:1 hv:1 but:2 hk:2 state:2 harwood:2 absent:1 made:1 algorithm:19 versions:2 minkowski:2 us:7 assume:2 below:2 limit:1 demonstrate:1 similar:1 called:2 mechanics:5 replacing:4 coincides:2 abstract:1 contribute:1 evidence:1 exist:2 dθ:7 formulation:2 ottingen:1 constructed:2 functions:14 qν:2 nx:5 field:10 nz:1 other:4 details:2 np:1 massless:5 conclusion:2 algorithmes:1 elements:4 4i:1 includes:2 a0:4 qσ:1 important:1 dividing:1 sides:2 kiev:2 coulomb:1 practically:1 dφ:1 rule:1 zhelobenko:1 mass:8 time:10 restored:1
|
quant-ph9612050.txt |@word ψcs:1 concept:1 squared:1 lack:1 results:1 four:1 eds:1 broader:1 follow:4 ρss:15 whose:1 calculate:1 alamos:2 concerned:1 equivalence:1 finally:2 breach:1 oberhettinger:1 division:1 very:1 soni:1 wave:20 figs:2 experimentally:1 emphasized:1 difference:1 2rs:1 roy:1 zeit:1 positions:1 michael:1 large:2 epstein:2 harry:1 small:1 optics:5 noted:2 upper:1 picket:1 foundation:2 oscillator:2 sin2:3 za:1 cosh:25 located:1 further:1 odd:2 even:3 what:2 brackets:1 sum:10 agrees:2 current:1 annals:1 above:1 new:4 acknowledgments:1 ibid:1 kennard:2 respectively:1 identifications:1 operating:1 cos2:1 sinh:22 others:1 along:1 invented:1 observing:1 z1:2 z2:1 extreme:1 obtained:5 hansen:1 shift:1 studied:1 commonly:1 round:1 amount:1 products:3 published:2 complicated:1 narrow:2 changes:1 numerical:2 matos:1 followed:1 ions:1 hermite:1 summations:1 yuen:1 plenum:1 addressed:1 apply:1 analyses:1 plot:4 use:1 would:2 positive:1 πbb:4 plebanski:3 next:1 bialynicki:1 call:1 therefore:2 wondering:1 theoretical:1 started:2 px2:1 odinger:4 ip0:9 normalized:1 particular:1 known:2 must:1 entangle:1 topic:1 springer:1 recall:1 equation:1 work:6 iα1:1 iα2:1 fock:6 values:1 ulm:2 sandberg:1 dec:1 example:3 history:1 f1:7 f2:11 f3:5 f4:11 figure:9 calculation:1 organized:1 states:37 lorentz:2 tan:5 keep:1 viewpoint:1 rather:1 verify:2 discussion:3 how:2 frontiers:1 answer:1 instead:1 ordinary:2 sin:17 product:1 algebra:2 zimmerman:1 earlier:1 bothered:1 produce:1 demonstrating:1 coming:1 fi:3 short:2 third:1 ss:1 filho:1 yielding:1 thorne:1 so:1 keeps:1 definitions:2 order:1 interpretation:1 zek:1 over:3 mainly:1 soon:1 produced:3 paper:3 pulses:1 looks:1 statistical:1 husimi:2 letters:2 still:1 tops:2 its:2 before:2 f42:9 τj:1 if2:1 la:1 ln:12 takahasi:1 boson:1 writing:1 forms:3 humboldt:2 fig:4 saxon:1 easier:1 correspondence:1 non:1 thereby:2 conversations:1 elementary:1 they:9 now:5 yu:1 discuss:1 2s2:1 2t:4 easily:1 term:1 equality:2 2r:2 2s:1 university:1 2x:2 academic:1 knight:3 2l:1 found:3 universit:1 cliffs:1 2j:12 reproducing:1 square:1 doing:1 series:4 energy:1 gaussian:1 x20:1 obtains:2 combining:1 quantum:7 laboratory:1 eq:15 special:2 er:2 shown:2 electronic:1 since:1 rev:14 particles:1 re:1 gaussians:3 drever:1 formula:1 gov:1 ref:10 interchanging:1 shows:1 benjamin:1 sinh2:1 after:2 routine:2 seventh:1 given:6 possibility:1 standard:1 mmn:1 california:1 york:3 besides:1 moore:1 org:4 beginning:1 definition:1 created:1 widths:3 could:2 similarly:1 times:2 motion:4 appearing:1 iz2:3 place:1 gordon:1 onto:1 gif:8 first:1 features:1 probability:10 number:24 iht:1 philosophical:1 xy:2 done:1 another:1 brychkov:1 xs:2 tf1:1 xt:1 h2n:1 little:3 checked:1 glauber:2 eqs:3 prudnikov:1 relations:2 their:3 cooling:1 too:1 molecular:1 final:1 1n:1 trapped:1 centered:1 exactly:1 took:1 artifact:2 part:1 nieto:4 authors:3 x2:10 x0:31 than:1 oscillate:1 peaked:2 king:2 unfortunately:1 optimism:1 future:1 historical:1 were:5 sophie:1 p20:1 san:1 ann:1 modern:5 locations:1 manner:1 any:1 relatively:1 magnus:1 studying:1 ryzhik:1 able:1 note:1 oliveira:2 potential:1 singh:1 techniques:1 rediscovered:1 calculus:1 formulas:1 begin:1 normal:1 who:1 most:5 germany:1 significant:2 preliminary:1 phase:3 formalisms:2 especially:2 later:3 looked:1 bracket:1 principle:2 exp:55 velocity:2 maxima:4 physics:3 quantity:1 show:3 supported:1 discovered:1 feat:1 find:1 ground:4 based:1 state:18 elucidated:1 should:4 ψss:13 only:1 various:1 interested:1 hope:1 exchanged:1 do:2 his:1 legendre:1 dk:1 notation:3 dependent:3 displayed:1 de:3 broadest:3 expectation:1 da:2 nonequilibrium:1 dx:3 dy:2 parlance:2 klein:1 ds:1 alexander:1 evolution:4 spikes:4 densities:2 arxiv:5 yield:1 αl:1 bf1:1 4πc:1 activity:1 view:1 fair:1 national:1 packet:1 observed:1 edition:1 see:4 sec:1 result:5 captions:1 discussions:1 best:1 subject:1 closer:1 review:1 motional:1 αa:3 case:11 written:2 identification:1 closed:1 between:2 neither:1 caves:1 conditions:1 email:1 αn:1 available:4 notice:1 amplitude:1 nature:1 however:3 gratefully:1 comm:1 p2s:1 group:1 configuration:1 ix0:5 both:1 cos:19 last:1 2n:13 limits:1 many:1 taking:1 uncertainty:2 heating:1 marichev:1 forgotten:4 finds:4 x2s:1 mechanics:2 point:1 appeared:1 leipzig:1 narrower:1 harmonic:2 dimensional:5 cx:1 scully:1 table:1 schleich:2 math:2 ps:6 described:2 basis:3 three:7 been:4 workshop:1 change:1 prentice:1 itano:1 ph:6 pn:2 systems:1 generating:1 wheeler:1 essentially:1 coherent:7 bull:1 c3:1 those:1 applied:1 p0:24 laser:2 tanh:5 straight:1 starts:1 evaluated:1 will:1 near:2 involved:1 squeezed:28 aid:2 polon:1 identical:2 vogel:1 mexico:1 vol:1 von:1 vk:1 humps:2 vs:1 monroe:2 combination:1 perhaps:2 same:3 shorter:1 unity:1 complex:1 quant:6 wolfgang:1 start:2 higher:1 development:1 investigated:1 http:4 trivially:1 i2:4 sudarshan:3 flurry:1 uses:1 kim:2 infinite:2 changing:3 normalization:1 destruction:1 schr:4 acknowledge:1 person:1 greatest:1 english:1 position:5 consisted:1 cosh2:1 being:4 obtain:2 dowling:1 shape:1 distant:1 klauder:3 campbell:1 paul:1 eigenstates:1 previous:1 tables:1 gmn:2 integer:1 density:7 had:1 hall:1 setting:1 lett:4 easy:1 iπ:2 eigenstate:1 iφ:5 real:2 iκ:1 format:4 sums:2 early:1 know:1 background:2 press:1 using:11 emergence:1 mod:2 displaced:12 englewood:1 necessary:1 follows:1 reduces:1 shapes:1 yields:3 either:1 integrals:2 martin:1 translated:1 page:1 mathematical:1 parity:1 because:1 often:1 classical:5 people:1 library:1 born:1 acad:1 peter:1 separately:1 f3n:1 quantenphysik:1 prog:1 prof:1 demonstrated:2 bb:5 bc:1 equivalent:1 bu:1 abteilung:1 eiφ:9 plots:1 imaginary:1 bx:1 properties:3 science:1 central:1 theorems:1 o:2 2k:9 fertile:1 wineland:3 communication:1 into:2 gradshteyn:1 integral:3 functional:9 appropriate:2 right:1 references:1 operator:20 uncertainties:4 there:7 los:2 naturwiss:1 forward:1 ψn:3 was:12 combined:1 function:16 form:8 fundamentals:1 opt:2 but:5 displacement:8 properly:1 hn:13 hm:1 squeeze:5 true:2 he:2 applying:2 whether:1 smooth:2 maximum:2 ur:2 excitement:1 limit:1 problem:2 semiclass:1 vourdas:2 aa:6 ae:1 ad:2 defined:2 abstract:1 am:1 general:4 our:2 formalism:2 bishop:1 again:2 functions:7 no:4 when:6 ne:2 meekhof:2 ny:2 other:1 papers:2 department:1 conclusion:1 francisco:1 h2k:4 calculating:1 problems:2 polynomials:1 hausdorff:1 reiφ:1 recent:1 variable:1 birula:1 bch:3 pion:1 4v:3 baker:1 lanl:1 packets:8 together:1 having:3 equivalently:1 mimic:2 time:16 n1:1 n2:3 4c:2 basically:1
|
quant-ph9612051.txt |@word πk:2 creation:2 consider:2 moments:1 lewis:1 find:1 tcs:8 nφ:1 russian:2 paper:2 solutions:3 expressions:1 dt:1 caldirola:2 µm:1 revived:1 imb:12 number:2 thank:1 yu:2 solving:1 γt:15 jan:1 only:2 potential:1 systems:1 γm:1 mω02:7 trifonov:1 momentum:3 real:1 p2:4 rev:4 dependent:1 kanai:2 methods:1 prog:1 simmons:1 maslov:4 polytechnic:1 2γt:5 using:4 nieto:2 now:2 exact:3 condition:3 2t:14 eigenvalue:1 mir:1 necessary:2 dubey:1 hamiltonian:6 fields:1 university:1 arxiv:1 solution:3 damped:6 orthonormal:1 solved:2 investigate:1 differential:1 t02:1 t01:1 activity:1 analytical:1 2m:6 optics:1 by5:1 constructing:1 classical:4 problem:3 energy:1 successfully:1 some:2 cosh:4 approximation:1 operator:5 zero:2 complete:1 quantum:6 further:3 hartley:2 neighbourhood:1 um:2 shown:1 nonlinear:1 αw:1 nuovo:1 αz:1 lagrangian:1 expressed:1 eigenstates:1 particles:2 pˆ2:4 expressing:1 example:2 reb:1 formula:2 xˆ2:4 ref:2 method:4 math:1 shows:1 satisfy:3 sinh2:5 recently:1 theory:1 minimization:4 mω:1 instants:1 arbitrary:1 obtain:7 given:1 sinh:8 bose:2 equations:4 properties:1 obtained:1 operational:1 tomsk:2 instant:3 many:1 could:1 aˆ:3 equal:2 o:1 russia:1 preceding:1 hψ:1 ims:1 place:1 permutation:1 hence:1 expression:1 finds:1 first:1 eˆ:3 useful:1 besides:1 follows:1 moscow:3 harmonic:7 system:4 phase:1 xx:1 set:1 choose:1 been:1 cs:52 δn:1 should:2 illustrate:1 iω:1 pp:1 quasi:1 described:1 yeon:2 basis:2 introduction:1 trajectory:5 2ωt:10 initial:2 approximate:2 construct:2 glauber:2 cauchy:2 therefore:2 interest:1 bagrov:2 ph:1 type:1 theoretical:1 relations:8 define:2 function:8 nauka:2 wkb:4 corresponding:1 easy:2 ωt:19 sin2:5 operators:3 exactly:2 odinger:5 fortschr:1 coherent:14 construction:3 arctanh:1 t1k:1 becomes:1 x2:5 x0:3 denote:1 present:2 case:7 obeying:3 p0:2 valued:1 showed:1 tanh:1 prof:2 equation:10 work:1 oscillator:6 hxp:2 aim:1 belov:2 were:3 mechanical:5 averages:4 called:1 mechanics:1 references:1 unitary:1 choosing:1 defined:3 cimento:1 abstract:1 describe:1 thus:1 general:2 states:14 discussions:1 pˆ:8 tan:1 2cs:14 check:3 constructed:3 functions:1 hpx:2 uncertainty:8 variations:1 hpp:2 xˆ:11 detail:1 arctan:1 note:2 acknowledgments:1 complex:6 quant:1 special:1 widely:1 mx:1 so:1 hxx:2 parameter:3 sin:5 difficult:1 heisenberg:1 annihilation:2 used:2 ray:1 calculating:1 shall:2 any:2 symbol:1 who:1 ternov:1 t2k:1 potentials:1 linearization:1 ago:1 schr:5 coincides:1 theor:1 rule:1 solve:1 exp:23 time:6 coordinate:4 quadratic:1 physics:1 terms:1 usual:2
|
quant-ph9612052.txt |@word represent:4 concept:1 semantic:2 consider:4 springer:1 mnp:1 results:4 four:1 mild:1 subterms:1 computation:7 edu:1 follow:2 adhere:2 reasoning:2 whose:4 certainly:1 cardinality:6 depend:1 γq:1 γp:1 editors:2 languages:6 finally:5 program:1 those:1 under:3 analogous:1 presumed:1 p2:2 predicate:1 expressing:3 far:1 fas:1 account:1 electron:1 every:6 nesting:1 decide:1 rec:5 affect:1 difference:2 tran:1 obvious:1 unlike:1 presented:1 did:1 induction:21 solution:3 fewer:1 juxtaposition:1 solved:2 insights:1 section:1 possibilities:1 enforce:1 work:2 deutsch:4 consistent:1 barendregt:1 sign:20 second:4 evaluated:1 dynamics:1 mj:5 expressive:2 substitute:1 subscripts:1 employ:1 what:6 appear:2 specification:3 selected:1 expressed:6 find:1 henceforth:1 waiting:1 transformed:1 above:3 lond:2 new:8 increasing:1 method:2 seeks:1 mp:1 body:2 ensure:1 error:2 modify:2 preserves:1 here:5 understanding:2 asymmetry:1 objects:1 focused:1 possibility:1 address:1 represented:3 consideration:2 november:1 fred:1 observing:13 implicit:1 change:1 intension:1 property:1 provably:1 mathematics:1 formalizing:1 recursive:3 allows:6 sx:3 prior:1 resulting:1 permutation:3 usually:1 suitable:1 inspires:1 followed:2 falsity:2 substitution:9 logical:2 boolean:1 inductive:1 apply:2 operational:1 denotes:1 alamitos:1 presents:1 use:7 expresses:1 superpositions:2 would:8 prove:2 distinct:2 positive:11 readable:1 negative:9 unsigned:2 axioms:1 call:10 therefore:15 m3:1 m2:22 taken:3 scope:1 jonathan:1 type:3 until:2 reorder:1 more:5 chapter:1 ambiguity:2 problem:2 refrain:1 concatenation:4 backwards:1 particular:8 foundations:1 cases:3 hold:2 must:2 worst:2 states:5 none:4 isomorphism:7 word:1 permits:1 mm:3 science:2 mn:9 mi:34 mk:9 axiom:5 mq:1 syntactically:3 following:15 erm:6 closing:1 example:9 reordering:4 proof:15 claim:4 computers:2 give:2 process:3 december:1 allowed:2 share:1 sample:4 effectively:1 assumptions:6 numbers:8 want:6 sense:2 david:4 distinguishable:1 unordered:4 string:1 ones:1 end:1 goal:1 syntactic:8 provide:6 s2:5 s1:5 holds:4 negation:2 write:14 how:5 fourth:1 significance:1 answer:1 instead:5 verlag:1 inputs:2 abstraction:17 binary:2 specifications:1 turing:10 after:2 mapping:3 collection:73 walk:2 applications:8 tries:1 abuse:1 parallel:1 efficiently:4 sy:2 transitive:1 natural:2 remember:1 third:2 sq:3 sp:6 explicit:3 element:4 greek:1 si:3 maintain:1 so:16 sn:3 allow:6 keeps:1 definitions:1 observability:1 operate:1 order:5 typical:1 innocuous:1 six:2 interpretation:1 words:2 pointed:1 summarized:1 equally:1 nii:4 produced:1 coll:2 paper:2 including:1 statistical:4 signs:13 differs:2 satisfies:1 still:4 ieee:1 its:15 before:4 observational:6 machine:4 group:1 fit:1 chosen:1 highlights:1 actually:1 forms:3 holland:1 differently:1 hidden:1 alter:1 happened:1 them:3 good:1 return:3 than:8 reordered:3 rosser:3 regarding:1 introduce:4 bound:1 framework:1 subtraction:2 they:8 symposium:1 now:7 nor:3 successor:1 easily:4 term:103 finite:2 equality:1 name:2 always:4 university:1 level:5 identified:2 intermediary:2 oppositely:1 luca:1 truth:3 each:20 notated:5 found:1 soc:2 higher:1 associative:4 mean:2 schneider:1 preceded:1 another:4 arbitrariness:1 numerals:6 generation:1 hard:1 programmed:1 conventions:3 elementary:1 used:3 computable:7 remove:7 quantum:22 our:5 satisfied:1 special:1 out:1 ultimately:1 monographs:1 exponential:1 since:7 crucial:1 recalculate:1 research:2 may:19 daniel:1 denoted:3 formula:8 get:2 evaluation:17 philosophy:1 theory:3 barrier:1 pieter:1 contain:1 differ:2 free:4 standard:4 reason:1 base:1 advantages:1 york:3 imagine:1 philip:1 remainder:1 generate:3 rewritten:2 definition:16 pairs:4 qj:3 βp:1 βq:1 language:3 v1:4 recast:1 starts:1 could:4 omit:4 programming:8 v2:4 times:1 thing:1 american:1 produce:2 onto:1 first:11 rand:1 intuition:2 xn:2 reflexive:1 probability:4 encoding:2 chance:1 question:2 variables:12 confuse:1 number:8 explored:1 nested:2 randomized:13 xx:4 xy:1 done:4 relations:2 directly:2 specificity:1 impossible:1 clarity:1 extendible:1 size:2 given:11 discussed:1 workaround:1 become:1 introduction:1 top:1 system:4 least:1 returns:5 assumption:7 too:1 passed:1 convention:2 scheme:2 luck:1 final:1 discussion:1 relationship:5 recursively:1 proving:1 took:1 tokens:1 arity:1 part:3 simulate:7 haven:1 semantics:22 unfortunately:1 gotten:1 see:1 limiting:1 matter:1 contrary:1 negatively:2 providing:2 solely:1 minus:2 occurences:1 exhibit:2 lowest:1 motivation:1 generality:2 rewrite:4 ran:1 pϕ:2 argument:12 spelled:2 randomly:2 say:2 rees:1 manner:1 need:4 seen:4 any:11 viewed:1 mii:28 traditionally:2 angle:1 unsatisfiable:3 expressibility:1 harper:1 latter:1 aside:1 note:12 instance:4 concerns:1 machines:4 finding:1 algorithms:15 heisenberg:4 even:4 disambiguate:1 multiple:3 sm:2 axiomatic:1 opposite:5 compress:1 most:6 importantly:1 plus:2 letter:1 pair:2 formalisms:1 probabilistic:2 why:1 observation:18 clear:1 adopt:4 stronger:1 proceedings:1 bracket:1 principle:1 parenthesis:1 man:1 superscript:3 typically:1 notion:4 interchangeably:1 prim:5 subtly:1 show:11 reductions:2 random:10 syntax:12 unsolvable:1 relation:22 solutions:1 byproduct:1 analogue:1 nϕ:2 help:1 q1:2 ni:12 trying:1 based:1 just:5 proportion:2 state:1 should:10 jan:1 lemma:1 only:10 generators:2 positively:2 matters:1 invocation:1 over:2 nj:4 predecessor:2 do:11 his:1 notation:10 means:3 william:1 express:2 ϕq:5 ϕp:4 bear:1 truly:1 cannot:7 preparing:1 occurrences:1 numeral:3 report:1 during:1 disadvantage:1 contextual:1 closure:3 processes:1 fields:1 arxiv:1 yield:5 checks:1 bad:1 contrast:1 though:1 mapped:1 qi:1 comma:3 qk:1 fixed:2 knowing:1 set:14 metalanguage:3 reference:5 parenthesized:3 imposing:1 generally:1 testing:1 observed:6 slowdown:1 computes:1 computer:6 w3:1 result:8 best:2 clarifies:1 phases:4 said:1 exponent:2 ways:2 subsequent:1 review:1 underline:1 symmetric:2 tantamount:1 written:17 identification:4 correctly:3 between:11 exploration:1 neither:6 bunch:1 approach:1 email:1 choose:3 terms:116 statistically:7 extend:5 nature:1 confusion:1 however:13 harvard:2 hypothesis:16 answers:1 key:2 distinguish:2 picking:1 come:1 relying:1 suggested:1 both:5 parentheses:1 last:1 many:3 annual:1 according:1 against:1 distinguished:2 context:1 interesting:1 distinction:1 expression:6 finds:1 comes:1 arbitrarily:3 point:4 had:1 ca:1 sampling:1 ab:1 simply:2 church:15 associated:2 writing:1 better:2 pp:5 pq:1 occured:1 basis:2 addition:3 a400:1 three:3 been:6 alters:1 mart:1 careful:1 calculi:10 much:2 stripped:1 expected:1 extends:1 ph:1 pi:6 pn:8 universal:1 empty:2 define:14 surjective:2 cardelli:1 direction:1 rather:1 versa:1 observable:1 sufficient:3 formed:12 uncommon:1 moment:1 ordering:5 observe:3 understand:1 opposites:2 c2:9 c1:9 resultant:1 irrelevant:1 former:1 present:2 case:5 p3:2 p1:4 conception:1 formalization:1 contexts:1 wff:1 value:14 will:29 while:1 replaced:1 applies:2 cancelled:1 properly:1 renaming:1 35th:1 procedure:1 real:1 seven:1 eral:1 thus:5 non:3 equal:2 hardware:2 grammars:1 itself:3 refl:3 claimed:2 affected:2 mod:6 capture:1 different:5 author:1 journal:1 arguments:1 make:3 isomorphisms:1 indistinguishable:4 same:14 orders:1 shorter:1 read:5 discourse:1 drawback:1 quant:1 emphasize:2 modification:1 several:1 events:2 difficult:3 evolve:1 extended:3 temporary:1 trivially:1 assignment:1 sequel:1 effect:1 hand:2 grammar:14 running:2 uses:1 composition:1 invariance:6 justifiable:1 identity:4 possibly:2 los:1 whole:1 variety:1 well:18 thought:2 without:2 sets:3 position:1 model:2 left:2 things:1 λq:53 λp:107 precedence:3 being:1 λz:1 λy:11 λx:52 networks:2 underlying:2 identify:11 integer:1 λk:2 useful:2 alternative:4 yet:1 captured:1 previous:1 unique:4 generator:2 conclude:1 seems:1 except:3 sometimes:2 add:1 setting:1 collections:25 easy:3 theorem:14 input:7 structural:4 solvable:1 remaining:1 ought:2 take:2 identical:16 satisfiability:3 represents:5 rules:16 big:1 possible:5 judgement:1 formalize:2 denotation:2 press:1 world:11 execution:2 formal:4 loss:1 modifications:1 necessary:1 like:5 identifying:5 follows:9 reduces:1 indisputable:1 continue:1 steps:1 either:11 arbitrary:12 translated:1 output:4 works:1 essential:1 specifies:1 calculus:126 because:23 old:1 classical:2 formulas:6 njj:7 conditional:1 some:14 somehow:1 fifty:2 examples:3 choosing:1 redexes:12 indistinguishability:2 exists:5 brothers:1 happens:1 provided:1 total:4 exhausts:2 avoid:1 normal:10 does:13 provides:1 pattern:1 semantically:1 proc:2 subexpressions:1 refer:1 algorithmic:1 power:2 equivalent:2 communicate:2 sequentiality:1 step:12 substituted:1 although:5 served:1 described:1 major:2 periodically:1 takes:2 gained:1 integers:2 about:2 actual:1 extension:7 extending:1 abadi:1 theorems:1 introduces:1 generated:1 recognized:1 reduced:2 probabilities:1 nothing:1 pran:2 introduced:4 software:1 primitive:3 computational:2 into:6 functional:1 phase:7 appropriate:3 right:4 references:1 restatement:1 determine:2 strip:1 operator:3 additions:1 risk:2 deal:1 prepare:1 abstractions:12 strictly:1 there:23 combinator:1 reduction:25 specifically:1 fully:1 strict:1 describes:3 way:3 forward:1 m1:32 was:5 lambda:9 function:21 considerably:1 revised:1 north:1 totality:1 form:11 identities:2 differences:1 removes:2 but:15 notate:1 pj:1 construction:7 goals:1 encoded:1 removed:5 true:1 he:1 made:1 applying:3 intuitive:2 society:1 whether:2 up:2 signed:8 insert:3 below:2 samples:1 limit:1 demonstrate:2 distribution:11 similar:1 called:8 pii:1 later:2 ordered:6 computing:1 defined:6 certain:3 abstract:1 specified:1 general:4 operand:1 single:5 exist:6 together:1 formulation:1 formalism:2 distributions:2 physical:1 incorrect:1 again:3 functions:8 compared:1 us:3 nn:3 no:13 werner:1 whereas:2 when:11 reality:2 rewriting:3 application:26 other:15 tii:1 np:2 nq:1 you:1 satisfiable:3 shrink:1 unobservable:2 conclusion:2 draw:1 elements:1 kinds:1 superposition:8 completes:5 separate:1 preceding:1 june:1 shown:1 helpful:1 iterators:1 meaning:1 important:1 allowing:1 eval:3 variable:16 singleton:1 yields:2 structure:3 hendrik:1 simon:1 longer:1 algorithm:9 vice:1 assume:3 physics:3 proposed:1 required:1 pseudo:1 rule:7 time:2 n1:5 n2:3 having:1 once:2
|
quant-ph9701001.txt |@word logarithms:2 surrounded:1 transitions:1 consider:5 remarkable:1 similarity:1 pairing:1 keep:1 particular:2 unique:1 results:8 four:2 rapid:1 montr:3 computation:22 edu:1 consists:1 query:35 denotes:4 whose:12 preserves:1 simon:3 depend:3 magnitudes:4 producing:2 technique:2 factoring:3 spirit:1 languages:9 finally:5 asking:1 restriction:3 those:1 bqp:26 under:2 must:13 norm:1 alternating:1 division:1 conjecture:1 random:29 string:16 straightforward:1 returning:1 reversibility:1 rise:1 ψk:3 choice:3 corollary:5 fragmenting:1 worst:1 interpreting:1 decide:3 difference:6 høyer:1 ai:11 entire:3 randomness:1 specify:1 evaluation:1 solution:1 occurs:1 leave:2 solved:11 undone:1 pspace:2 recall:3 small:5 markov:1 optics:1 boyer:1 configurations:5 ville:1 squared:6 broader:1 deutsch:6 consistent:2 direct:1 sign:1 zero:1 cost:1 design:2 follow:1 7th:1 further:1 permutations:2 machines:25 even:8 established:1 what:4 appear:2 iterating:1 giving:2 section:8 supplied:1 uniform:3 henceforth:1 version:1 above:10 new:5 boost:1 equivalent:2 halts:7 evolving:1 construct:5 reverses:3 q0:4 a400:1 applies:2 modify:1 residual:1 gilles:1 desired:5 explore:1 inverse:3 focused:1 separation:4 berkeley:3 path:2 method:1 observing:1 change:3 calculate:1 box:2 tapp:1 great:2 property:1 tapes:1 transition:1 institute:1 leaves:4 studied:1 allows:3 step:9 leaving:2 membership:2 suggests:1 accomplished:2 calculations:1 loop:1 permutation:18 domains:1 complicated:1 bob:1 fourier:2 changes:2 uniquely:1 appropriately:1 deterministic:5 useful:4 triplet:1 bounds:2 applying:2 logical:1 put:1 boolean:6 amherst:1 moran:1 org:1 apply:2 total:3 establish:1 imaginary:1 unit:4 readily:1 solovay:1 use:6 dnf:1 superpositions:6 usa:3 prove:5 distinct:1 stated:2 ψt:1 next:2 classically:1 ψi:1 overhead:1 therefore:19 m2:7 taken:5 tape:18 associated:1 25th:1 type:1 theoretical:2 more:12 separated:1 introducing:1 bennett:3 formally:1 relevant:1 outputs:1 ti:1 constructs:1 reversibly:2 informally:1 known:1 foundations:4 cardinality:1 preserving:6 presumed:1 logarithm:1 lengths:1 ma:1 ibm:4 science:5 challenge:1 work:8 modified:3 london:3 remain:1 grover:9 values:2 syntactically:1 following:7 making:2 root:1 example:6 proof:15 control:2 claim:1 impose:1 give:2 december:2 sense:1 purposes:1 accept:9 states:2 caused:1 performed:1 allowed:2 times:10 conversely:1 worse:1 information:4 available:1 φx:2 end:1 recursive:2 rather:1 drags:1 acts:1 machine:39 how:6 subroutines:3 pair:3 fourth:1 reject:3 answer:24 optimal:1 explains:1 brassard:6 belongs:1 inputs:9 product:2 blanks:1 blocks:1 circuit:1 our:3 turing:27 laf:1 weaknesses:1 space:1 containing:2 spot:1 storage:3 modest:1 produce:2 scratch:4 lay:2 structure:1 lat:4 φt:24 grow:2 consisting:2 efficiently:7 natural:3 outline:1 effective:1 whenever:1 lemmas:3 goal:1 like:3 perform:4 complexity:6 maintain:1 so:12 specifying:2 allow:3 enter:1 every:8 subsequently:1 m1:8 order:1 terms:1 operations:1 exclusive:1 executed:1 help:1 ith:3 produces:3 hierarchy:2 developed:1 pointed:1 find:1 flips:1 interpreted:1 looping:1 umesh:1 including:1 berthiaume:3 differs:1 existence:3 still:5 ieee:4 its:13 before:4 destructively:1 member:1 derive:1 thank:1 la:15 chosen:11 fix:1 solving:2 xik:2 actually:3 forms:1 complex:3 systems:1 main:1 might:5 into:7 arguments:1 non:4 crucial:1 return:1 similar:1 safe:3 runs:5 massachusetts:1 break:1 try:1 they:8 instead:1 querying:2 now:4 structural:1 2t:10 ebec:2 inversion:3 finite:2 lies:1 always:1 university:2 cell:8 identified:2 establishing:1 sufficiently:1 magnitude:7 behaves:2 each:21 inherent:2 2n:35 polynomially:1 traces:1 constraints:3 constructing:1 square:2 ei:7 another:3 formulate:1 map:1 contiguous:1 slowdown:2 deterministically:1 reader:1 used:6 computable:3 measure:1 quantum:74 laboratory:1 mapping:2 beyond:1 special:7 out:8 canada:2 respects:1 them:2 jackson:1 discrete:3 restricted:1 since:20 interference:3 research:3 may:11 contained:3 vector:3 maximized:1 suggesting:1 squares:1 issue:1 correct:5 shows:4 after:14 theory:8 interactions:3 npa:3 contain:2 differ:2 possibility:2 standard:4 vazirani:6 difficulty:1 california:1 york:1 boosting:3 ask:2 heads:1 jozsa:2 card:4 definition:14 pairs:3 interaction:2 language:10 best:2 could:3 computers:8 βx:1 wrong:4 quantummechanical:1 counterpart:1 unitarity:1 length:28 explored:1 place:3 exponentially:5 tempting:1 hence:2 quadratically:2 discussions:1 onto:1 think:4 first:10 xj:2 major:1 initial:5 saving:1 features:2 probability:67 prevent:3 u1:1 pa:1 powerful:3 number:7 oracles:15 restrict:1 randomized:1 done:1 approximately:4 directly:2 blank:8 vote:1 decides:3 precisely:1 open:2 between:9 xt:3 size:1 passes:2 given:9 checked:1 similarly:1 introduction:1 unknown:3 top:1 πi:8 system:4 least:24 heights:1 their:6 intermediate:1 statement:2 siam:2 cycle:1 bits:1 final:23 recovered:1 gives:9 collapse:1 reversed:1 exactly:7 proving:5 accurately:1 larger:1 part:2 simulate:3 correctness:1 x0:2 x1:1 than:11 coefficients:1 xi1:2 finitely:1 distance:7 subroutine:12 target:6 showed:2 holds:1 behaved:5 require:5 database:1 likely:1 strategies:1 computations:1 individual:1 amplitude:3 were:2 1n:34 distinguished:3 threefold:1 fcar:1 generality:2 involution:2 respecting:1 boston:1 unchanged:4 modern:2 tidy:3 locations:1 randomly:2 already:2 say:6 substantial:1 constructible:2 close:2 need:2 seen:1 recover:1 seek:1 any:25 contents:3 complete:4 paths:9 permuted:1 efficient:1 convenient:2 answering:1 able:1 maximum:1 note:5 majority:6 costs:1 take:3 online:1 xi:8 algorithms:4 strengths:1 qtms:14 gill:1 sure:1 fundamental:1 centre:1 track:15 ideally:1 sets:1 fails:6 most:17 definitions:1 device:2 coin:1 probabilistic:9 class:15 spaced:1 workshop:1 cause:1 takes:1 considered:2 σi:1 clear:2 sometimes:1 stronger:1 countable:4 feynman:2 proceedings:11 principle:1 clean:2 mechanical:3 physics:5 microsoft:3 fact:3 erasing:1 shor:4 copy:3 programming:2 show:17 november:1 charles:1 large:6 carry:2 term:3 carefully:1 subtle:2 analogue:1 longer:1 imagined:1 agrees:1 current:2 touches:1 merlin:2 simulating:2 less:1 written:2 should:4 jan:1 lemma:9 only:16 black:2 ethan:1 factor:4 invocation:3 iterations:1 bernstein:5 over:9 do:8 cryptography:1 get:2 de:2 overall:1 expectation:1 watson:2 cannot:12 reversal:2 international:1 during:2 conjunction:1 unfortunately:1 qq:1 acm:3 evolution:7 qu:2 qy:7 transposition:1 arxiv:1 borrow:1 yield:1 calling:2 qa:1 whether:13 paper:8 34th:1 queries:9 albeit:1 through:2 fixed:2 valid:1 view:2 conversions:1 strengthened:1 set:16 modulo:1 computed:8 exists:1 achieved:3 generally:1 testing:1 up:2 relative:18 arise:1 see:5 computer:15 result:10 fail:2 contains:3 qtm:50 analog:1 techniques:3 babai:1 hilbert:1 invoked:1 αik:2 attempting:1 αy:3 subsequent:3 justifies:2 state:26 classes:1 various:1 subsection:1 correctly:3 iro:2 αi:2 according:2 hold:1 approach:3 email:4 sciences:1 notice:1 never:1 recently:1 ability:5 wa:1 initially:1 confusion:1 attention:1 however:8 interfere:4 concentrate:1 would:9 configuration:11 distribution:2 σk:2 both:6 essentially:1 improved:1 σn:1 many:1 region:1 annual:6 3j7:1 nserc:1 etc:1 games:2 context:4 contribution:1 mean:1 com:2 asked:2 comes:1 otherwise:3 unitarily:1 mechanics:2 unclear:1 co:6 necessary:1 conclude:9 simple:3 royal:3 ca:2 address:2 corresponds:1 insist:1 sampling:2 dimensional:1 exploit:2 cx:2 simply:1 learning:3 church:1 cs:1 constant:4 writing:3 along:1 succeeds:1 erased:2 better:3 pp:16 described:2 transformations:1 second:1 basis:3 addition:2 invert:1 acceptance:4 copies:4 been:5 extraction:1 yao:2 much:4 recognize:2 expected:1 αx:5 ph:1 abstract:1 empty:8 define:6 optionally:1 corresponding:2 versa:2 sufficient:1 formed:4 overwhelmingly:1 search:2 argument:1 coherent:1 epartement:1 last:2 general:6 former:2 present:3 reverse:4 case:10 multi:2 ahead:1 exponential:5 contexts:1 defining:2 value:2 choices:4 will:24 euclidean:4 while:6 suppose:2 evaluating:2 error:13 determinism:1 situation:1 2k:1 35th:2 taking:1 procedure:1 h3c:1 unitary:16 dictum:1 almost:3 thus:4 concatenation:1 equal:6 ik:2 good:1 properties:1 against:1 primitives:1 rid:1 increased:1 binary:2 different:9 moves:2 verified:2 eighties:1 grant:1 supported:2 alphabet:8 make:2 belong:1 same:13 clearly:6 answers:9 parts:2 quant:1 emphasize:1 copying:4 modification:1 φi:20 several:4 events:2 development:1 independent:7 extended:1 http:1 lie:1 i1:2 pick:3 upon:3 effect:1 hand:3 average:2 running:15 purpose:1 infinite:2 changing:1 qf:4 recent:2 lower:1 expense:1 acknowledgement:1 safely:2 ingredients:1 well:11 analysis:1 ccr:1 thought:2 without:3 solve:2 machinery:1 simulated:2 model:2 researchers:1 left:4 composed:1 mapped:1 facto:1 just:6 among:2 isolate:1 αi1:2 networks:1 obtain:1 rest:1 distinguishing:1 formulated:1 questions:2 followed:1 yes:2 speed:1 yet:1 alignment:1 manuscript:1 superficial:1 enters:1 tight:3 regarded:1 extra:2 had:1 except:5 improvement:1 add:1 setting:2 location:4 easy:6 theorem:24 relevance:1 input:54 intersection:2 nos:1 solvable:2 transformation:3 ought:1 gave:2 real:4 εt:1 around:3 depends:4 easily:6 rules:1 possible:4 spanned:1 early:2 department:1 working:1 af:2 entangled:1 using:13 bit:11 accepted:3 nondeterminism:3 formal:1 loss:2 imposed:2 replacing:2 success:8 abstraction:3 follows:3 performing:1 bpp:9 arthur:2 steps:8 either:3 arbitrary:8 evolutions:1 output:10 accuracy:2 stationary:8 essential:1 maximize:2 because:6 often:2 deal:1 sequence:4 conditional:1 some:16 back:2 certain:1 polynomial:22 dragging:1 growth:1 nonetheless:1 28th:1 moreover:1 proper:2 proofs:2 ourselves:1 intractability:1 happens:1 provided:3 vol:8 operation:1 nonempty:7 decision:2 shall:3 nonclassical:1 classical:20 probed:1 does:6 linearly:1 provides:1 yields:3 ct:2 numbers:1 refer:1 constructively:1 conference:2 run:9 obey:1 power:5 uniformly:11 journal:6 pose:1 evolve:1 substituted:1 machta:1 variation:2 found:1 post:5 exciting:1 universit:2 hiding:1 integers:1 about:2 asserting:1 actual:1 carried:1 pre:3 interfering:2 certainty:2 theorems:4 accepts:11 o:15 simulation:4 probabilities:1 carries:2 ensure:1 introduced:2 block:1 op:1 considerations:1 equally:1 computational:15 statements:1 computes:1 umontreal:1 within:3 bound:6 nsf:1 ut:5 down:1 phase:8 appropriate:1 weighted:1 references:1 inverting:1 operator:2 england:1 fixing:2 per:1 notion:1 weight:1 log:6 area:1 suffice:1 there:23 question:4 fast:1 why:2 start:6 quadratic:2 inner:2 way:8 call:8 was:3 naturally:1 function:19 head:2 redmond:1 eal:3 form:19 enough:2 erases:1 conclusively:1 but:13 searching:1 designated:1 here:1 construction:2 skip:1 gain:1 scope:1 encoded:1 trying:1 he:1 reset:1 made:3 compute:3 algorithm:8 society:3 circuits:1 wish:3 cells:3 yorktown:1 us:5 lead:3 below:1 samples:1 ui:6 sum:6 problem:5 broadly:1 called:5 uc:1 detailed:1 tε:1 proved:5 computing:8 defined:6 countably:1 universal:3 aj:1 evidence:5 single:7 scanned:1 right:6 together:2 simulations:1 ay:12 formalism:1 distributions:3 internal:3 constructed:1 again:1 functions:2 compared:1 entirely:3 know:1 no:19 corporation:1 whereas:1 when:12 ny:1 build:3 other:13 details:1 normal:17 np:24 approximated:1 shrink:1 4k:1 symposium:5 denote:7 superposition:43 calculating:1 separate:2 symbol:4 problems:13 inherently:2 important:1 bounded:15 allowing:1 vectors:2 variable:1 seeing:2 careful:1 tracks:4 building:1 rejects:2 faster:1 calls:2 vice:2 assume:2 requires:2 required:2 resolving:1 δx:1 rule:3 having:2 write:4 parallelism:6 image:1 time:69 oracle:103 starting:1 strings:15 8th:1
|
quant-ph9701002.txt |@word sci:1 consider:3 similarity:1 rev:4 results:1 calculate:1 θv:2 young:1 γt:2 program:1 squeezing:8 th:2 pilot:1 applied:3 straightforward:1 g0:8 far:1 wave:9 2γt:3 exact:2 condition:1 solution:12 t0:23 damped:6 solved:1 pˆ2:1 guiding:1 dealt:1 zn:1 wronskian:1 sin2:6 cosh:3 chem:1 linear:2 expressed:2 ˆb:9 above:1 sup:1 new:1 respectively:1 bsri:1 here:3 cos2:6 sinh:2 kwang:1 obtained:8 institute:1 study:1 published:1 uniquely:2 qˆ:2 rπ:3 univ:1 causal:1 linearly:1 stated:1 noting:1 ψn:2 therefore:2 m2:1 type:1 theoretical:1 introducing:1 operators:7 odinger:1 riesenfeld:2 known:2 cases:1 rα:2 science:1 equation:8 work:1 oscillator:17 modified:1 following:3 example:3 f1:1 f2:1 give:1 states:7 tan:2 normalize:1 instead:1 sin:4 oscillatory:1 description:4 may:2 oscillators:1 snu:2 explicit:1 so:1 sn:1 interpretation:1 interpreted:2 motions:1 e2σ:4 argued:1 satisfies:1 before:1 fix:1 solving:2 forms:1 lr:6 systems:1 jacobi:1 them:1 good:1 combination:2 hamilton:1 they:1 bogoliubov:2 now:1 easily:3 hereafter:2 invariants:6 university:1 2g:7 trap:2 each:1 found:9 2n:1 2i:1 square:2 related:2 expect:2 quantum:37 our:1 eq:1 seoul:2 shown:2 since:4 interference:1 research:1 fellowship:1 rn:2 ref:6 integrated:1 math:1 theory:7 mω:1 given:4 free:1 πg:3 ministry:2 motion:13 barriers:1 christoph:1 number:2 another:7 electronic:2 differ:1 iω0:1 system:2 construct:2 2ωi:7 scheme:1 gives:1 park:1 sˆ:6 iωt:1 holland:1 annihilation:7 were:1 rewrite:1 qˆ2:1 any:2 note:1 potential:3 take:2 korean:1 heisenberg:1 broglie:7 wells:1 letter:1 remarks:1 analytically:1 adopt:1 kr:2 exp:1 mechanical:1 physics:2 lewis:2 supported:2 relation:1 solutions:8 find:5 ground:1 q2:2 parameters:1 explain:1 state:18 should:2 jan:1 only:2 explicitly:3 factor:2 dependent:10 uncountable:1 de:7 dt:7 evolution:1 reis:1 arxiv:1 summary:1 snutp:1 fixed:2 national:1 see:1 result:3 recently:3 jeong:1 αq:2 project:1 ways:1 motional:1 yet:1 written:2 αe:1 closed:1 between:2 invariant:17 αn:2 korea:1 terms:2 however:2 jr:1 ji:4 analyzed:1 cos:7 many:2 according:1 whole:3 sα:1 simple:1 address:2 harmonic:7 constant:2 described:2 aˆ:1 trajectory:10 been:3 describes:1 damping:2 basic:1 expected:1 ph:1 choose:6 corresponding:1 mω02:1 coherent:12 c3:1 c2:1 c1:2 denote:1 irrelevant:1 θu:2 case:1 transformation:3 while:3 squeezed:9 tunneling:1 unitary:1 vf:1 thus:4 im:1 vanish:1 2g0:1 different:1 education:3 verified:2 same:1 clearly:1 quant:1 units:1 independent:9 used:1 trajectories:9 moving:1 kim:4 2mω0:1 schr:1 center:1 well:1 bohm:7 displacing:3 sets:2 position:1 world:1 paul:3 scattering:1 eigenstates:4 except:1 mathematically:1 setting:1 hirschfelder:1 eigenstate:9 real:1 iθ:5 dewdney:1 hiley:1 press:1 using:5 mod:1 displaced:3 particle:4 follows:1 because:1 classical:13 creation:6 examples:1 choosing:2 specified:3 eiθ:1 2xz:2 provides:2 bf:5 oscillating:1 viewpoints:1 2m:6 post:1 comparison:1 freedom:1 introduced:2 soc:1 cambridge:2 soh:3 numerically:1 acad:1 references:1 operator:5 there:3 was:1 function:7 form:2 construction:1 hn:2 atom:1 ωt:4 us:2 ωi:15 uf:1 mechanics:2 ac:2 associated:1 abstract:1 general:2 pˆ:3 formalism:1 constructed:2 functions:1 no:1 when:2 other:2 department:1 picture:1 generated:1 mω0:2 structure:1 auxiliary:1 equivalently:2 mass:1 time:16 2mω:1
|
quant-ph9701003.txt |@word represent:1 concept:4 grobe:2 consider:8 remarkable:1 forbidden:3 theoretical:2 results:17 leads:3 eds:2 scalar:1 higher:1 consists:5 follow:1 expressions:17 disk:6 compact:1 whose:4 depend:2 calculate:1 re:3 orthonormalized:2 noncompact:1 tn:4 investigation:1 squeezing:4 those:1 include:1 norm:2 case:53 abelian:2 zhang:4 very:1 choice:5 every:1 nieto:3 exact:6 condition:27 treating:1 tani:1 immediately:1 presented:1 irreducible:5 tanh:3 t2:5 solution:19 deals:1 admissible:4 differential:11 optics:8 upper:2 zn:2 2k3:1 hillery:10 cosh:4 hyperboloid:1 second:6 bg:12 j22:1 gn:3 linear:8 reviews:1 what:2 moments:6 lublinsky:1 section:13 analogously:3 expressed:3 annals:3 above:3 overcomplete:1 new:2 consisting:1 satisfy:5 κn:1 full:2 κj:1 2ks:2 respectively:12 2ky:1 here:18 lαn:1 groups:12 address:1 represented:5 σab:2 quite:1 equations:3 z1:3 z2:3 extreme:1 obtained:14 great:2 institute:1 study:1 studied:4 through:2 eberly:6 nagel:8 action:1 ξk:2 quotient:9 examining:1 buˇzek:2 via:1 regardless:1 yuen:2 malkin:1 sgn:1 summation:3 apply:2 unit:10 derivatives:2 use:24 asymptotic:1 distinct:1 positive:2 contains:1 lagrange:2 hilbert:17 comparing:3 bases:1 call:1 therefore:12 taken:2 robertson:3 ψg:8 more:5 lowering:6 israel:2 formally:3 definition:3 zeitschrift:1 operators:17 odinger:6 berlin:1 normalized:4 particular:14 known:3 cases:11 verified:3 must:5 springer:1 quantized:2 henri:1 equation:99 work:5 oscillator:4 modified:2 erd:9 fock:2 values:11 kν:1 following:6 my:2 example:9 stimulating:1 compare:2 transition:1 degenerate:8 figure:1 give:1 calculation:4 expanding:5 allowed:3 states:50 sphere:1 minimum:1 performed:2 employs:1 sense:2 tan:3 nonnegative:2 occur:1 firmly:1 information:3 vanish:1 provide:4 bargmann:4 discussion:1 orthogonal:3 s4:2 write:2 how:2 nontrivial:2 pure:4 puri:7 intelligent:12 sin:13 product:2 express:1 description:1 algebra:44 easily:4 ζj:1 ζk:1 mapping:1 ζn:1 applications:7 produce:1 physik:1 improving:1 representations:18 ζz:1 types:6 man:2 dynamical:3 third:2 light:1 explicit:1 correspond:1 su:69 element:15 s3:2 secs:1 so:6 fundamental:1 s2:4 taking:1 representation:26 integrand:1 order:7 terms:1 transformation:2 reproduced:1 least:2 help:1 developed:1 over:11 satisfied:3 years:1 stability:1 paper:3 including:3 statistical:6 signs:1 mentioned:1 satisfies:1 y2:2 brif:25 depending:1 derive:4 group:36 2kβ:2 chosen:3 continued:1 solving:2 actually:2 forms:1 choose:5 jacobi:7 mail:1 decades:1 them:5 ya:1 integral:2 rasetti:2 fig:2 introduce:2 mention:1 equidistant:3 they:6 half:2 yp:2 now:3 yu:3 ordinary:8 possess:2 2t:6 eigenvalue:27 several:1 equality:1 parameter:13 hermitian:4 2z:2 orthonormal:15 mode:2 2b:2 each:6 colleagues:1 found:3 l149:1 2i:2 2j:25 referred:2 subset:8 domain:1 weyl:3 financial:1 significantly:2 generation:1 series:12 hypergeometric:6 reduce:2 1996a:6 related:7 applicable:1 elementary:3 ξj:2 investigated:1 obtains:2 measure:1 quantum:23 infinity:1 special:13 out:1 leave:1 shown:4 space:34 restricted:1 since:8 si:2 acting:4 vector:5 hill:1 formula:8 2k:47 integrated:1 bz:2 constantin:1 theory:6 clarifies:1 given:14 standard:61 approaches:3 complicated:2 york:2 j32:1 salamo:2 incorporates:1 skagerstam:2 βp:2 r2:1 similarly:1 m20:1 times:2 turn:1 american:1 plane:2 hence:3 first:12 symmetry:3 laguerre:1 powerful:2 number:14 done:1 construct:3 another:1 precisely:1 xt:3 interchange:1 differ:1 sheet:1 exists:1 their:5 introduction:1 eqs:2 system:6 relations:11 glauber:5 normalization:17 calculations:2 realization:2 gives:2 m0:53 acquire:3 part:1 too:3 j3:29 representing:2 coefficients:2 wide:2 kind:2 ben:11 effective:1 accordance:1 was:1 wodkiewicz:6 zero:1 project:1 k22:1 solomon:2 determined:14 amplitude:7 were:4 enables:4 integer:5 descriptions:1 function:68 cn:4 acknowledged:1 modern:4 spectrum:12 discussions:1 manuscript:1 4k2:1 vilenkin:2 recover:2 any:25 lie:24 min:1 studying:1 ideas:1 note:6 k2:19 k1:17 generalized:26 simplified:2 finding:2 coincide:6 canonical:1 accuracy:2 heisenberg:3 formulas:2 continuous:4 reach:1 systems:1 most:5 definitions:5 phase:3 acknowledgements:1 class:7 kb:2 technion:4 especially:2 considered:4 clear:2 ko:2 physica:1 optical:3 exp:20 ky:1 usual:1 physics:27 bateman:1 fact:1 dover:1 2m0:1 show:1 text:1 spaces:1 relation:10 solutions:3 1994b:2 d2:2 find:16 naturwissenschaften:1 feng:1 based:5 knowledge:1 parameters:3 situations:1 λt:1 written:8 should:3 jan:1 analytic:74 only:11 explicitly:1 generators:6 transcendental:1 factor:16 hamiltonians:1 do:4 his:1 notation:6 means:5 df:1 familiar:2 simplest:3 expectation:3 cannot:4 dz:6 dx:1 iγb:1 combinations:2 determines:4 horwood:1 ahlerian:2 treatise:1 normalizable:6 aes:61 die:1 conditions:1 arxiv:1 yield:1 method:6 common:1 dodonov:4 wish:1 dpn:1 fixed:1 valid:8 view:1 ik3:1 ik2:4 requirement:3 set:19 reference:11 frame:1 aragone:4 j1:14 j2:10 up:2 y1:2 see:11 sec:12 result:2 ηk1:2 iδj:1 dµ:17 theoretic:3 acquires:1 instance:1 commutation:2 ωh:1 review:17 uζ:2 its:2 symmetric:1 state:82 classes:2 various:4 closed:4 between:13 invariant:2 approach:4 recently:7 jy:1 extend:1 importance:1 however:1 gratefully:1 fluctuations:1 kummer:3 holds:1 jb:2 thank:1 concentrated:1 both:4 cos:10 last:2 kluwer:1 always:2 many:4 vanden:2 uncertainty:8 according:6 constructed:1 quantization:1 present:4 casimir:2 variance:1 vourdas:1 whole:2 mann:6 sinh:7 cm:2 point:2 simple:12 peˇrina:2 harmonic:3 america:2 dimensional:2 analyzed:1 luis:2 cs:48 respect:2 improvement:1 considering:2 pp:1 described:1 basis:26 bertrand:1 2kh:1 three:8 been:8 annales:1 rhode:1 reduction:1 treat:1 interest:2 pj:5 ph:3 pn:11 pl:4 define:3 gerry:2 generating:4 k3:30 corresponding:47 restrictions:3 photon:2 covariance:2 ik:2 coherent:58 berezin:2 convergent:1 spin:1 manifolds:1 applied:3 srivastava:6 subsets:3 developing:1 truax:3 expanded:2 value:7 choices:1 will:10 euclidean:3 while:2 optimization:1 bergou:2 compactness:1 squeezed:2 property:3 region:6 procedure:1 stoler:3 unitary:4 vol:8 thus:5 non:3 reads:4 examined:1 il:2 iν:1 ib:1 technology:1 agarwal:10 different:16 develop:1 journal:14 belong:4 same:2 poincar:1 k2k:1 complex:23 quant:3 finite:3 subalgebra:1 difficult:1 independent:2 used:8 http:1 closest:1 singapore:1 hand:3 parametrized:1 usually:1 iζ:1 identity:7 recent:1 lower:1 schr:6 ik1:1 minimize:1 expression:3 k32:1 well:2 barut:12 de:1 i2k:14 sets:10 position:1 model:1 jackiw:2 soviet:1 subgroup:3 unified:4 world:1 manifold:1 just:3 1994a:4 being:2 λz:2 obtain:21 2jy:1 detail:1 orthonormality:1 unifies:2 klauder:2 useful:2 alternative:2 eigenstates:34 z0:3 2jh:1 segal:2 intersection:6 preprint:2 generator:4 conclusions:1 z01:1 iϕ:8 except:2 discuss:4 belongs:2 transformed:1 versa:1 theorem:2 trifonov:14 eigenstate:13 momentum:1 take:5 real:15 2j3:1 represents:13 iγ:9 possible:2 spanned:4 corresponds:5 vζ:2 vacuum:1 using:14 unique:1 apart:1 semiclassical:2 excluding:3 follows:2 isotropy:4 specific:2 communications:4 continue:1 yields:1 arbitrary:12 mcgraw:1 works:1 reduced:4 replacement:1 mathematical:12 www:1 because:3 dordrecht:1 methods:2 classical:2 discrete:15 successfully:1 some:5 back:1 identified:2 supplementary:1 polynomial:1 gilmore:4 choosing:1 specified:2 describing:1 eiδ:1 lead:1 measurements:2 integration:1 subclass:2 providence:1 does:2 decomposition:7 provides:3 bessel:3 refer:1 ba:1 ij1:1 ij2:3 ij3:1 obey:1 power:6 equivalent:5 confluent:2 agreement:1 expansion:11 eiφ:2 imaginary:3 includes:3 properties:10 after:2 ηj1:1 integers:1 about:1 carried:1 extension:1 island:1 discussed:2 generated:1 o:1 practical:1 convenient:3 a2:1 act:4 introduced:1 consequently:1 elyi:9 perelomov:15 homogeneous:7 letters:4 ηa:1 h2:2 prakash:3 into:11 within:1 obtaining:2 due:1 lies:1 appropriate:1 references:1 operator:19 next:2 often:1 k12:1 statistics:2 institut:1 fields:1 iβ2:7 there:10 transform:2 specifically:1 start:1 way:5 scientific:1 sections:2 naturally:1 lowest:3 complete:2 form:18 analyse:2 but:11 idea:1 construction:1 1996b:2 delta:2 convergence:1 haifa:1 lindblad:4 j12:1 raising:3 absent:1 coset:1 society:3 laplace:2 girardello:12 maximum:1 us:9 ur:1 international:1 url:1 converted:3 limit:1 demonstrate:2 problem:3 similar:1 called:4 ex:1 mechanics:1 ac:2 ab:2 associated:4 uspekhi:1 introducing:3 defined:22 curve:1 abstract:1 general:27 single:5 exist:2 our:3 dζ:8 formalism:7 iδk:1 physical:20 again:2 functions:13 d2z:1 analyticity:18 no:5 when:10 vanishes:11 illinois:1 field:2 other:10 department:1 mathematics:3 briefly:2 elements:22 kinds:2 chichester:1 preceding:2 problems:1 polynomials:10 interferometric:2 meaning:1 important:6 ellis:1 sides:3 structure:5 correlated:1 factorized:1 vice:1 requires:12 pseudo:2 bergh:2 equivalently:1 time:1 observables:1 resolution:4 once:2
|
quant-ph9701004.txt |@word limited:1 managed:1 excellent:3 results:3 quadrature:9 consists:1 remarkably:1 contributions:1 certainly:1 deterministic:1 ıa:1 estructura:1 efficiencies:1 squeezing:27 spain:2 stable:4 stabilizing:1 γa:4 tb:3 applied:1 very:6 frequencies:1 2γa:1 2γb:1 wave:1 denoted:1 wishes:1 summarized:1 resonant:6 impressive:1 hamiltonian:1 transmission:1 cause:1 mild:1 cascading:1 large:3 vector:1 eigenvalues:1 optics:2 configurations:1 force:1 specially:1 direct:1 located:1 second:8 enhancement:3 estimated:1 expressions:1 even:4 nonlinear:2 advantageous:1 collet:3 bergman:2 expressed:1 experiment:3 above:7 3b:1 3a:1 increasing:1 pioneering:1 advantageously:1 chose:1 elect:2 respectively:3 equals:2 here:3 asymmetry:2 excess:3 ratio:2 quite:1 equations:4 appears:2 obtained:4 instituto:1 shift:2 study:1 studied:2 reason:1 resulting:1 fernandez:1 proportionality:1 weird:1 suitable:3 york:2 holmes:1 stabilization:1 namely:1 yuen:1 plenum:1 highly:1 scaled:2 glance:2 total:2 linearly:2 technologically:1 use:2 takes:1 would:3 remains:1 finally:2 intense:1 therefore:2 m2:2 taken:1 associated:1 resonator:1 theoretical:1 more:2 compensated:1 formally:1 guckenheimer:1 operators:1 under:1 mismatch:1 purposes:2 berlin:1 γb:5 cases:3 must:1 account:1 setup:1 work:4 iλα:1 values:2 following:1 example:4 proof:1 control:2 figure:6 near:1 implementations:1 high:1 minimum:1 numbers:2 degenerate:2 verlag:2 requirements:2 fortunately:1 feature:1 how:1 pure:5 instead:1 those:1 simplicity:1 product:1 s_:1 modulation:1 different:3 demanding:2 applications:1 plane:1 improving:1 data:1 natural:1 dynamical:2 effective:2 light:3 explicit:1 serrano:1 so:3 fundamental:8 representation:1 order:9 displays:1 sundar:1 pulsed:2 words:1 indeed:2 altogether:1 balanced:1 interpreted:1 stability:1 course:2 experiments:1 through:1 mentioned:3 ieee:2 its:2 sirtori:1 perfect:5 lc:1 la:1 energies:1 interesting:3 decreases:1 better:3 systems:6 reachable:1 defining:1 eventually:1 non:18 good:3 affected:1 fourth:1 conversations:1 material:1 band:1 walls:2 hamilton:1 they:3 symposium:1 now:3 easily:1 february:1 always:1 kerr:4 mw:3 grows:2 realistic:1 mode:11 2b:1 instabilities:1 found:1 difficult:1 characterized:1 differential:3 directly:1 generation:5 energy:1 related:1 applicable:1 inhomogeneous:1 frequency:7 combining:2 quantum:7 wavelength:1 tuned:1 nonlinearities:2 out:3 shown:6 tombesi:4 matrix:1 driving:1 since:3 rev:11 denotes:1 increase:1 re:2 investigation:1 suggesting:1 got:2 induced:1 ref:1 shows:1 turning:1 linear:5 interactions:1 gardiner:2 possibility:4 standard:3 cabrillo:3 completely:3 complicated:1 term:2 8r:2 generate:1 definition:1 interaction:2 benefits:1 could:4 bistability:1 diminished:1 used:2 feasible:1 turn:1 length:2 place:1 consequence:1 diminishes:1 eqs:1 first:6 fourthly:1 probability:1 opez:2 number:5 reaches:2 another:1 reached:2 ring:1 electronic:1 dispersive:1 given:3 necessarily:1 similarly:1 interact:1 moderately:1 system:12 reflectivity:1 needed:2 rates:1 linearities:8 white:1 gives:1 shifted:1 centered:1 part:3 squeezer:1 authors:1 than:2 specify:1 modes:4 relative:2 third:6 double:1 see:3 annihilation:2 future:1 intensities:2 amplitude:1 were:1 providing:1 powers:2 aout:4 perspective:1 san:1 spectrum:3 conjugate:6 controlled:1 take:1 st:1 demonstration:1 relatively:1 zero:3 convenient:1 self:2 mechanism:1 k3:1 k2:3 ideal:2 materials:3 build:1 k4:1 performance:1 heisenberg:1 added:1 multiple:1 normal:3 mlynek:1 object:1 reach:1 wells:1 asymmetric:1 most:2 optimized:2 poled:1 thank:1 definitions:1 phase:4 analytically:1 measured:1 why:1 zealand:1 nonlinearity:2 kurz:1 proceedings:1 properly:1 homodyne:1 principle:2 ky:1 intensity:2 detection:2 supported:1 rotating:1 bright:1 threshold:1 enjoyed:1 giant:1 based:1 parameters:1 implementation:2 edited:2 state:1 jan:1 only:6 going:1 candidates:1 coefficients:1 adequate:3 hopf:2 achieve:1 beat:1 beams:1 de:2 db:12 dc:1 cannot:1 instance:1 nearly:1 closely:1 competing:3 dv:1 unfortunately:1 regarding:1 fields:1 arxiv:1 summary:1 europhys:2 predicted:1 shg:13 doubler:1 pulses:1 fixed:2 enhances:1 set:1 reference:2 achieved:3 physically:1 frame:1 respect:2 maximum:8 observed:1 depends:1 result:1 enhanced:2 suited:1 preparation:1 exploited:1 interacting:1 harvey:1 currently:2 µm:1 favor:1 written:1 between:4 limit:2 approach:2 available:1 notice:1 recently:2 cabrera:1 nature:1 however:5 efficiency:7 csic:1 news:1 configuration:2 suppressed:1 improve:1 both:5 essentially:2 limits:1 theoreticians:1 equal:1 chosen:3 improves:1 figures:1 marte:2 experimental:5 arbitrarily:3 colons:1 point:10 simple:2 harmonic:5 normandin:1 twin:1 applicability:1 constant:4 quan:2 cw:2 schleich:1 tuning:1 serna:1 been:2 shortening:1 reduction:9 expected:1 ph:1 hardly:1 fig:3 bermejo:2 corresponding:4 am:2 wheeler:1 photon:9 new:3 coherent:1 external:1 maximally:1 obtainable:1 present:3 bifurcations:1 case:12 rueda:1 abandoned:1 stochastic:3 pacs:1 value:3 will:1 while:3 ain:2 behavior:4 squeezed:6 procedure:2 losses:3 almost:3 triply:1 thus:2 iv:1 disappointing:1 need:1 im:2 increased:1 confirmed:1 twofold:1 russell:1 fibers:1 lengths:1 make:1 lett:13 same:6 shorter:1 shifts:2 drawback:1 quant:1 coworkers:4 units:1 finite:1 showing:2 higher:2 extended:1 infinity:1 imply:1 schiller:4 diego:1 numerical:1 effect:4 hand:1 mandel:1 v2:2 levels:1 appreciable:1 resonance:3 normalization:2 task:2 center:1 well:3 analysis:2 thought:1 academic:1 bifurcation:2 does:1 studying:1 landmark:1 model:3 usual:1 proposed:1 being:4 obtain:1 valuable:1 λb:3 useful:1 λn:1 previous:2 bibliography:1 cm:1 candidate:1 density:1 absorption:3 conclude:1 seems:2 k1:3 evidences:1 source:4 interested:1 attractive:1 input:4 5a:1 5b:1 opt:7 around:3 couple:1 possible:3 corresponds:3 early:1 possibly:1 increases:2 vacuum:4 press:1 using:2 opo:1 αf:5 loss:1 maybe:1 imposed:1 like:2 obvious:1 interestingly:1 susceptibilities:2 benefit:1 yields:1 experimentalists:1 signal:1 classical:1 madrid:1 some:3 springer:2 competition:2 towards:1 mirror:3 oscillations:3 γa2:1 kdp:2 sufficiently:1 cavity:9 broad:1 shall:1 intracavity:1 critical:9 assuming:1 demonstrated:2 2a:2 measuring:1 noise:23 reasonable:1 power:2 slight:1 each:1 although:3 output:5 properties:2 proceed:1 comparison:1 working:1 discussed:1 o:3 practical:1 range:3 wolf:1 steadily:1 s66:1 introduced:1 slightly:2 soc:2 ηb:2 ηa:5 into:1 garc:1 cascaded:1 schemes:1 determine:1 operator:1 proportional:2 janz:1 there:1 detuning:1 dong:1 appl:1 low:2 way:1 was:2 naturally:1 function:3 project:1 medium:1 complete:1 form:2 enough:1 phenomena:1 but:5 hi:1 larger:2 sustained:1 embedded:1 eiωτ:1 up:4 devices:1 crystal:3 below:1 ωm:2 distribution:1 similar:1 strongly:2 ordered:1 defined:1 certain:1 linearity:3 surpassing:1 tric:1 denote:1 our:3 accounting:1 dβ:1 intra:5 dα:1 again:1 materia:1 compared:1 no:3 eq:1 nc:7 when:4 slusher:2 field:3 other:3 rold:1 optimization:2 revision:1 coherence:1 kinds:2 fabre:2 a2:2 bounded:1 suppression:5 linearization:1 ago:1 implies:1 coupling:2 assume:1 dτ:3 changed:1 4n:1 time:6 international:1 n2:3 augmented:1 tsuchida:2
|
quant-ph9701005.txt |@word ideality:1 bypassed:1 consider:1 switched:1 dynamic:2 results:7 leads:1 scalar:1 contains:1 reynaud:3 whose:1 depend:1 calculate:3 shall:2 hca:2 present:3 analogous:1 c0s:2 amplitudes:1 advantage:2 orthogonal:1 very:5 frequencies:16 tends:1 focus:3 electron:1 softened:1 resonant:6 fac:1 capillary:3 deformations:6 minute:1 purely:1 transmission:1 knight:1 anisotropy:2 list:1 applicable:1 maia:1 large:1 mm:1 vector:1 math:2 small:4 smaller:1 force:20 oscillation:1 prediction:1 literature:2 sign:1 second:4 perspective:1 qualitatively:1 quite:2 linear:4 even:2 will:1 what:1 appear:3 apparatus:1 sum:4 abk:1 uniform:1 reminiscent:2 experiment:1 above:1 waals:1 method:3 contrast:1 iran:2 evaluating:1 degree:2 respectively:1 residual:1 here:1 atoms:1 reported:2 objects:1 separation:4 represented:1 path:7 along:1 xα:2 implicit:1 change:4 obtained:4 institute:3 involved:1 study:4 studied:1 allows:1 vibrating:2 amount:1 resulting:6 action:5 resonance:4 implement:1 studies:2 scales:1 requiring:1 integrations:2 replace:1 inequality:1 rg:1 sgn:2 summation:1 total:1 readily:1 would:3 transmissivity:1 negative:1 jaekel:2 next:2 comparing:1 depicted:1 opposed:1 conservation:3 associated:1 more:4 separated:2 flat:2 becomes:1 mismatch:1 about:1 mashhoon:1 iia:4 iib:3 known:2 sample:2 must:2 logarithm:1 involve:1 ma:1 deformed:1 science:1 der:1 modified:1 mk:1 reproduce:1 remain:1 paragraph:1 could:1 following:3 modifies:1 example:4 decoupled:1 renormalization:3 mirrors:8 calculation:1 expanding:1 reach:1 ann:1 high:2 unphysical:1 eberlein:2 sense:1 yα:4 deforming:1 keep:1 occur:1 junctions:2 axis:1 sis:1 information:1 holds:1 roughness:1 write:1 occuring:1 nontrivial:1 answer:1 instead:1 those:1 parameter:3 sin:3 tension:3 may:1 after:1 dc:1 davis:2 plane:4 δcs:2 waves:3 fi:2 law:1 parallel:4 natural:3 dynamical:1 third:1 computations:1 light:1 spectra:2 explicit:1 cosmology:1 so:1 correlation:1 observability:1 acknowledges:1 order:3 gignoux:1 prefactor:3 neto:1 restriction:2 rounded:1 developed:3 over:4 satisfied:1 presence:2 gauged:1 thermal:1 through:2 its:8 perfect:2 regions:3 decay:3 ln:2 interesting:2 lateral:6 relativity:1 daemi:1 coordinates:2 li:2 forms:3 previously:1 absence:1 production:1 microscopic:1 fig:3 derivative:2 deformation:2 shear:3 them:1 h1:13 greater:1 combination:2 matches:1 practice:1 introduce:1 effects:4 rotation:1 now:2 easily:3 february:1 profound:1 barton:1 2d:1 realistic:1 vibrations:1 mode:2 found:2 difficult:1 characterized:1 constraints:2 golestanian:1 generation:2 series:1 energy:5 displacement:2 related:3 frequency:16 static:2 obtains:1 quantum:8 our:5 beyond:1 extract:1 χij:4 special:1 out:2 δri:1 shown:1 resonators:1 space:13 furthermore:1 since:3 rev:9 denotes:2 unrelated:1 suggesting:1 wick:1 induced:2 ref:6 rj:1 theory:2 interactions:2 divergence:4 free:1 standard:1 approaches:1 complicated:2 term:1 care:1 enormous:1 qj:1 r0:1 geometry:1 starts:2 collapsing:1 linearized:1 counterpart:1 place:1 corrections:5 δseff:1 undergo:2 first:4 corrugated:8 already:1 attractions:1 number:2 xd:1 reflectivity:2 another:3 representations:1 impossible:1 precisely:1 size:1 mercury:3 πc:2 given:2 perturbation:1 checked:1 similarly:1 system:1 vibrate:1 unruh:1 zanjan:2 their:4 assumption:1 calculations:3 perfectly:2 exerted:1 gives:1 exploring:1 wavelength:1 explanation:1 continuous:4 artifact:1 oscillates:1 part:2 somewhat:1 manifestation:1 x2:1 x3:1 x1:1 than:5 modes:4 connections:1 effective:6 was:1 require:1 zero:2 final:2 states:1 future:1 were:1 powers:2 perturbative:1 function:8 symmetries:1 fluctuation:2 correction:5 spectrum:3 generalization:1 crossover:1 say:2 vilenkin:1 close:1 controlled:1 cumbersome:2 any:4 angle:1 randjbar:1 latter:2 mid:1 note:4 sciences:2 emphasis:1 potential:1 generalized:2 forces:2 davies:1 many:1 formulas:2 akad:1 normal:2 viscosity:4 simplify:1 connected:1 but:3 letter:1 phase:3 ford:1 causality:2 parametrize:1 consequences:1 kj:1 calculated:3 kh:4 playing:2 reflecting:2 dynes:1 principle:1 exp:2 mechanical:9 velocity:5 typical:1 physics:1 ned:1 wavenumber:1 phenomenon:1 supported:1 dependences:1 implying:1 gauge:1 thickness:1 d2:9 find:5 fifth:3 d1:2 current:4 q2:11 ratio:1 should:1 jan:1 only:4 explicitly:1 black:1 factor:2 pointed:1 hope:1 plate:20 distance:3 dependent:7 dd:1 fluid:2 superconductor:1 dynamically:1 cannot:1 closely:1 gen:1 exhibiting:1 continuum:1 fields:1 arxiv:1 motion:6 summary:1 predicted:1 dodonov:1 qi:1 fixed:1 voltage:1 intervening:2 kernel:2 requirement:1 set:4 undergoes:1 sensitivity:1 relative:1 depends:2 individual:2 bare:1 result:3 eliminating:1 discussions:1 terms:2 analog:1 subject:2 satisfying:1 tensor:2 speed:1 review:1 nature:3 motional:1 fulling:2 diverge:3 boundaries:4 difficulties:1 various:1 closed:1 between:7 iqi:1 boundary:3 approach:3 emitted:2 recently:1 2m:1 attention:1 however:8 vanishing:2 cut:2 multiplier:1 both:6 cos:5 limits:2 freely:1 taking:2 density:2 hence:2 quantization:1 casimir:5 candidates:1 expression:1 regarded:1 experimental:1 ck:6 presumably:1 subdivides:1 cm:2 point:3 cb:2 height:2 dimensional:4 directions:1 simply:2 applicability:1 lagrange:3 cs:2 respect:2 cq:2 actually:1 fdc:1 considering:3 kernels:9 sine:1 corrugations:1 hd2:1 geometries:1 due:8 been:5 appears:2 much:1 damping:1 hawking:1 basic:2 anisotropic:5 degrees:2 ph:1 ak:1 define:1 determinant:1 partly:1 deeper:1 reaction:1 wet:1 photon:1 wires:1 1mm:2 external:4 wavevectors:1 c2:6 israelachvili:1 dmr:1 manifolds:3 c4:1 case:3 intriguing:2 josephson:3 examine:2 hz:2 intimately:1 while:8 overcome:1 behavior:3 promising:2 ramin:1 conformal:1 region:7 real:6 larger:1 conjugate:1 thus:5 non:1 surface:7 quantize:1 technology:1 different:3 grant:1 divergences:1 radiation:5 lett:6 same:3 kardar:3 parts:4 quant:1 plates:20 finite:6 consequence:2 higher:5 independent:3 used:1 see:2 numerical:1 effect:4 parametrized:1 moving:2 infinite:4 symmetric:1 αth:1 off:4 reflection:1 changes:2 lambrecht:1 well:1 concrete:1 c5:2 comes:1 components:2 fixing:1 coordinate:1 dimension:3 bodies:2 usual:1 manifold:1 proposed:1 less:2 being:1 generally:1 observed:1 obtain:3 atomic:1 integer:2 momenta:1 macroscopic:4 multiples:1 previous:2 enters:1 candidate:1 vibration:1 photons:8 seems:1 wavevector:3 add:2 valid:1 extends:1 attractive:2 theorem:1 extensive:1 gava:1 excited:4 momentum:2 take:1 resolved:1 around:1 possible:3 seff:2 vacuum:9 using:4 advanced:2 helpful:1 necessary:1 like:2 particle:1 contradict:1 performing:1 accelerating:2 specific:2 δm:7 integrals:2 arbitrary:2 response:13 stationary:1 reduced:3 accessible:1 velocities:1 methods:2 classical:1 discrete:2 resonances:2 creation:2 some:2 mirror:5 2qh:1 describing:1 dimensions:6 cavity:9 electromagnetic:4 footing:1 electrodynamics:1 does:2 assuming:1 proc:2 demonstrated:1 ict:1 measuring:1 power:2 uniformly:1 equivalent:1 oscillating:2 perpendicular:1 expansion:1 although:2 accompanied:1 described:2 imaginary:8 exciting:2 kd1:2 conducting:3 actual:1 most:3 freedom:1 dependence:2 o:3 range:3 extensions:1 2ck:1 analogy:1 diverging:1 other:1 enhancement:1 cutoff:1 soc:1 cambridge:1 plethora:1 h2:13 h3:1 into:1 within:2 integral:7 nsf:1 three:1 variable:2 appropriate:1 references:1 proportional:3 theoretically:1 van:1 additional:1 area:1 support:1 there:13 signifies:1 strict:1 restricts:1 quadratic:2 quanta:1 low:3 way:1 bubble:1 lowest:2 interest:1 phenomena:2 agrees:1 extended:1 gaussian:2 hk:1 illuminating:1 link:1 gain:1 garnered:1 delta:2 optical:4 versatile:1 2πc:1 embedded:2 characteristic:1 up:2 us:2 placed:1 below:1 limit:3 ωn:1 fluctuations:9 problem:4 similar:1 average:2 mechanics:1 ac:1 partition:1 constant:2 moore:2 48h:1 defined:5 ki:1 describe:1 condition:1 direction:1 single:9 fi0:2 formulation:4 corresponding:1 uniaxially:1 formalism:1 regime:3 again:1 functions:6 compared:1 no:3 eq:2 zang:1 when:2 treatment:1 multipliers:2 field:7 conditions:2 role:2 department:1 calculating:1 separate:1 problems:2 inherently:1 emission:1 generated:1 massachusetts:1 dissipation:17 euclidian:1 correlated:1 implies:1 dφ:1 required:1 holes:1 mass:13 time:19 requires:1
|
quant-ph9701006.txt |@word consider:1 gf:1 scalar:3 computation:1 gn:3 expressions:2 reasoning:1 gi:2 gh:2 compact:1 inverse:1 bivector:1 tv:1 graph:1 present:2 th:4 under:3 worth:1 norm:5 alternating:4 vert:4 g1:2 very:3 induce:1 ǫlmn:3 difference:1 deformations:1 nijenhuis:2 annihilated:1 hamiltonian:4 leave:2 vector:24 gauge:5 div:7 equation:3 givental:1 work:2 takhtajan:4 sign:1 zero:1 perspective:1 hungary:1 xf1:1 dynamics:8 canonical:2 even:1 abc:2 developed:1 incompatible:1 section:7 expressed:1 new:5 nln:1 preserved:1 satisfy:1 modify:1 desired:1 groups:2 address:1 alone:1 wachs:1 quite:1 obtained:1 remark:3 antisymmetric:2 institute:1 leaves:3 vectors:4 leaving:2 suggests:1 periodic:1 poisson:13 action:4 suitable:3 changes:2 f0:5 formulated:1 shorthand:1 extra:2 pp:2 total:1 use:1 prove:5 sake:1 contains:3 next:1 xh2:1 xh1:16 approach:1 type:1 decomposable:1 more:3 preserving:6 operators:2 inherited:1 hurt:1 basically:1 known:1 must:1 deformed:2 xhi:1 mn:22 modified:23 remain:1 infinitesimal:2 flm:5 concepts:1 following:7 drops:1 example:1 proof:4 lφ:1 f1:16 f2:3 process:1 permutations:2 ann:1 dxn:4 fulfillment:1 dxi:1 sense:2 orbits:1 verlag:1 dh:13 provide:1 holds:5 maps:1 lh1:6 instead:1 map:1 perms:7 de:3 algebra:3 after:1 different:2 dx1:4 levi:1 plane:1 fi:22 fj:2 fk:1 compatibility:1 fn:23 goal:1 drop:1 natural:2 dynamical:2 third:1 yπ:1 steinheimer:2 trilinear:4 element:1 diffeomorphism:7 s3:1 hfk:1 lhs:4 fundamental:4 representation:1 pulled:1 order:1 restriction:1 words:1 indeed:3 ǫi1:2 satisfied:2 th1:2 existence:4 satisfies:9 its:5 le:1 group:8 ln:1 interesting:1 masses:1 forms:3 connes:1 condition:3 jacobi:10 derivative:1 main:1 might:6 deformation:3 non:1 l151:1 introduce:4 modification:6 arnold:1 now:1 discuss:1 nor:1 kirillov:1 term:3 university:1 level:1 2e:1 2f:1 2g:1 l2:1 each:1 2n:8 2h:3 side:2 subset:1 differential:1 bueno:4 eg:1 product:5 related:1 extended:3 expect:1 quantum:3 relates:1 operation:1 aˆ1:5 special:1 2hf:2 space:6 since:14 rev:1 re:1 fronsdal:1 rn:13 induced:1 occurs:1 math:6 shows:1 foundation:1 fiber:1 linear:5 bayen:1 mapped:3 divergence:1 diagonal:1 possibility:1 standard:5 completely:1 complicated:1 lajos:1 put:2 generate:2 xg1:1 derivation:1 r2:8 r3:4 geometry:3 phrases:1 could:1 motion:1 terribly:1 int:1 consequence:1 generalizations:1 xij:2 first:3 xi:12 xn:7 xf:2 nhk:1 xin:1 carry:1 clarity:1 given:4 arraga:3 introduction:2 top:1 behaves:1 system:6 construct:1 their:1 dfn:13 encyclopaedia:1 too:2 dfk:1 structures:5 fˆi:1 somewhat:2 x2:3 probably:1 x1:10 dvol:1 unfortunately:2 cyclic:2 df1:14 second:1 xi1:3 determined:3 hφ:1 unchanged:1 nonabelian:1 generalization:7 unlikely:2 need:1 paris:1 any:6 lie:5 constructions:2 damental:1 note:1 sciences:1 generalized:8 jacobian:1 so:11 heisenberg:1 lectures:1 play:1 multiple:1 normal:1 rhs:5 systems:1 most:1 but:4 automorphism:5 remarks:2 probabilistic:1 commutation:1 hj:2 constructed:2 brackets:8 flow:5 erez:4 ext:4 hi:8 exp:5 mechanical:1 hietarinta:1 usual:4 abj:1 fact:1 show:2 leibniz:5 anyway:2 relation:6 civita:1 d7:1 trivial:1 find:1 help:1 invariantly:1 only:5 factor:1 hamiltonians:5 local:1 over:3 abelian:2 dl:1 dk:2 notation:1 means:1 df:18 dg:15 express:1 ˆi:7 gef:1 dx:5 dy:8 dt:4 geometric:1 evolution:6 fields:6 arxiv:1 divergenceless:2 dx2n:1 set:5 δa1:2 δa2:1 aai:1 hη:3 see:1 result:2 terms:9 analog:1 points:2 surfaces:1 satisfying:6 tensor:4 inappropriate:1 nondegenerate:1 review:2 functionals:1 symmetric:1 closed:1 between:4 invariant:9 neither:1 conditions:4 deforms:1 preserve:1 nambu:61 recently:2 vertical:1 nature:1 attention:1 however:5 cycl:7 derive:1 comm:2 key:1 multiplier:1 solv:1 tensors:1 both:1 interpretations:1 last:1 reverse:1 region:1 equal:2 quantization:13 connection:1 chatterjee:1 symplectic:8 embedding:2 whole:3 ll:12 ci:1 point:3 simple:1 cohomology:1 dimensional:7 polynomial:1 respect:4 better:1 ensures:1 described:1 transformations:5 basis:1 union:1 locally:1 three:4 been:1 ai:5 ph:1 algebras:4 ak:1 annihilating:1 define:6 generating:2 corresponding:1 cyclical:1 mail:1 presented:1 manifolds:7 case:6 novel:1 debrecen:1 appearance:1 value:1 while:1 study:2 schouten:2 inherits:1 ix:1 cont:2 vol:2 a29:2 formulation:1 surface:1 iv:1 ii:1 cocycle:1 triple:1 vanish:1 containing:2 φt:18 dhj:1 commuting:1 make:1 same:4 quant:1 arguments:1 deletion:1 φh:3 φi:1 defines:1 subalgebra:1 higher:2 fairly:1 used:2 cocycles:1 i1:3 assignment:1 hand:4 birkhauser:1 purpose:1 infinite:1 invariance:1 identity:11 task:2 framework:1 nevertheless:3 expression:2 well:3 contact:19 consistency:1 coordinate:6 dimension:1 left:2 surveys:1 manifold:4 just:6 λy:1 homogeneity:1 unifies:1 λn:1 previous:2 adv:1 adding:1 generator:3 seems:2 leibnitz:1 other:1 lett:1 transformation:8 aspects:1 evaluate:1 possible:2 confined:1 using:1 dito:2 necessary:1 like:1 unnecessary:1 imposes:1 δi:1 works:1 mathematical:1 reidel:1 right:2 classical:1 some:10 back:2 onto:1 sight:1 peter:6 nonzero:1 does:3 intersections:1 straightforward:1 vaisman:1 equivalent:1 ruining:1 variation:1 although:2 informatics:1 hanlon:1 refers:1 properties:2 commutative:1 gained:1 extension:2 algebraic:1 ack:1 carries:2 theory:3 discard:1 introduced:2 consequently:2 perelomov:2 homogeneous:2 subbundle:1 h2:28 into:8 h1:38 integral:2 functional:1 phase:3 appropriate:1 weyl:2 references:1 operator:2 proportional:1 hep:4 few:1 there:2 strict:1 way:2 was:1 function:2 form:18 jul:1 hu:1 volume:16 hh:2 construction:1 hn:33 hl:1 russian:1 line:2 hf:4 hg:1 hd:1 he:1 pull:1 flato:3 embedded:1 fulfilling:1 ut:1 azc:3 smooth:1 up:2 us:1 those:1 planes:1 problem:2 similar:4 called:1 mechanics:16 fulfills:1 popularity:1 constant:1 defined:10 certain:1 abstract:1 aj:1 am:1 proven:1 general:3 dπ:2 our:5 identities:1 aˆ3:5 dα:1 nh:1 functions:6 nk:6 varga:7 no:2 deserve:1 field:11 bracket:63 role:1 aˆ2:5 papers:1 mathematics:1 out:2 briefly:2 generates:3 symbol:1 bundle:1 generated:7 bounded:1 sides:2 structure:4 implies:3 proposed:1 rule:5 4c:3 ternary:1 far:1 original:1
|
quant-ph9701007.txt |@word neighbors:1 represent:4 measurements:1 partial:1 consider:9 limited:1 recreate:1 rev:8 magnetic:13 global:3 desirable:1 results:2 amorphous:1 leads:4 proposition:2 consists:2 follow:1 gm:2 mesons:1 contributions:1 reˇ:1 localized:4 extra:1 whose:1 simon:3 depend:1 re:2 graph:40 concerned:2 equivalence:2 noncompact:1 presents:1 γj:4 finally:2 chaps:1 vec:1 th:2 under:7 nodes:1 stark:1 γe:5 ajm:5 subtleties:1 belonging:2 adiabatic:2 amplitudes:1 ajn:3 g1:1 returning:1 misunderstanding:1 wave:5 lengths:1 endpoint:1 putting:1 difference:1 matrices:4 encounter:1 common:1 four:1 indicate:1 riemann:1 hamiltonian:4 did:1 turns:1 criterion:1 solution:4 large:2 discrete:3 vector:3 small:2 eigenvalues:8 anal:1 added:3 possibility:1 upper:1 wronskian:2 disordered:1 b26:1 variables:1 ηl:1 literature:1 sign:1 approximation:1 go:1 integrability:2 traveling:1 zz:1 gn:3 link:7 further:1 dynamics:1 rectangular:1 odd:6 substitute:2 linear:5 spectral:5 aim:1 kinetic:1 superlattices:2 euclidean:1 singularly:1 section:7 interactions:4 while:5 current:3 experiment:3 poles:5 above:7 new:4 falling:1 commensurate:1 method:4 mp:1 satisfy:3 outgoing:1 full:3 fiz:1 respectively:4 l1:1 component:6 equals:2 here:6 met:1 inverse:1 tangent:3 ansatz:1 sinh:1 eikx:3 concluding:2 along:1 standard:2 equations:7 implicit:1 change:1 wait:1 obtained:2 remark:1 endpoints:1 incoming:1 institute:2 shift:2 study:6 studied:1 allows:2 later:1 suggests:1 simultaneous:1 resulting:1 krohn:1 situations:1 identity:1 resonance:5 suitable:1 makes:1 cancellation:1 relation:3 golden:1 named:1 shorthand:1 love:1 family:3 danger:1 belongs:3 eiφ:2 prefer:1 f2:1 analytically:1 replace:4 analyzing:1 apply:1 albeverio:1 lima:1 imaginary:1 unit:2 until:1 derivatives:1 use:4 quasi:1 kα:3 figure:8 prove:1 sake:3 nine:1 ψp:4 contains:1 bundles:3 charge:2 next:3 ψj:9 calculation:1 explicitly:5 call:1 therefore:3 fixed:2 marchand:4 schulman:1 type:4 theoretical:1 corners:1 more:10 chem:1 introducing:1 pavlov:1 gaveau:1 coupled:2 duality:3 h1:6 ua:2 operators:7 occurred:1 curvature:1 interaction:1 normalized:2 sharply:1 particular:11 known:2 souillard:1 preserved:1 goes:1 me:2 topic:1 springer:1 valued:1 electron:5 reed:1 recall:2 equation:8 functional:1 modified:1 mj:9 values:17 achieve:1 ladders:1 following:4 about:1 metal:3 arrive:3 my:2 example:1 decoupled:3 initial:3 f1:2 compare:1 links:13 solved:3 process:1 discussed:3 arise:1 states:9 assumptions:2 numbers:1 want:5 sense:1 sought:1 iφ:2 quasistationary:1 robinson:1 tan:1 axis:3 uψ:2 feynman:1 requirements:2 straightforward:1 αj1:1 rather:3 discussion:1 acts:2 occur:1 write:4 how:2 nontrivial:1 avron:4 pair:3 pure:1 instead:2 those:1 happens:1 parameter:9 sin:31 circular:1 simplicity:3 express:2 description:1 algebra:1 transforming:1 ψac:3 ladder:1 earlier:1 derived:2 tor:1 produce:2 inst:2 antoine:1 coming:2 end:3 fj:2 choice:3 journals:1 concerns:1 fn:5 realized:1 natural:5 decaying:2 imply:1 whenever:1 consequently:1 gratefully:1 spectra:1 explicit:2 correspond:1 provide:1 switch:3 interior:3 so:9 every:1 sa:1 looking:1 typical:1 oper:1 holds:2 a27:2 words:2 reservoir:2 quasiperiodic:1 dy:4 satisfied:1 years:1 symbols:1 course:6 surviving:1 paper:1 through:6 signs:1 differs:1 existence:2 satisfies:1 still:2 its:10 discretizing:1 respect:5 derive:2 symmetry:2 fit:1 decay:17 chosen:2 vicinity:1 sixties:1 writing:1 mπ:1 complex:2 systems:10 insulator:1 jacobi:2 derivative:2 might:1 bjm:3 outside:1 them:10 good:1 return:2 horwitz:7 lambert:1 numerically:1 detour:1 introduce:1 reflected:1 tucker:1 yields:2 exhibiting:1 effects:3 they:5 half:2 arriving:1 now:9 discuss:1 eigenvalue:3 term:2 finite:4 rocky:1 2r:2 fully:4 university:1 identified:2 instant:1 l2:10 each:7 crossing:1 2m:1 difficult:1 2i:1 characterized:1 mean:3 homogeneous:3 domain:3 square:2 directly:1 formulate:3 ej:1 mesoscopic:2 energy:6 identifying:1 related:5 applicable:1 elementary:1 conductance:2 decays:5 begun:1 sketched:1 quantum:16 our:9 differ:1 out:2 living:1 shown:1 matrix:7 space:7 continuity:2 furthermore:1 since:6 squared:1 semiconductor:1 may:7 multiply:1 perturbatively:1 rational:1 denoted:1 formula:2 get:3 induced:1 occurs:1 math:8 shows:2 b32:1 exactly:1 doppler:1 theory:5 reformulated:1 found:4 singularities:3 given:13 free:4 quite:1 ψjm:2 reason:1 necessarily:1 york:1 violation:1 put:1 card:3 additional:1 definition:1 dirichlet:6 organic:1 sigal:1 geometry:1 aj1:2 could:1 transition:1 excluding:1 used:2 times:1 motion:2 turn:1 length:3 birthday:1 place:1 vjn:16 arccos:1 hence:5 teor:1 repeats:1 howland:2 first:9 xj:13 already:1 xn:1 probability:4 kernel:1 relate:1 e2iδ:1 number:7 restrict:4 featured:1 smaller:2 done:1 adopted:2 another:4 indices:1 ring:1 open:2 horizontal:1 captions:1 illustrate:2 take:1 passes:2 properties:4 law:5 sheet:1 requirement:2 attach:1 introduction:1 xii:1 adjoint:2 πn:4 system:18 construct:1 parallel:1 πr:1 their:2 always:2 brevity:1 iax:2 pavel:1 zeros:1 scheme:1 structures:1 too:2 holden:3 shell:1 deo:1 mostly:1 academy:1 convention:1 plane:3 required:2 ix:1 employ:4 assumption:1 part:10 authors:1 x2:1 kept:1 representing:1 than:4 coefficients:4 wide:1 resolvent:8 sections:1 intensity:1 lim:2 quarkonia:1 a42:1 supposed:1 amplitude:5 represents:1 radius:1 treated:1 distinguished:1 result:4 generality:1 remained:1 appreciate:1 ann:3 lnj:1 spectrum:6 mts:1 say:2 wannier:1 need:2 seen:1 handled:1 clearly:1 contents:1 generalizes:1 strength:1 zero:6 academic:1 check:1 convenient:2 latter:4 able:6 isolated:1 contact:1 segments:1 sciences:1 emphasis:1 potential:6 amusing:1 analogy:2 band:1 finding:2 lhs:2 strengths:1 modulus:3 channel:1 even:4 begin:1 continuous:6 multiple:2 gα:1 shall:12 nonexponential:1 rhs:3 knew:1 what:1 metrics:1 most:3 involving:1 connected:9 ensure:1 preliminary:1 remarks:3 uttiker:1 segment:2 class:2 avishai:1 appear:3 subspaces:1 branching:2 demand:1 considered:1 clear:2 adopt:1 flow:1 vertices:7 physica:1 kl:31 graphs:10 points:5 principle:1 exp:3 mechanical:1 χn:1 charged:2 physics:4 notion:1 fact:4 quantity:1 b45:1 semiinfinite:2 particularly:2 ikµ:4 show:3 nπ:2 appendix:1 supported:1 b49:1 discovered:1 helv:4 gauge:1 solutions:6 threshold:1 substituting:2 dimension:1 find:6 help:2 meromorphic:1 parameters:6 series:1 halfline:11 written:4 should:1 jan:1 analytic:2 only:12 going:1 høegh:1 molecules:1 local:6 interested:2 columns:1 regularly:2 do:2 his:1 αg:1 notation:4 means:9 dependent:1 αf:3 overall:1 methods:1 tailor:1 reversal:2 invariant:2 interpreted:1 him:2 becomes:1 evolution:2 αj:7 covering:1 transposition:1 arxiv:1 modern:1 yield:2 consisting:2 qa:1 threading:1 investigate:1 asymptotics:2 mapped:1 analytical:1 including:1 previous:1 ψjn:22 krein:1 view:6 κl:3 declared:1 set:5 computed:1 reference:1 achieved:1 ωu:1 prague:2 hα:21 choose:1 ends:2 observed:2 mentioned:1 see:7 arc:4 sec:2 us:6 ihα:1 equip:1 recently:3 heavy:1 electrode:1 outward:2 subject:3 instance:2 wire:2 eigenfunctions:2 delyon:1 consistency:1 ways:1 nuclear:1 review:2 definite:1 shabani:1 symmetric:1 state:14 various:1 µk:1 between:7 progress:1 boundary:27 µf:1 conditions:22 preserve:1 notice:1 attention:2 terms:1 extend:1 missing:1 initially:2 complement:1 ikx:3 however:7 ikb:1 jn:7 sadun:2 french:1 separately:2 configuration:2 come:1 regular:1 both:6 cos:35 last:4 cot:1 limits:1 experimentalist:1 career:1 many:3 region:1 ika:1 acknowledged:1 sov:1 ln:3 connection:3 poincar:2 context:1 κx:1 contribution:1 expression:3 decayed:1 experimental:2 otherwise:4 kirsch:1 hac:1 eiky:1 nonrelativistic:2 simple:6 continuation:1 uniformly:1 vast:1 corresponds:4 ω2k:1 parametrization:1 dimensional:2 represented:2 pole:14 grants:1 simply:1 singha:1 cancel:2 constant:6 throughout:1 expensive:1 speak:1 described:3 second:5 addition:1 create:1 locally:1 three:2 been:5 strategy:1 gerasimenko:1 much:1 slowly:1 treat:4 interest:1 basic:2 ph:1 empty:1 define:2 gesztesy:3 life:1 relations:3 corresponding:9 kronig:1 dashed:2 quantities:2 sufficient:2 countably:1 joined:1 maps:1 substance:1 external:5 essentially:2 c2:2 worked:1 denote:3 despite:1 former:2 present:3 case:20 exception:3 disconnected:3 subsets:1 solid:1 value:3 remaining:1 will:10 technical:1 near:1 suppose:8 behavior:3 involved:2 situation:7 eik:1 2k:10 c1:2 couplings:4 loop:33 a20:1 due:1 unitary:3 elucidation:1 satisfying:1 vg:2 a28:1 a29:1 metric:3 ir:4 thus:2 non:3 iv:1 ii:6 ik:8 iκ:1 im:4 il:5 ia:3 junction:7 ib:1 currents:1 bellissard:1 different:7 recover:1 lemma:1 combination:3 halfinteger:7 make:4 gacr:1 lett:3 same:5 any:3 dordrecht:1 stimulated:1 parts:5 quant:1 viewed:1 evaluate:1 units:2 several:1 higher:1 perimeter:1 independent:2 wires:2 percolation:1 luck:1 trajectories:11 effect:3 hand:3 usually:1 edges:1 internal:1 potentials:1 infinite:2 changing:1 opportunity:2 tune:1 recent:1 eigenvectors:2 prescribed:1 lower:1 fourier:2 schr:11 reflection:4 scenario:1 mention:1 gaps:2 substantially:1 xjn:2 well:4 analysis:3 person:1 ujn:4 without:1 solve:2 components:1 noncircular:1 exponentials:1 model:17 self:2 usual:5 just:4 less:1 being:3 generally:2 obtain:1 press:1 integer:9 useful:1 scattering:24 multiples:2 lasso:8 adv:2 enters:1 preprint:1 lebesgue:1 conclusions:2 regarded:1 point:11 had:1 ideal:3 iω:5 lattice:2 add:2 setting:1 conjugated:1 treatment:2 easy:1 theorem:1 attracted:1 ejm:3 mod:2 solvable:6 app:1 generalized:2 real:9 acta:4 spinless:2 aspects:1 depends:1 easily:4 replaced:3 couple:4 decomposed:1 sums:1 possible:5 iη:1 matters:1 know:2 appendices:1 confined:2 world:1 almost:1 subfamily:1 moreover:2 apart:1 loss:1 replacing:1 particle:8 shaped:1 ljn:5 cannot:1 specific:2 flux:10 unstable:3 integrals:1 arbitrary:2 become:1 stationary:4 replacement:1 mathematical:5 reidel:1 because:1 old:1 often:1 namely:2 exposed:2 czech:2 halfplane:2 some:5 draw:1 pacific:1 understood:1 growth:1 choosing:1 specified:1 root:1 extended:1 ourselves:4 transport:1 superposition:3 nonzero:4 provided:4 scale:1 describing:2 abuse:2 lead:5 collect:1 nonempty:1 resonances:7 opposite:2 coth:1 integration:1 cast:1 does:4 decomposition:2 transmitted:1 particles:1 sided:1 refer:1 denominator:2 obey:1 power:1 rep:1 vertex:10 equivalent:1 wavefunctions:1 aj:2 perpendicular:1 defines:1 step:1 br:1 cusps:1 relating:1 prepared:1 hilbert:4 after:2 asymptotic:3 zur:1 comparison:1 acquire:1 freedom:1 commun:1 numerator:1 factors:1 important:4 extensions:1 rule:2 neighbor:1 positive:2 meson:1 introduced:1 slightly:1 kaons:2 subset:3 iµk:2 b53:1 h2:6 into:17 within:2 integral:1 bound:7 negative:3 phase:3 appropriate:2 right:1 references:1 strip:1 operator:15 thm:1 screened:1 neumann:1 performing:1 fast:1 deal:1 seba:2 periodic:4 transfer:1 support:3 there:13 long:2 intention:1 conservation:2 weakly:1 way:5 ballistic:1 ψn:7 conceivable:1 analyze:1 was:2 cosφ:2 naturally:1 function:9 survives:1 complete:1 form:6 penney:1 hp:1 regard:1 denoting:1 sum:1 but:4 neutral:4 larry:2 trum:1 bj1:3 larger:2 russian:1 hc:2 line:4 trying:1 true:2 illustrative:2 scales:1 network:1 made:2 embedded:7 deficiency:2 ut:4 mat:1 attached:6 up:1 devices:1 2πn:1 placed:6 below:3 ωj:3 limit:4 reflects:1 ωn:4 problem:9 uf:2 similar:6 eigenvector:1 ωf:1 mechanics:5 digression:2 associated:2 heidelberg:1 wjn:10 certain:3 describe:3 condition:15 proceed:1 general:16 loops:1 single:5 xiii:1 exist:4 governed:1 formulation:1 simplest:1 physical:3 vertical:1 again:2 functions:4 dotted:2 no:8 amounts:1 index:1 wavefunction:7 when:10 vanishes:1 arctan:2 nx:1 field:6 other:9 republic:1 details:2 normal:1 papers:1 puiseux:1 picture:2 briefly:1 elements:1 conventionally:1 separate:2 models:5 dies:1 symbol:5 problems:4 kirchhoff:1 bundle:3 odinger:11 deriving:1 meaning:2 a2:1 bounded:2 cos2:1 vectors:2 variable:2 fermi:1 formal:1 exner:12 structure:2 acknowledgment:1 ago:1 independently:1 kx:5 coupling:33 using:3 assume:6 interval:2 curve:1 persistent:2 together:1 original:1 4m:1 smooth:1 time:9 appl:3 having:2 2ik:1
|
quant-ph9701008.txt |@word limited:1 consider:2 holthaus:1 rev:6 varying:1 results:34 zoller:3 leads:3 commute:1 overlap:1 go:2 expressions:2 factorizing:1 whose:1 depend:1 calculate:11 re:1 effort:1 lasers:1 γt:1 outside:1 finally:1 does:6 pathria:1 those:3 th:2 under:1 perature:1 stochastic:4 include:1 tc:19 p2:5 random:3 advantage:1 orthogonal:1 far:3 implicitly:1 rise:3 wave:3 sons:1 every:1 decide:1 difference:1 exact:1 cool:1 four:2 disturb:1 presented:1 did:1 integrating:4 solution:9 correct:1 large:3 discrete:7 convenience:1 vector:7 science:1 small:9 markov:6 eρ:1 configurations:1 dilute:1 tem:1 foundation:1 10b:1 oscillator:18 consistent:2 10a:1 d3:6 factorization:1 filled:1 approximation:16 second:3 7tc:1 evaluated:1 equal:7 qualitatively:1 dynamics:1 canonical:13 even:4 will:25 plays:1 trapping:10 rate:8 giving:1 section:3 unwieldy:1 mechanics:2 brief:1 uniform:2 cell:1 version:3 3n:1 above:6 new:3 gmin:1 ground:17 consisting:3 contrast:4 3d:30 body:1 condensed:1 full:1 behavior:2 exchange:2 respectively:1 error:4 spacing:5 equals:1 here:6 atoms:4 highly:5 asymmetry:1 erb:1 possibility:1 separation:1 relaxation:2 represented:1 standard:8 equations:5 change:9 extreme:1 box:21 deriving:2 shift:1 study:4 larger:4 allows:4 reason:2 significantly:1 amount:1 periodic:4 hospitality:1 studies:1 plotted:2 named:1 azimuthal:1 regardless:1 divide:1 discontinuous:1 explained:2 replace:5 scaled:1 visible:1 austria:1 decrease:2 e4:8 summation:1 apply:1 total:10 unit:6 readily:2 plot:3 use:6 takes:2 would:2 probabilities:5 e1:9 until:3 contains:1 de4:2 physics:1 guideline:1 occupying:1 m4:6 ψi:2 m1:2 therefore:13 m3:6 m2:9 taken:2 conservation:3 themselves:1 type:2 emin:4 more:5 integers:1 started:1 neglected:2 postulated:1 validity:2 appendix:3 normalized:11 particular:8 cases:3 iii:10 must:1 high:2 account:4 crosses:2 bagnato:1 quantized:1 effectively:1 ml:1 equation:30 work:4 mi:6 modified:1 mk:1 tne:4 labeled:3 fock:1 values:8 temperatures:15 macroscopically:1 burnett:1 following:6 coherences:1 stimulating:1 numbers:23 grained:1 compare:7 degenerate:18 give:8 process:5 permutations:1 organized:1 trap:11 states:41 collision:45 assumptions:3 performed:4 want:3 sense:2 keep:1 reynolds:1 occur:6 δm1:2 counting:1 goal:1 rather:1 discussion:1 get:7 write:3 how:2 varies:1 instead:1 ensemble:5 exponentially:1 de:1 ft:1 description:6 may:1 thermodynamic:16 numerically:3 after:5 derived:3 containing:2 physik:1 coming:1 4tc:2 summarize:2 choice:1 setting:2 excited:19 curve:2 whenever:1 lines:2 summing:1 assign:1 secs:3 ones:1 so:4 increasing:2 decreasing:2 definitions:1 lined:1 order:4 restriction:1 holds:1 interpretation:2 n0h:4 developed:1 over:16 move:1 vary:1 soon:5 interpreted:1 produced:1 course:1 thermal:13 paper:3 including:1 statistical:6 austrian:1 kinetic:6 its:7 before:2 regions:1 rapidly:1 exclusion:1 fit:2 energies:4 interesting:1 fix:2 solving:1 boson:1 systems:6 nf1:1 h3:1 decreased:1 might:1 into:13 underestimate:1 versus:13 non:6 good:1 obtaining:1 outlined:1 runs:2 scaling:3 framework:2 hamilton:2 effects:4 they:5 mxi:2 now:5 yu:1 discuss:4 bigger:1 going:1 pumping:1 several:1 d3x:2 fully:1 university:2 level:9 sufficiently:1 magnitude:5 l3:5 reasonable:1 each:6 2m:5 universit:1 difficult:1 side:1 mean:45 walraven:1 el:3 square:5 ei:13 directly:1 kleppner:1 oneparticle:3 energy:67 reduce:1 gaussian:2 eb:8 frequency:2 obtains:2 proportional:4 quantum:20 our:17 approximated:4 transitions:1 eq:32 es:1 really:1 maximizes:1 shown:9 matrix:6 space:5 restricted:3 furthermore:4 since:8 crucial:1 semi:2 denotes:3 particles:85 collisions:30 contained:2 denoted:1 formula:1 transfer:1 ref:3 occurs:3 shows:6 plotting:1 trajectories:1 theory:2 interactions:1 gardiner:3 mω:2 diagonal:2 free:2 treatments:1 indices:4 completely:2 necessarily:1 complicated:1 york:2 put:1 van:1 fits:2 rises:2 beginning:1 e3:8 e2:6 degeneracies:1 interaction:4 derivation:8 language:1 r3:1 kagan:1 transition:12 times:8 motion:1 length:6 period:1 isotropic:6 removing:2 hence:1 degeneracy:4 neglect:3 first:18 origin:1 qki:16 already:2 probability:8 occupations:2 number:49 reaches:1 system:22 restrict:2 minimum:1 smaller:4 choose:1 neglects:2 another:1 carry:1 reached:4 πm:1 size:9 5tc:2 given:15 long:3 temperature:42 similarly:2 introduction:1 data:2 condensate:42 smoother:1 theoretische:1 approximately:2 mal:1 acknowledgment:1 cooling:9 intermediate:1 master:12 calculations:4 hπ:1 hundred:1 final:1 speaking:1 gives:6 fraction:8 trapped:1 continuous:2 serve:1 redistribute:1 assumption:23 part:4 simulate:5 representing:1 than:22 specify:1 population:1 jump:4 kind:1 john:1 determines:1 holland:5 tcoll:6 bec:5 approximations:3 depends:2 determined:1 williams:2 were:3 ber:1 evaporated:3 treated:1 8πa2:1 grossmann:1 lowest:1 fig:50 shrinks:1 us2:1 fluctuation:1 unchanged:2 spectrum:2 curves:2 correspond:1 e1234:6 chosen:2 depleted:1 need:1 seen:4 occupied:5 any:1 thermalize:1 genuine:1 zero:4 depending:1 efficient:1 tends:1 responsible:2 able:2 onset:3 fitting:1 potential:16 take:3 finding:2 transferred:2 play:1 exactly:2 unless:2 optimizes:1 2tc:1 opposite:1 track:1 whole:1 simulated:2 reach:4 victoria:1 most:4 boltzmann:14 involving:1 connected:2 comparing:2 pair:1 capacity:2 colliding:1 eigenfunctions:1 zealand:1 found:4 wiley:1 considered:1 calculated:11 steady:2 chemical:1 qbe:15 exp:5 mechanical:2 velocity:8 seventeen:1 typically:1 sum:11 lying:5 laws:2 slope:3 momenta:3 selected:1 nπ:1 text:4 delta:2 scattered:1 connect:1 relation:1 solutions:7 svistunov:1 find:6 occupation:35 highest:1 based:5 ensembles:2 parameters:2 distributed:3 state:38 should:5 jan:1 only:17 explicitly:1 factor:4 employed:1 a1:1 marsden:1 local:1 interested:2 equilibrium:19 do:7 cube:2 notation:2 means:2 familiar:1 between:19 expectation:1 cannot:4 report:1 during:4 distortion:2 collisional:2 becomes:5 evolution:3 contributes:1 continuum:2 approach:1 arxiv:1 coll:7 yield:1 method:2 twice:1 investigate:2 experiments:1 common:1 contain:2 fixed:3 kernel:2 bars:3 set:2 computed:2 achieved:1 unpublished:4 vol:1 σv0:2 maximum:1 relative:5 see:4 individual:1 sec:12 result:15 w0:1 discussions:1 close:5 semikoz:1 best:1 appear:1 lost:2 mechanically:1 interacting:3 record:1 ways:3 macroscopic:3 review:2 currently:1 definite:1 tend:1 symmetric:1 vki:1 written:1 wavelet:2 simplest:3 boundary:4 conditions:4 mainly:1 available:1 multiplied:1 terms:10 sections:1 wn:16 wm:1 attention:1 combining:1 however:3 wi:4 p3:3 concentrate:3 jh:1 huang:1 bose:21 configuration:3 come:1 luiten:1 both:4 collaborators:1 last:2 2n:1 limits:2 many:4 region:4 conclusions:1 ramp:2 according:7 against:3 agree:5 ln:1 hω:6 context:1 vth:2 variance:1 0h:2 argue:1 expression:5 comes:2 among:4 druten:1 relevant:2 p2i:1 very:8 point:2 poissonian:2 eikx:1 harmonic:20 formalism:1 factorize:1 cirac:1 adding:1 modeling:1 moreover:1 factors:6 considers:1 broadening:1 ensures:1 jetp:1 described:2 collides:1 basis:1 addition:1 simplification:1 due:5 been:2 quickly:5 ml2:3 ml3:2 reduction:1 much:15 treat:1 interest:1 kronecker:2 expected:6 pritchard:1 ph:1 wait:1 pl:1 define:3 obtained:6 ergodic:35 corresponding:4 restrictions:1 quantities:4 transferring:1 gas:32 requires:1 fund:1 coherent:1 buildup:1 equilibration:1 present:6 case:16 randomly:1 p1:4 look:1 p4:3 solid:10 reliable:1 value:4 remaining:2 aim:1 while:5 replaced:5 leaves:1 involved:3 hωi:3 taking:2 opt:1 n2i:1 changed:3 orientation:1 a4:2 almost:5 vk:2 thus:7 them:2 iv:6 ii:5 ih:1 vs:1 vt:3 increase:4 tkachev:1 around:4 binary:1 different:11 ing:1 etc:1 supported:4 make:1 cross:1 same:9 check:1 shifts:1 quant:1 arguments:2 grand:13 finite:12 start:1 higher:6 calculation:4 used:3 spectively:1 equalizing:1 closest:1 again:4 cloud:2 numerical:7 hand:3 v0:7 v1:3 levels:22 potentials:2 fellowship:1 mzi:2 normalization:2 recent:1 lower:2 off:4 rederive:1 nevertheless:1 changes:2 min:1 well:12 wellington:1 obviously:1 without:10 solve:1 sets:2 coordinate:2 position:1 model:1 ne1:1 thc:1 usual:1 nc:22 nv1:1 less:6 being:1 nonergodic:1 distribute:1 rates:1 obtain:7 shape:1 thanks:1 immediately:1 useful:1 am3:1 scattering:5 eigenstates:7 network:1 previous:3 note:4 cut:4 integer:3 density:16 conclude:3 character:1 ideal:2 other:6 expecting:1 easy:1 wiseman:1 eigenstate:3 momentum:10 divided:2 ami:1 nvt:3 eigenfunction:1 insert:1 innsbruck:2 papers:1 sums:4 possible:15 corresponds:3 increases:7 makes:1 confined:3 using:6 8πa:1 outcomes:1 loss:2 necessary:2 like:3 particle:66 follows:2 microcanonical:3 serves:1 specific:1 yields:4 either:2 integrals:4 δi:1 become:2 δe:1 stationary:11 reduced:1 cooled:3 replacement:1 tm:4 because:10 often:2 classical:18 smoothly:1 creation:1 some:3 back:1 born:2 repeat:1 equivalent:1 δp:1 choosing:1 specified:1 extended:2 ourselves:1 pronounced:1 tmr:1 scale:7 describing:1 bruck:1 broad:1 avoid:1 per:9 instantaneous:1 arguing:1 critical:18 linearly:3 assuming:3 shlyapnikov:1 refer:1 inserting:1 slight:2 dropped:1 jumps:1 wavefunctions:1 agreement:1 thermodynamically:1 disappeared:1 step:2 although:2 putting:2 properties:7 comparison:7 about:1 works:1 um1:3 simplify:1 discussed:1 dependence:2 o:3 simulation:35 range:6 a2:5 ensure:2 equalize:1 introduced:1 de2:2 block:1 peak:1 equally:2 de3:2 significant:1 h2:8 pergamon:1 h0:10 within:5 integral:5 h4:1 three:1 down:1 phase:4 right:1 determine:2 einstein:5 operator:6 accumulated:1 next:2 methods:2 a3:1 statistics:2 institut:1 additional:1 elastic:3 few:6 assumed:2 strictly:2 there:13 approximate:2 gases:1 width:4 describes:6 pi:3 low:4 way:1 series:1 forward:3 call:2 was:3 assumes:1 coarse:1 function:14 irreversibility:1 form:10 differences:2 agrees:5 but:5 volume:1 heat:2 hi:6 evaporative:6 atom:3 line:18 removed:1 irreversible:1 ramped:1 faster:4 count:1 made:4 compute:2 builds:2 versions:1 angels:1 cells:2 smooth:1 up:3 us:4 ur:1 ωi:5 perturbatively:1 below:8 growth:2 limit:15 fluctuations:9 distribution:40 semiclass:1 similar:1 average:5 clear:1 expect:4 strongly:1 required:1 constant:9 conserves:2 computing:1 defined:7 certain:7 decreases:4 describe:6 influence:3 direction:1 myi:2 substantially:1 single:6 initial:7 simulations:27 hamiltonian:4 distributions:10 happen:1 regime:3 nh:4 ni:27 functions:6 compared:7 dotted:4 no:6 dashed:8 whereas:3 populations:2 when:6 field:5 valid:8 role:2 details:1 spatial:3 department:1 out:1 deviation:10 ketterle:1 briefly:1 elements:9 calculating:3 kt:5 distance:1 includes:2 evaporatively:3 develops:1 important:5 a5:2 allowing:1 included:4 cooper:3 needed:1 feasible:1 jila:1 condensation:4 implies:1 longer:2 algorithm:1 assume:4 starting:1 interval:2 kinetics:3 δx:2 mass:1 fitted:1 time:65 n0:3 n1:9 n2:8 n3:5 n4:5 lett:1 1tc:1
|
quant-ph9701009.txt |@word precise:1 monte:3 depends:3 depend:1 departing:1 compensate:1 th:1 dramatically:1 divergent:1 far:1 wave:1 treating:1 ref:11 damped:1 large:4 indices:1 commented:1 programme:1 direct:2 titles:1 value:6 concludes:1 carlo:3 even:1 index:8 errors:7 apparatus:1 sum:1 homodyning:1 experiment:2 reconstruction:1 new:1 method:4 edited:1 evolving:1 equals:1 here:2 atoms:1 growing:1 smearing:1 inversion:1 concluding:1 knowledge:1 obtained:3 studied:1 studi:1 via:1 banaszek:1 plenum:1 logical:2 herzog:4 summation:1 apply:1 establish:1 unit:1 would:1 prove:2 negative:1 therefore:2 means:1 theoretical:2 reorder:1 more:3 door:1 successful:1 thus:3 apparent:1 odinger:1 particular:3 foundations:1 cases:1 must:3 states:3 account:1 crosses:1 erp:1 work:1 fock:2 values:9 following:1 root:1 example:1 leonhardt:5 figure:2 stated:1 haroche:1 involve:1 want:1 allowed:1 domokos:1 respective:1 rather:1 holds:2 how:1 sig:3 parameter:1 priori:1 alternative:1 our:1 data:3 stress:1 correspond:2 element:6 so:1 representation:1 acknowledges:1 playing:1 dx:1 over:2 thermal:5 paper:2 through:3 statistical:10 existence:1 volta:1 vari:1 before:2 decay:1 chosen:1 actually:2 detected:2 fig:5 pavia:2 versus:7 violating:1 within:2 bernoulli:1 evolution:1 nonunit:2 framework:1 effects:1 kiss:4 half:1 oxford:2 now:1 easily:1 meas:7 finite:1 always:1 university:1 each:1 2n:1 macchiavello:1 2j:2 referred:1 square:1 series:19 idea:1 measure:3 quantum:25 laboratory:1 eq:3 out:1 shown:3 matrix:18 rev:13 holevo:1 research:1 re:1 squares:1 issue:1 correct:1 approached:1 circumstance:1 fisica:1 manifestly:1 reason:1 orm:1 york:1 estimate:1 starts:1 transition:1 bassi:1 place:1 hence:1 jex:1 size:1 number:1 diagonal:3 open:1 illustrate:1 given:9 dipartimento:1 system:1 their:1 hypothetical:1 scheme:4 gives:1 shifted:1 unboundedly:1 exactly:1 part:1 authors:2 off:1 than:2 coefficients:3 finiteness:1 compensation:8 determined:1 were:1 bare:3 treated:1 argument:5 any:4 walser:1 parks:1 converges:4 generalized:1 detector:1 circles:1 though:1 iterated:1 analytically:1 measured:6 inconsistency:1 considered:3 clear:1 detectors:1 kn:3 order:1 points:2 principle:2 oscillates:1 slope:1 show:2 supported:1 converge:2 odkiewicz:1 based:1 just:1 ox1:1 should:1 jan:1 only:4 explicitly:1 factor:1 constant:1 above:5 di:3 overall:2 expectation:1 cannot:2 words:1 report:1 procedures:2 regarding:1 caves:1 bar:1 arxiv:1 saturates:1 analytical:1 london:1 fixed:1 approaching:1 kernel:1 set:1 detection:3 alessandro:1 individual:1 radius:4 result:2 fail:1 terms:2 uncorrelated:1 violates:1 still:3 outside:2 c2j:2 contaminated:1 brune:1 notice:1 recently:1 statistically:1 weak:1 however:5 efficiency:12 comm:1 overestimated:1 jm:11 region:1 according:1 ln:1 raimond:1 variance:1 contribution:1 estimation:1 experimental:2 con:1 comment:2 cj:3 relevant:1 continuation:1 homodyne:12 moreover:1 schleich:2 described:1 publishing:1 basis:3 union:1 due:1 pj:5 ph:3 ariano:5 corresponding:2 photon:1 assert:1 those:1 case:2 ǫj:6 ǫn:2 evaluated:4 will:1 behavior:2 error:13 richter:1 taking:1 procedure:5 opt:2 vogel:1 refs:3 verges:1 non:1 itself:2 vanish:1 different:4 italy:1 perform:1 make:1 radiation:3 same:8 quant:3 largest:1 proved:3 several:1 european:1 used:2 see:2 effect:5 3pu:1 infinite:1 robust:1 cycle:1 lower:4 schr:1 unconditionally:1 well:1 analysis:2 simulated:1 very:1 arising:1 parametrically:1 proposed:4 increasingly:1 sources:1 lossy:1 paul:3 indexes:1 zoller:1 density:3 photons:2 guaranteed:1 other:1 lett:4 real:2 saturation:2 lacking:1 devised:1 possible:3 increases:1 mayr:2 press:1 using:3 loss:9 like:1 signal:2 accessible:1 because:1 methods:1 truncated:3 some:3 experiments:3 provided:1 tmr:2 scale:1 measurements:6 does:1 linearly:1 refer:1 core:1 noise:4 oscillating:1 clarendon:1 yuen:1 universit:1 raymer:1 actual:1 o:1 road:1 communication:1 into:1 photodetection:1 integral:1 bound:13 degli:1 additional:1 interacted:1 support:1 there:1 fast:1 noticed:1 low:1 stars:1 was:5 function:3 regard:1 but:2 repeated:2 state:24 convergence:5 true:1 exhaustive:1 truncation:8 prevents:1 below:2 uk:1 semiclass:1 similar:2 mechanics:2 cirac:1 associated:1 computing:1 measurement:11 meaningless:1 doesn:1 convergent:2 separating:1 relates:1 tomography:8 triangles:2 regime:1 functions:1 no:2 dressed:2 whereas:1 when:3 vanishes:2 valid:1 role:1 papers:2 conclusion:1 picture:1 elements:11 kinds:1 preceding:1 hirota:1 cos2:1 network:1 independently:1 longer:1 algorithm:2 dφ:1 time:1 indirectly:1
|
quant-ph9701010.txt |@word consider:5 remarkable:1 focus:1 leads:2 quadrature:4 whose:1 depend:1 calculate:3 paris:1 technique:1 tr:2 finally:3 efficiencies:1 squeezing:4 th:3 must:6 dramatically:3 amplitudes:3 far:2 emphasizes:1 choice:1 electron:1 summarized:1 experimentally:2 exact:1 condition:1 smithey:1 presented:1 large:9 optics:1 still:1 slower:1 oscillation:4 direct:3 approximation:1 rate:2 evaluated:3 further:1 errors:50 section:5 celebrated:1 analogously:1 expressed:2 homodyning:13 experiment:1 new:1 increasing:2 method:7 mea:1 behavior:6 degree:3 respectively:2 here:2 fisica:1 desired:2 asymmetry:2 cos2:1 eikx:1 along:2 strong:1 change:1 obtained:5 suitably:1 shift:2 study:4 larger:7 approaches:1 resulting:1 usually:1 opinion:1 studi:1 changes:1 nmax:2 via:1 useful:2 convolution:1 merely:1 outcomes:1 decrease:2 summation:1 eiφa:1 total:1 establish:1 unit:11 plot:4 use:2 asymptotic:1 call:1 therefore:3 theoretical:6 possible:1 more:6 introducing:1 becomes:1 operators:4 semilogarithmic:1 appendix:3 basically:1 particular:6 known:1 cases:2 pη:5 reconstructed:2 account:1 recall:2 equation:4 oscillator:6 reads:3 values:8 ρt:11 concepts:1 following:5 example:7 f0:9 leonhardt:5 figure:11 states:18 minimum:3 performed:3 arise:2 sharp:1 standard:1 rescaling:1 absolute:6 information:1 respective:1 end:1 turn:1 provide:1 means:5 feature:2 how:1 criterion:2 parameter:2 simplicity:1 max:1 after:7 derived:1 confirmed:1 drastic:1 law:1 data:11 introduced:1 light:1 explicit:1 element:7 so:1 fundamental:1 representation:5 integrand:1 order:4 holds:1 wigner:1 words:1 indeed:5 over:5 eqs:1 paper:2 through:1 statistical:27 volta:1 its:1 rapidly:2 decay:1 ln:1 laguerre:1 writing:1 resorting:1 fig:13 pavia:2 decreased:1 main:1 overcome:1 versus:5 non:7 greater:2 uhn:1 numerically:2 introduce:2 effects:1 they:2 oxford:2 now:2 developments:1 eigenvalue:2 february:1 hereafter:1 university:1 2x:4 2e:1 mode:1 each:4 found:3 universit:1 higher:2 macchiavello:1 mean:7 ed:1 energy:2 reduce:1 gaussian:2 related:2 expect:2 measurement:15 quantum:27 laboratory:1 eq:14 out:3 shown:4 matrix:67 space:3 furthermore:1 since:1 rev:7 denotes:2 increase:13 re:1 conclusions:1 suggesting:1 formula:1 squares:5 ref:2 shows:2 sinh2:1 written:2 diagonal:31 possibility:2 quite:1 reason:1 complicated:1 estimate:2 generate:1 derivation:1 re2:3 surement:1 bassi:1 introduction:1 hence:1 think:1 first:4 major:1 already:1 features:2 probability:5 kernel:25 number:29 relations:1 directly:3 noticed:1 open:1 size:1 given:6 necessarily:1 needed:6 ordering:2 leading:1 dipartimento:1 adopted:1 their:1 intermediate:1 calculations:1 perfectly:1 gives:5 part:2 x2:6 kept:1 than:6 oscillate:3 distance:6 kind:2 see:2 tomographic:1 limiting:1 annihilation:1 contrary:1 exhibit:1 generality:1 beck:1 seed:1 iφa:1 close:1 exchanging:1 any:8 zero:1 convenient:2 parks:1 indexes:5 k2:1 ideal:3 generalized:1 negligible:1 accuracy:5 circles:6 towards:2 trace:1 normal:2 phase:12 analytically:2 measured:10 deviations:1 considered:5 calculated:4 later:2 detectors:8 kn:4 exp:1 oscillates:1 fact:2 quantity:1 paul:3 show:10 random:3 relation:2 threshold:2 substituting:1 longer:1 based:1 knowledge:2 distributed:2 ox1:1 should:1 jan:1 analytic:1 factor:1 parabolic:1 constant:1 local:3 achieve:1 do:2 dj:1 dk:3 di:2 expectation:3 ones:1 dx:7 report:2 dt:5 normalizable:4 arxiv:1 factorization:2 investigate:1 analytical:1 fixed:11 view:1 scanning:7 set:3 achieved:2 detection:8 depends:2 individual:1 result:3 recently:1 contour:3 techniques:1 reconstructing:1 phases:12 detect:1 eigenfunctions:3 pattern:1 review:2 state:20 between:3 progress:1 notice:1 attention:1 terms:5 spectroscopy:1 2m:1 ikx:2 however:4 efficiency:19 comm:1 recent:1 demonstrate:1 distinguish:1 both:12 cos:1 reported:1 many:1 region:2 uncertainty:2 according:1 sensitive:1 variance:1 contribution:1 disappears:1 experimental:13 comment:1 filtering:1 conclude:1 simple:2 asymptotically:1 harmonic:3 nˆ:3 sampling:4 analyzed:1 respect:7 considering:2 pv:1 due:4 been:3 much:2 slowly:1 interest:1 ph:1 abstract:1 ariano:5 asymmetrically:1 corresponding:3 observable:5 photon:7 precision:5 coherent:15 determination:2 systematic:11 mail:1 denote:1 present:4 case:5 exception:1 value:6 will:3 evaluating:1 error:5 squeezed:15 situation:1 richter:4 procedure:4 opt:3 cylinder:1 sizeable:1 vd:2 shumovsky:1 averaging:2 vj:5 thus:9 vm:8 ik:1 vs:7 im:1 disappear:1 different:7 italy:1 propagation:1 generic:1 recursion:2 radiation:9 same:2 clearly:1 parts:2 quant:1 advances:1 finite:1 difficult:1 independent:6 used:2 upon:1 hand:1 v0:3 average:6 levels:1 purpose:1 noticeably:2 identity:3 cycle:1 lower:7 off:6 well:1 analysis:1 obviously:1 solids:1 without:2 sets:1 very:6 dimension:2 kiss:1 just:1 generally:1 accurate:5 obtain:5 relevant:2 alternative:1 converges:1 previous:1 exceptions:1 kluwer:1 density:27 photons:3 point:3 setting:1 lett:2 iφ:2 real:4 saturation:3 around:1 easily:1 read:1 evaluate:3 results:4 3pu:1 homodyne:14 increases:6 press:1 using:2 mod:1 loss:1 displaced:1 follows:2 steps:1 either:2 integrals:1 become:1 essential:1 because:1 methods:3 namely:1 experimentalist:1 creation:1 some:4 growth:2 moreover:2 oscillations:2 indirect:2 investigating:1 scale:1 dimensions:1 avoid:1 measurements:5 per:1 does:2 eliminate:1 prog:1 welsch:1 demonstrated:1 measuring:4 selfadjoint:1 noise:1 power:1 derivatives:1 processing:1 oscillating:1 clarendon:1 step:2 rhombi:1 eiφ:2 imaginary:3 raymer:3 takes:1 comparison:1 about:1 carried:1 vogel:2 saddle:1 dependence:5 reduced:1 range:4 a2:2 insufficient:1 2x2:4 slightly:1 road:1 considerations:1 raised:1 offdiagonal:1 previously:1 into:1 integral:4 bound:5 appropriate:3 references:1 operator:7 amsterdam:1 degli:1 additional:1 intrinsic:2 there:1 u0:7 fast:4 smoothing:1 anderson:1 modifications:1 stars:1 was:3 function:7 form:5 enough:4 but:1 convergence:2 true:4 faster:4 infn:1 made:1 algorithm:2 characteristic:1 maximum:1 us:1 um:8 below:2 uk:1 uj:5 fluctuations:2 distribution:1 semiclass:1 similar:2 called:2 detailed:1 saturate:10 ae:2 defined:3 universal:1 measure:1 influence:1 general:3 examine:1 our:6 tomography:1 distributions:4 triangles:6 functions:32 no:3 extract:1 whereas:1 when:1 detail:1 field:4 other:2 conclusion:1 deviation:6 briefly:3 elements:24 generates:1 calculating:2 polynomials:1 faridani:1 important:2 bounded:1 studied:1 risken:1 factorized:2 4x:1 dφ:7 required:1 equivalently:1 observables:4 n2:6 starting:1
|
quant-ph9701011.txt |@word limited:2 customary:1 consider:2 maximum:1 results:2 leads:1 quadrature:3 whose:1 amplification:2 depend:1 calculate:1 paris:2 fokker:1 eˆ:5 tr:8 commonly:1 finally:3 kη:7 those:2 th:3 include:1 norm:1 comm:1 g2:1 eiλx:1 wave:1 every:2 experimentally:4 exact:1 condition:3 northwestern:1 2κd:1 smithey:1 exponential:1 presented:2 turns:3 solution:2 damped:1 large:2 vector:1 small:2 eigenvalues:1 optics:1 upper:1 averaged:1 slower:1 consistent:3 sign:2 feasibility:2 zero:1 fiber:1 evaluated:2 concludes:1 further:1 estimated:1 marginal:1 4x2:1 goes:1 even:9 established:1 errors:7 appear:1 giving:1 d2:6 section:2 xφ:1 uniform:1 homodyning:17 reconstruction:5 new:3 method:12 confluent:1 submitted:1 respectively:1 here:2 understanding:1 following:5 inverse:1 nonunit:5 eikx:3 along:1 equations:1 differential:1 obtained:5 generalizing:1 2x2:2 leaves:1 vectors:2 allows:1 typically:1 through:4 products:2 pick:1 action:1 fourier:3 changes:1 via:1 convolution:2 extra:1 hermite:1 eiφ:1 plenum:3 outcomes:2 flexibility:1 analyzing:2 achievable:2 sgn:1 planck:1 confidence:1 additive:4 ˆs:1 would:2 positive:1 lasing:1 hudson:3 negative:1 a50:1 approach:1 therefore:3 squeezing:1 theoretical:2 more:6 integers:1 becomes:3 operators:21 oregon:1 particular:5 known:2 central:1 cases:1 hold:1 easiest:1 rη:12 recall:1 equation:3 work:1 oscillator:4 fock:4 values:1 evolved:1 concepts:1 growing:1 making:1 example:4 compare:1 give:1 91a:1 inaccessible:2 states:2 minimum:1 numbers:2 want:2 absolute:1 information:3 needs:2 end:1 s2:1 discussion:1 means:3 surpassed:1 how:3 nontrivial:1 pure:1 answer:1 acta:1 parameter:4 may:3 db:1 after:2 designed:1 date:1 representations:7 data:13 diagonal:1 short:1 undesired:1 dynamical:1 effective:4 beam:1 light:2 lines:2 trilinear:1 element:7 so:2 fundamental:1 things:1 representation:7 typical:1 holds:1 wigner:6 eigen:2 produces:2 over:7 soon:2 dv:4 thermal:6 paper:2 london:3 statistical:4 dw:1 existence:2 belavkin:3 still:2 covariance:1 bunch:4 perfect:1 group:2 probability:11 chosen:1 lo:4 fix:1 expectations:1 actually:5 better:1 estimating:2 detected:1 pavia:3 communication:4 schmidt:2 eugene:1 versus:3 non:1 nonideal:1 focus:1 splitter:1 pag:1 regarding:1 effects:1 they:1 half:3 eµ:4 now:5 hall:2 2t:1 eigenvalue:1 term:3 gets:1 2s:1 always:2 university:1 level:1 2x:10 normally:2 establishing:1 sufficiently:3 theory:1 inequality:1 mode:3 each:1 repeating:1 ηv:1 mean:6 domain:1 schemes:1 ei:2 generation:1 ed:4 energy:1 hypergeometric:1 gaussian:8 extended:2 obtains:8 measurement:7 quantum:27 happen:1 eq:37 out:6 shown:4 matrix:27 borderline:1 space:5 rev:11 denotes:6 looking:1 re:5 contained:1 istituto:1 formula:4 ref:8 viable:1 math:1 earlier:1 linear:1 interactions:1 mechanisms:1 fisica:1 possibility:1 quite:1 admits:2 completely:3 york:3 estimate:3 definition:1 r1:1 misuse:1 determining:1 bassi:1 ordering:6 place:2 exponentially:3 leading:2 hence:4 first:1 exotic:1 already:2 symmetry:1 scanning:2 variables:1 number:18 eqt:1 channels:1 simplified:1 least:2 directly:1 robust:1 take:1 given:7 introduction:1 unknown:1 eqs:4 amsterdam:1 system:2 adopted:1 needed:1 master:1 worlds:1 ordered:9 gives:2 unobtainable:1 ryzhik:1 proving:1 environmental:1 2at:1 optical:2 focusing:1 undoubtedly:1 than:10 remember:1 diffusion:1 kind:3 determines:1 double:1 namely:7 tomographic:1 limiting:1 annihilation:1 validity:1 fˆ:17 were:2 e2iφ:4 outcome:1 explicit:1 beck:1 argument:2 attenuation:1 randomly:1 say:1 idler:1 exchanging:1 seen:1 recover:1 any:12 conversion:1 genuine:1 depending:1 lim:1 k2:1 ideal:1 εn:1 generalized:4 detector:3 heisenberg:1 formulas:1 allow:1 trace:2 normal:16 mlynek:2 price:1 measures:1 most:3 regular:1 gradshteyn:1 nothing:1 assessed:1 measured:14 class:2 stands:1 considered:1 average:11 later:2 detectors:1 principle:1 exp:17 physics:1 fact:5 show:5 random:9 converge:2 x2:4 relation:3 substituting:1 trivial:1 lindblad:1 principal:1 slov:1 based:2 knowledge:2 aφ:1 unrealistic:1 distributed:1 written:2 should:3 jan:1 analytic:2 only:11 corresponds:2 convoluted:1 factor:2 parabolic:1 αe:5 local:2 achieve:1 equilibrium:1 dk:2 di:2 overall:2 expectation:12 satisfied:1 joint:1 cannot:6 dx:15 despite:1 report:2 reconstruct:1 dt:2 ds:2 evolution:2 fields:1 linearity:1 arxiv:1 factorization:1 imposed:2 experiments:2 common:1 though:4 prevents:1 including:1 valid:1 kernel:17 set:2 tation:1 exists:1 achieved:1 sensitivity:1 bounds:2 detection:9 eia:1 see:15 computer:1 radius:1 result:2 arg:4 terms:4 frequency:1 best:1 phases:4 satisfying:1 ways:2 pattern:1 review:1 currently:2 αa:6 state:15 various:1 heterodyne:12 use:2 between:4 progress:1 before:1 µa:1 multiplied:1 notice:4 ikx:1 recently:1 statistically:1 attention:2 weak:1 however:9 moyal:1 efficiency:15 ws:7 spoil:3 analyzed:1 ket:1 both:7 cos:1 toward:1 2n:3 irregular:1 desired:1 many:2 taking:2 according:3 admit:1 iv:2 smearing:1 fnm:4 expense:1 expression:1 finds:1 experimental:10 otherwise:1 cl:5 simple:2 continuation:1 homodyne:29 sampling:3 dimensional:1 simply:1 invariant:1 polynomial:1 respect:4 forms:1 described:1 basis:5 due:6 been:4 cauchy:1 interest:1 2ds:2 ph:1 δs2:2 universal:3 lett:7 ariano:12 generating:2 corresponding:3 2ix:2 observable:5 quantities:1 sufficient:3 photon:19 coincides:1 gen:1 coherent:3 systematic:2 input:1 idφ:2 denote:1 giacomo:1 present:1 case:13 laser:1 being:1 single:1 value:13 will:17 cast:1 while:1 suppose:1 error:4 squeezed:2 situation:3 richter:4 ill:1 procedure:2 iy:2 cylinder:1 larger:1 shumovsky:1 averaging:2 refs:3 thus:3 them:1 vn:4 equal:2 tomography:14 reads:2 il:1 affected:3 different:8 italy:2 generic:4 pay:1 make:1 same:12 clearly:1 complex:3 quant:1 emphasize:1 advances:1 filtered:1 proved:1 finite:2 grows:2 independent:3 used:4 schiller:2 upon:2 effect:2 hand:6 moment:1 levels:1 infinite:2 changing:1 invariance:1 identity:7 eigenvectors:1 recognized:1 lower:3 estimation:2 maximizing:1 nucleare:1 nevertheless:2 min:1 well:3 analysis:1 concrete:1 solids:1 without:1 consistency:2 model:1 parametric:1 dimension:1 usual:1 kiss:1 just:5 less:3 moments:2 generally:4 obtain:8 cˆ:2 saturates:1 sources:1 intervals:1 atomic:1 immediately:2 uller:1 paul:3 eigenstates:1 sampled:2 kluwer:1 density:7 conclude:1 guaranteed:2 evanston:1 other:8 ok:1 easy:1 theorem:1 relevance:1 electrical:1 excited:1 iφ:10 opt:2 iλ:1 fluctuating:1 insensitive:5 depends:3 easily:3 evaluate:1 iε:1 possible:4 admitting:1 harmonic:3 press:5 using:4 highly:1 loss:1 necessary:1 particle:1 follows:4 specific:1 either:1 sezione:1 anti:10 pereira:1 terminology:1 2qt:1 because:4 classical:1 truncated:1 rms:1 creation:1 some:8 underly:1 examples:1 table:8 indirect:1 1un:2 scale:1 lead:2 2e:1 electromagnetic:1 eiλ:2 measurements:3 2xe:1 does:3 provides:1 assuming:1 2a:1 measuring:6 noise:32 integrals:2 bl:1 equivalent:1 processing:1 continuing:1 agreement:2 expansion:12 binomial:1 output:2 super:1 hilbert:6 raymer:3 noisy:4 comparison:1 actual:3 pη:11 concretely:1 extending:1 macchiavello:4 aˆ:2 introduces:1 o:31 nonvanishing:1 whence:4 involving:1 greatly:1 2iφ:1 gβ:1 referred:2 book:1 presence:1 unbounded:4 into:2 integral:10 bound:5 phase:14 appropriate:1 references:1 yuen:2 operator:18 proportional:1 vj:1 rely:1 statistics:1 additional:2 there:1 question:1 transform:2 noticed:1 anderson:1 describes:3 102a:1 low:2 way:9 series:1 analyze:1 was:2 function:24 academic:1 complete:1 form:6 denoting:1 but:11 displacement:2 volume:1 hk:1 repeated:1 hn:5 gain:4 hm:1 convergence:2 line:1 true:4 raising:1 tempered:1 made:1 photocurrent:1 leonhardt:4 characteristic:1 robustness:1 up:3 us:4 achieving:1 below:1 un:1 limit:1 spectroscopy:1 uj:1 distribution:11 semiclass:1 detailed:1 wants:2 diverges:2 ae:2 defined:8 recognize:1 abstract:1 measure:2 am:3 general:5 engineering:1 scanned:1 exist:1 dλ:2 nazionale:1 lifetime:1 unsaturated:2 mauro:1 again:3 functions:5 compared:2 completeness:1 nm:6 nn:3 extract:1 whereas:6 populations:1 when:9 vanishes:1 field:25 priori:1 compares:1 department:2 scan:1 conclusion:1 polar:1 briefly:1 elements:7 kinds:1 models:1 symbol:2 hirota:3 uniformly:1 polynomials:1 includes:1 faridani:1 a2:6 bounded:6 allowing:1 suited:1 studied:1 variable:7 astronomy:1 sides:2 independently:1 implies:1 faster:2 algorithm:4 dφ:9 resolution:1 interval:1 dσ:1 factorizes:1 time:2 observables:2 n2:2 starting:2 having:1
|
quant-ph9701012.txt |@word proposition:2 represent:3 consider:7 limited:1 lack:1 results:3 four:3 commute:4 generalize:2 expressions:1 aˆ1:2 compact:2 excludes:1 violate:3 iii:1 deterministic:3 tr:40 answered:1 restriction:1 otv:1 th:1 under:1 stochastic:1 worth:1 accardi:2 conjecture:1 straightforward:3 orthogonal:1 very:2 frequencies:13 springer:1 choice:8 every:2 orientations:1 experimentally:1 instituut:1 encounter:2 generalised:1 switches:1 p4:3 presented:1 notes:1 magnet:2 vector:20 indices:4 ups:1 sin2:4 measurable:3 conjunctions:11 second:2 theory:3 spectral:2 aim:1 appear:2 incompatible:4 section:4 experiment:8 en:1 above:1 new:1 consisting:2 simultaneously:3 respectively:1 never:1 here:3 free:1 represented:2 σab:2 along:3 equations:1 xε:1 obtained:3 sending:1 remark:7 incoming:1 technical:1 conformity:2 vectors:4 allows:1 reason:1 commonly:1 p2:5 simultaneous:1 published:2 formulated:2 spatially:1 elaborated:1 outcomes:5 stern:3 apply:1 use:1 proceed:1 would:1 prove:8 probabilities:42 ψs:1 etc:1 chooses:1 emits:2 classically:1 therefore:1 taken:3 selects:4 theoretical:2 more:5 separated:2 operators:3 testified:1 validity:1 berlin:1 carrying:1 particular:3 known:2 foundations:3 cult:1 must:2 account:2 recall:3 work:4 theories:2 reproduce:1 remain:1 assumptions:2 values:4 three:3 following:10 making:3 my:1 example:3 proof:10 f1:1 f2:1 give:1 table:4 pk1:2 performed:9 sense:1 µj:7 verlag:1 respective:1 january:1 discussion:1 means:5 s4:1 regions:1 how:1 pure:2 sin:4 stand:1 product:3 algebra:2 may:2 after:1 variant:2 containing:1 plane:1 iuap:1 fi:1 geometrical:1 data:1 compatibility:2 fn:1 natural:2 effective:15 brussel:1 computations:1 consequently:3 explicit:2 switch:4 ones:1 so:6 fundamental:3 correlation:19 taking:1 representation:26 order:6 typical:1 horne:9 numbers:3 pointed:1 choose:1 held:1 experiments:8 through:1 statistical:2 argued:1 existence:3 satisfies:1 pj1:2 its:1 thank:1 chosen:1 arrangements:1 actually:1 degrees:1 condition:4 fij:1 mail:1 hidden:3 main:4 might:1 correspondence:1 them:6 good:1 combination:2 orthodox:2 budapest:2 introduce:3 emphasised:1 mention:1 p13:5 p14:5 they:8 half:1 formulating:1 now:10 discuss:1 similarily:2 easily:1 february:1 equality:1 always:3 university:1 identified:1 kern:1 realistic:1 inequality:1 each:4 accommodated:1 entirely:1 2j:1 constraints:2 subset:1 everyone:1 formulate:3 1996a:4 related:2 magnets:3 measurement:10 quantum:26 our:4 happen:1 event:5 aˆ2:1 out:5 deals:1 shown:3 matrix:1 space:5 god:1 furthermore:1 rev:2 denoted:1 lecture:1 get:2 occurs:1 shows:2 numerical:1 linear:5 aˆj:5 associate:2 hull:2 aˆb:3 admits:2 completely:1 toy:1 usual:1 beginning:3 axioms:1 definition:6 pairs:1 language:1 wetenschappen:1 could:1 orthocomplemented:1 voor:2 int:2 onto:1 think:2 first:3 initial:1 probability:19 xb:4 xa:16 restrict:1 multiplying:1 representations:3 impossible:1 precisely:1 given:7 necessarily:3 publication:1 introduction:3 πn:3 system:1 their:3 dichotomic:1 statement:1 gives:2 completed:1 exactly:2 assumption:6 sign:1 than:2 relative:5 last:3 showed:3 accordance:1 cimento:1 zero:1 claim:1 whenever:1 polarizer:2 were:2 providing:1 spins:1 generality:1 nuovo:1 epr:1 measure:6 generalization:3 already:1 say:1 elte:1 disjoint:1 any:2 generalizes:1 convenient:1 able:1 isolated:1 indexes:1 k3:2 k2:2 coplanar:1 εi:11 generalized:6 εj:1 objective:1 performance:2 detector:4 even:1 play:1 allow:1 opposite:1 measures:2 singlet:3 pair:1 acknowledgements:1 why:1 don:1 consequences:2 considered:1 performances:6 clear:1 sometimes:1 detectors:1 vertices:2 universiteit:1 mechanical:2 left:6 physics:8 fact:4 thomas:1 show:2 violation:2 supported:1 notations:3 uεi:4 gerlach:3 decompositions:1 substituting:1 find:1 based:1 dice:1 jan:1 dalibard:1 only:8 subsection:2 local:3 do:4 his:1 1995a:5 notation:2 1995b:2 dependent:1 express:1 macroscopical:1 cannot:2 altogether:1 during:3 symmetrically:1 bˆ:8 numerous:1 arxiv:1 yield:2 naked:9 polariser:1 roger:1 contain:1 valid:2 view:1 set:10 thesis:1 exists:1 violated:1 kolmogorov:1 j1:12 j2:10 j3:2 observed:7 p24:5 result:3 p23:5 discussions:1 terms:1 forthcoming:1 closer:1 ωj2:2 detect:1 inequalities:15 mentioned:1 uε:12 state:6 closed:2 between:2 incompatibility:3 ui:1 geometric:1 µa:2 supposed:2 notice:2 recently:1 extend:1 nature:1 εii:1 complement:1 however:1 hypothesis:2 censorship:8 article:2 come:1 distribution:6 both:3 interpretations:3 outcome:2 vub:1 µab:2 many:1 region:2 density:2 according:2 called:3 propagation:1 admit:3 logic:1 mean:1 expression:3 experimental:5 among:2 afterwards:1 point:1 simple:2 ac:1 directions:10 associated:9 fruitful:1 testable:1 november:1 described:1 basis:2 union:1 due:1 been:2 xai:19 xaj:6 pa:1 xan:2 basic:1 collected:1 ph:1 pi:7 pn:4 define:3 direction:15 aj:11 corresponding:8 observable:3 sufficient:2 wet:1 photon:2 precision:1 coherent:1 observe:1 proven:1 angles:1 polytope:5 general:1 spin:6 present:2 case:6 p3:3 p1:9 subsets:4 xa1:2 xa2:2 frequences:1 value:2 choices:2 will:7 institute:1 replaced:2 shall:8 involved:1 determinism:1 situation:2 property:2 σa:2 kolmogorovian:39 terminology:1 thus:1 ij:3 properties:2 ready:1 different:5 formalism:5 d10:1 author:1 lett:1 same:3 pab:2 complex:1 quant:1 events:18 used:3 i1:33 i2:24 disagree:1 πij:5 experimenter:1 brussels:1 framework:1 polarisation:3 well:6 analysis:1 without:1 components:1 sets:2 claims:1 model:3 know:1 just:1 generalisation:2 generally:1 obtain:1 via:1 aspect:2 useful:1 yes:2 previous:1 doctoral:1 instance:2 photons:2 bell:9 seems:1 empirically:1 source:3 belongs:2 describable:2 easy:2 theorem:20 usage:1 build:1 real:5 tests:1 vrije:1 articles:1 fulfillment:1 showing:2 k4:2 possible:4 department:1 entangled:1 world:1 accepted:2 moreover:1 pitowsky:19 theor:2 necessary:2 like:2 particle:5 follows:7 performing:1 arbitrary:2 become:1 conclusion:4 essential:1 szab:16 mathematical:2 because:6 methods:1 classical:18 conditional:5 some:7 examples:1 convex:4 measurements:24 defined:3 does:2 decomposition:4 refer:1 power:2 equivalent:2 ωab:2 perpendicular:1 found:1 hilbert:1 simpler:1 integers:1 about:2 carried:3 universe:2 aˆ:12 generated:1 o:16 compatible:8 aˆi:13 a2:7 obeys:1 introduced:2 os:1 projectors:8 contains:4 letters:2 into:9 predictions:1 multiply:1 right:6 references:1 operator:1 imposed:1 orsay:14 inspects:1 realisation:1 there:6 question:2 way:3 was:2 σj:1 form:5 forming:1 but:10 hu:1 pj:2 1996b:1 true:1 he:4 directed:1 made:1 whether:2 wish:1 up:5 devices:3 placed:1 ωj:9 those:1 ωa:2 problem:2 similar:1 agree:2 mechanics:3 pij:7 ab:8 proved:3 ai:27 abstract:1 describe:1 covers:1 denote:5 clauser:9 proves:1 exist:2 laboratory:1 durt:9 commuting:2 check:4 constructed:1 ni:5 functions:1 compared:1 paradox:1 us:8 no:6 when:2 reality:1 other:2 details:2 test:1 you:1 techn:1 polarisations:1 elements:1 gergely:1 models:1 symbol:1 representable:1 a1:15 meaning:3 important:3 realised:1 variable:4 pi1:1 sides:3 structure:1 suffers:1 implies:1 longer:2 assume:6 together:5 original:3 weights:1 observables:1 having:1 representative:1
|
quant-ph9701013.txt |@word neighbors:2 limited:4 logarithms:1 sci:1 consider:4 represent:1 control:1 magnetic:1 separates:2 results:3 existing:1 four:3 andre:1 england:3 notationally:1 computation:11 foundations:2 consists:8 expressions:1 adjustment:5 contributions:2 issues:1 soc:2 relationships:1 whose:2 ertel:1 impressive:1 terms:2 violate:1 graph:5 technique:1 vs:1 aggregations:1 factoring:4 finally:1 program:1 depending:1 decomposition:2 analogous:2 include:8 dramatically:2 indicating:3 applied:1 amplitudes:9 philips:1 takes:1 very:7 decreases:2 rise:1 emphasizes:1 choice:11 unstructured:20 vegas:1 worst:3 suggests:2 mixing:2 affect:3 ln:2 difference:2 nightmare:1 wolfgang:1 categories:1 severely:1 prespecified:4 subsets:7 immediately:1 presented:8 issue:1 michael:1 solution:54 fewer:4 try:3 solved:4 tightness:1 adjust:1 progress:1 section:3 small:9 enhance:1 society:1 inconsistent:2 smaller:8 neighborhood:2 abstracted:1 probabilities:1 consistent:3 edu:1 estimates:1 direct:3 maintain:1 rate:3 cost:42 design:2 value:13 incrementally:8 zu:1 nogoods:44 machines:3 theory:7 even:8 errors:2 adds:1 appear:1 richard:1 remi:1 giving:2 sum:6 selected:3 mechanics:1 while:8 uniform:3 current:1 grover:1 above:3 new:16 construction:2 contributes:2 method:16 contrast:3 satisfy:2 compact:1 full:3 simultaneously:1 policies:2 conf:2 respectively:5 fewest:1 never:2 csps:15 here:11 scott:1 ranges:3 reported:2 explore:1 slow:2 focused:1 web:1 groups:1 address:2 represented:1 consideration:1 november:2 quite:2 respect:1 appears:3 change:1 extreme:8 alto:2 search:139 dashed:2 hamiltonian:1 steven:1 institute:3 recursive:2 study:2 larger:9 allows:1 expression:1 commonly:1 ignoring:1 los:4 trial:2 amount:1 periodic:1 resulting:4 deutsch:4 sjl:1 pick:1 resonance:1 bob:1 suitable:1 changes:4 options:1 involves:1 plotted:2 examining:1 useful:11 hogg:6 scales:1 requiring:2 highly:6 initialize:1 neil:1 boolean:1 decrease:5 opportunities:2 incorporate:2 apply:1 orderings:1 total:1 propositional:2 linearly:3 readily:2 alamitos:3 plot:8 use:9 superpositions:2 would:12 analytic:2 remains:3 positive:3 contains:1 toffoli:3 negative:1 next:2 annealing:2 few:7 ψh:1 memory:2 25th:1 type:2 theoretical:3 today:2 more:19 separated:1 beyond:1 ftp:1 zecchina:1 comparison:2 clearly:1 becomes:3 about:6 monroe:1 tested:1 mmax:4 studied:1 particular:13 known:1 coyote:1 cases:11 nodes:3 must:4 tad:5 ma:3 extension:1 unruh:1 indexed:1 science:6 ρk:2 averaged:1 fast:1 london:1 theories:2 ρs:5 incremental:4 values:12 norm:1 morgan:1 following:1 strategies:1 specialized:1 example:8 minima:2 ions:1 compare:1 computers:12 challenging:1 figure:14 give:14 expanding:1 suggestions:1 haroche:1 implementations:1 states:16 effectively:4 successively:1 assumptions:13 numbers:1 νc:1 allowed:1 scheduling:1 standard:2 simulation:5 occur:2 philip:1 guarantee:1 feynman:1 end:1 advantage:2 rather:6 discussion:1 algorithms:17 menlo:2 located:1 varies:2 actual:1 field:2 instead:4 csp:6 brassard:1 pub:1 map:3 product:1 supersets:8 description:2 may:14 suppose:1 after:7 minimum:7 containing:3 reflect:2 davis:1 produce:2 inst:1 studies:1 improving:2 representations:1 concentrating:2 grow:3 types:3 efficiently:1 included:1 realized:1 effective:8 computations:3 jair:1 correspond:3 element:2 sk:3 mark:1 complexity:2 ones:2 so:13 specifying:1 allow:2 reduced:1 every:3 operate:4 dream:1 order:3 michel:2 typical:5 operations:1 restriction:1 havel:1 22n:1 developed:1 over:8 move:2 vary:1 major:1 selman:2 paper:2 through:6 enumeration:1 denotes:1 during:1 mentioned:1 cold:1 still:4 ieee:4 its:15 before:2 perfect:1 rapidly:8 how:16 chosen:2 interesting:3 solving:1 exhibits:4 edge:3 forms:1 complex:4 degrees:1 systems:4 annual:1 policy:1 potentially:1 might:2 easier:2 freeman:1 them:3 good:8 motivated:1 greater:2 combination:1 similar:3 questions:2 practice:1 number:33 scaling:11 framework:6 characterized:1 they:6 optimal:2 sleator:1 superset:1 developments:1 matched:1 represents:1 february:1 2k:2 characterizes:2 preclude:1 level:12 ensemble:3 possibilities:2 magnitude:2 l2:2 editor:3 andrew:1 each:35 found:8 2n:4 higher:2 decreasing:1 underconstrained:1 constraints:25 subset:5 just:9 determine:1 fairly:1 generation:1 series:1 alan:1 hard:8 reduce:1 related:1 slowdown:2 items:1 unitarity:1 abstraction:2 expect:1 combining:1 quantum:70 clauses:2 operation:1 transitions:8 eq:13 out:2 category:1 large:8 shown:9 reducing:2 matrix:30 space:5 restricted:1 furthermore:3 since:9 interference:5 research:3 increase:3 combinatorial:13 vector:4 multiply:1 hill:1 maximized:1 formula:5 illustrate:1 evaluation:4 bart:2 shows:12 earlier:1 drr:1 linear:3 lawrence:1 discrete:1 maintains:1 diagonal:7 possibility:1 mapping:16 vazirani:1 difficulty:1 completely:1 dependencies:2 complicated:2 dynamics:2 conflicts:6 intermediate:2 dmax:2 remainder:1 generate:2 log:5 kaufmann:1 definitely:1 work:1 determining:1 could:9 transition:12 benioff:1 running:1 times:2 ordering:1 v3:2 exponentially:4 incorporated:1 serge:1 hence:2 retain:1 hu:1 facilitate:1 assign:1 heuristically:1 singleton:1 initial:5 probability:12 edges:1 clause:4 variables:11 encouraging:1 lond:1 instances:11 simplified:1 approximately:3 directly:4 precludes:1 precisely:1 open:4 size:50 timothy:1 given:10 necessarily:2 asymptotic:2 similarly:2 introduction:1 data:1 berthiaume:1 structured:23 πn:1 least:5 minton:1 their:6 assumption:4 cirac:1 normalization:1 trend:1 perfectly:1 final:4 williams:2 gives:8 parc:1 las:1 relationship:2 ratio:6 johnson:1 recursively:1 exactly:4 park:2 wiley:1 immediate:7 task:1 part:2 too:1 somewhat:7 july:1 maintaining:1 than:23 specify:1 population:1 diffusion:2 relative:1 scheme:1 unfortunately:2 sections:1 require:3 database:1 likely:5 limiting:1 matter:1 classes:2 editors:4 doubly:1 amplitude:26 zx:1 toward:4 abstracts:1 turing:2 behaviors:2 function:2 motivation:2 false:4 san:1 generality:1 remained:1 jean:1 seth:2 predicts:1 10th:1 argument:1 curves:6 randomly:3 substantial:6 analysis:4 further:2 need:1 seen:2 concentration:3 constrained:11 saw:1 any:10 viewed:3 relatively:11 paths:5 built:1 zero:3 min:10 efficient:1 latter:1 governs:1 proportional:3 maximum:10 note:2 mix:1 empirically:2 without:5 harald:1 take:5 online:1 finding:3 performance:12 unconstrained:1 effectiveness:1 kirkpatrick:2 multiple:2 shade:1 though:2 sets:60 intl:1 whk:1 umesh:1 most:6 plus:1 significant:5 representation:2 phase:19 iterate:1 sophisticated:4 probabilistic:2 class:1 cs:1 observation:5 ψk:1 considered:2 incomplete:1 average:18 sometimes:1 differ:1 kl:5 qualitative:1 trapped:1 points:7 rev:1 error:5 urs:3 constrain:1 left:2 physics:10 review:6 fact:3 heuristics:8 shor:3 selection:1 particularly:5 show:5 random:5 gershenfeld:1 page:2 soluble:1 colors:2 spaces:2 chuang:2 solutions:31 binomials:2 degraded:1 find:11 tapp:1 feng:1 coloring:4 based:7 knowledge:2 ganguli:1 halves:1 implementation:1 distributed:1 enough:1 start:1 should:2 jan:1 increasingly:1 only:17 difficulties:1 black:4 ethan:1 factor:3 constant:2 bernstein:1 local:3 first:6 dn:2 do:7 intractable:1 insight:1 dk:5 stabilization:1 wide:1 fahmy:1 connections:1 simplest:1 overall:4 cannot:2 christopher:1 fastest:1 lighter:1 negated:2 report:1 dw:1 conjunction:1 neither:1 gray:6 evolution:1 increasing:3 colin:1 indicated:1 goldwasser:1 arxiv:1 encyclopedia:1 consisting:1 experiments:2 common:3 mapped:1 gilbert:1 including:2 fixed:2 shapiro:1 requirement:3 set:42 computed:1 exists:1 intelligence:6 testing:1 operates:1 observed:1 differs:1 depends:4 computer:5 result:1 ignores:1 discussions:1 close:3 best:6 techniques:1 phases:10 satisfying:1 mechanically:1 ways:2 nuclear:1 away:2 definite:1 artificial:6 tend:3 jt:1 state:12 determined:4 various:2 closed:1 between:2 drawn:1 moving:5 conditions:1 checks:5 berkeley:1 available:2 comparable:1 barenco:1 recently:1 ability:2 nature:2 initially:2 comp:1 focus:4 however:4 acknowledgements:1 equals:1 dmin:2 gilles:1 extent:1 limitation:1 distinguish:3 group:3 come:1 distribution:1 tycho:1 improve:7 suggested:1 both:7 aaai:2 providing:1 improved:1 gelatt:1 limits:1 many:24 region:1 conclusions:1 equal:7 etc:1 garey:1 improves:1 raimond:1 context:2 concentrates:1 35th:1 distinction:1 contribution:2 mean:6 com:2 dkk:1 boyer:1 otherwise:5 among:22 unclear:1 point:6 simple:9 ca:8 others:1 corresponds:3 satisfaction:4 levesque:1 exploit:3 taylor:1 simply:1 adding:1 maximize:2 church:1 cancel:1 ordered:3 throughout:1 vecchi:1 logic:2 considering:2 better:4 cory:1 contraint:1 described:8 second:4 basis:4 addition:1 dan:1 invert:3 computing:5 due:3 been:3 quickly:2 genetic:1 much:6 slowly:3 combined:1 interest:1 expected:7 applying:1 ph:1 wx:1 abstract:5 empty:2 fig:16 concentrated:1 coherence:1 corresponding:9 ψkl:2 natl:2 great:1 sh:1 locations:1 bulk:1 maps:3 coherent:2 backtracks:1 zurek:1 benefits:1 systematic:1 constructing:1 denote:2 αcrit:1 spirit:1 those:5 case:5 13th:1 exponential:5 solid:1 ensembles:3 expanded:2 harder:1 empirical:1 evaluated:4 choices:11 will:12 cast:1 near:4 optimization:2 abrupt:1 bounds:1 behavior:19 applies:1 stopping:1 situation:1 debatable:1 property:2 cheeseman:1 guide:4 procedure:6 manner:2 landauer:1 technical:1 unitary:5 n2n:1 laflamme:1 phenomenological:1 metric:1 luby:1 thus:36 pruned:1 encountered:1 continues:2 examined:3 hector:1 receives:1 illustrates:1 pruning:2 sequentially:1 binary:2 different:14 weinfurter:1 develop:2 prior:2 generic:1 suggest:3 lett:1 same:10 linked:2 another:5 parts:6 quant:1 emphasize:1 discussed:1 largest:1 modification:2 according:2 sat:1 grows:10 conflict:1 difficult:5 independent:2 used:18 http:1 assigns:1 see:5 again:1 assignment:5 numerical:1 upon:1 effect:1 v1:4 v2:2 levels:1 uses:5 variance:3 changing:2 dkl:1 single:19 mappings:4 relies:2 lower:2 weakly:1 off:2 center:1 fully:1 nevertheless:4 makes:2 variety:4 well:6 remain:3 deal:1 double:2 costs:2 solve:4 encounter:1 consistency:6 inability:1 benefited:1 lloyd:2 paradigm:1 wider:1 consisted:1 gates:2 world:1 construct:3 exploits:2 proposed:2 less:4 being:5 generally:2 guided:1 adjustments:1 networks:1 obtain:1 assigned:2 underlying:5 identify:1 entropy:1 actually:1 integer:2 followed:1 overconstrained:1 previous:15 drexel:1 heuristic:8 amr:1 multiplication:2 zoller:1 instance:3 informal:1 conclude:1 except:1 improvement:5 lattice:21 nor:2 easy:2 s01:1 skm:3 symp:1 ranging:1 guarantees:1 remaining:3 david:6 independently:1 tests:1 aspects:2 satisfiability:6 wrs:1 evaluate:1 showing:2 measurement:2 possible:15 usefully:1 early:2 np:3 increases:1 ρkl:2 press:7 using:11 variants:1 unique:2 vν:1 color:3 occurring:1 loss:1 modifications:1 necessary:11 helpful:1 identifying:2 exploiting:2 future:2 sizes:5 html:2 specific:5 steps:23 either:3 experimentally:1 follows:1 nonintegrability:1 become:3 works:1 reduces:1 depend:6 accessible:1 poor:1 beneficial:2 because:8 old:1 often:6 classical:35 hoyer:1 simplicity:2 decoherence:4 conditional:2 some:11 searching:2 polynomial:1 growth:5 examples:7 palo:2 specified:3 unless:1 peter:3 intractability:1 ψr:1 provided:1 scale:2 describing:1 bottom:1 parallelization:1 decision:1 overlap:3 does:5 connecting:1 select:4 provides:6 assuming:1 indication:4 proc:14 neatly:1 run:1 power:2 location:1 isaac:1 selecting:1 2c:1 continuing:1 illustration:1 step:11 uz:1 unlike:2 able:1 although:5 offset:1 plots:1 analyses:1 properties:2 simpler:5 integers:1 exhibit:1 goods:9 rare:1 bars:2 constraint:8 completing:1 prove:1 introduces:2 generated:2 o:25 mixes:2 practical:1 distinct:2 range:6 extensions:1 greatly:2 done:2 ψs:9 johnston:1 introduced:3 slightly:2 minimizing:1 road:1 peak:3 repair:5 equally:1 computational:6 letters:3 simulated:2 washington:1 assignments:10 wineland:1 acm:1 into:4 within:3 numerically:1 www:1 three:2 pair:2 appropriate:3 right:2 references:1 inverting:1 primarily:1 artur:1 couplings:1 strategy:2 theoretically:2 methods:28 clustering:1 analytically:4 span:1 additional:4 classically:2 transfer:2 there:13 question:5 approximate:1 specifically:9 pages:13 stuck:1 workshop:6 lov:1 low:1 way:5 analyze:1 was:8 third:2 lowest:1 considerably:2 complete:11 form:3 offer:1 forming:1 adjusting:2 alain:1 xerox:3 but:21 applicable:1 repeated:1 hierarchical:1 repeatedly:1 mitchell:1 riccardo:1 inverted:1 true:3 utilizing:3 especially:1 count:2 made:4 compute:2 builds:3 consist:1 versions:1 whether:7 selects:1 robustness:1 up:3 until:1 um:1 url:1 below:7 jozsa:1 critical:1 vhk:1 vhj:1 approaches:1 demonstrate:1 problem:76 adriano:1 nogood:11 realizable:2 multiplications:1 connect:1 detailed:4 laird:1 kh:1 associated:1 28th:1 item:2 defined:1 universal:3 measure:1 condition:2 deep:3 general:8 substantially:2 examine:3 proves:1 exist:2 periods:1 simulations:3 partly:1 moves:1 check:1 august:1 physical:7 incorrect:1 high:4 functions:1 avoided:1 nl:3 entirely:1 no:8 trials:2 ekert:1 monasson:1 when:13 treatment:1 spectroscopy:1 occasional:1 sk1:3 other:16 compares:4 details:2 rolf:1 test:2 francisco:1 principle:1 node:3 symposium:3 stat:1 elements:19 tight:1 superposition:4 divincenzo:1 models:1 mechanical:3 problems:69 variation:3 includes:1 william:1 chance:1 important:6 recent:1 allowing:4 suited:1 vectors:1 variable:8 maximally:1 disjunction:1 needed:1 structure:39 feasible:2 searches:16 max:8 regime:1 algorithm:71 u1:5 starting:8 statistical:1 required:6 changed:1 having:4 cambridge:3 parallelism:1 time:4 international:1 n2:2 requires:8 original:1
|
quant-ph9701014.txt |@word concept:2 partial:1 results:2 entropy:19 consists:3 compact:3 certainly:1 calculate:1 ohya:2 graph:1 tr:2 alberti:1 helps:1 belonging:1 straightforward:1 orthogonal:1 every:4 matrices:6 convexity:2 treating:1 z12:1 pullback:1 vector:1 work:1 zj:3 zk:1 sign:1 zero:1 dynamics:1 peredachi:1 canonical:1 aim:1 stands:1 ψn:1 sum:4 sup:3 new:2 exercise:1 coefficient:1 full:1 equals:1 understanding:1 behaviour:1 ansatz:1 address:1 quite:1 appears:1 extreme:3 obtained:1 benatti:5 allows:1 published:1 simplex:1 uniquely:1 projection:2 distinguishability:1 visible:1 tools:1 use:3 working:1 analytic:1 remains:2 positive:1 negative:1 next:2 ψk:7 live:1 m1:1 theoretical:1 more:1 optimizing:1 operators:4 berlin:1 appendix:1 known:2 cases:1 iii:2 springer:1 word:1 mn:4 roof:11 caratheodory:1 concepts:1 trans:1 my:2 example:3 proof:1 ωex:1 expanding:1 preserving:1 states:14 verlag:1 information:9 how:1 pure:11 optimal:9 ensemble:6 map:1 algebra:12 may:1 after:1 containing:1 applications:1 physik:2 short:4 dynamical:1 element:1 extremal:7 so:1 decreasing:1 definitions:1 order:1 restriction:1 indeed:2 paper:1 through:1 looks:1 mentioned:1 ieee:1 its:14 monotonicity:3 unitaries:1 ln:2 affine:2 connes:2 choose:1 constitutes:1 mail:1 rockafellar:1 versus:1 non:1 good:1 introduce:1 bound:1 framework:1 they:3 now:4 channels:1 term:2 equality:2 university:2 concave:5 identified:1 orthonormal:1 iff:5 repeating:1 characterized:1 2k:2 operator:7 sketched:1 quantum:9 our:1 shown:2 matrix:3 space:4 furthermore:1 rev:3 holevo:2 replacing:1 contained:1 denoted:1 suffices:1 zj2:1 math:3 shows:1 linear:1 associate:1 roofs:1 hull:7 diagonal:3 mapping:2 completely:1 stochasticity:1 institut:1 monographs:1 generate:1 definition:2 qj:1 r2:2 convexly:2 length:1 wehrl:1 hence:1 first:2 number:2 system:1 restrict:1 augustusplatz:1 another:3 open:1 properties:1 theoretische:1 tool:1 continuous:2 part:4 uhlmann:4 coefficients:1 observed:1 albuquerque:1 princeton:1 fuchs:3 require:1 see:5 argument:1 conjugate:1 need:1 seen:2 cumbersome:1 any:2 depending:1 convenient:1 latter:1 davies:1 coincide:1 channel:11 trace:1 though:1 object:1 systems:1 germany:1 appear:1 considered:1 coincides:2 face:1 proceedings:1 points:1 physics:2 fact:1 probl:1 show:3 notations:1 relation:2 decompositions:2 find:1 q1:1 based:2 writes:1 jan:1 lemma:5 only:5 inherited:1 continuity:2 mixture:1 handle:2 get:2 beat:1 de:1 methods:1 ones:1 international:1 runs:1 qr:1 dissertation:1 arxiv:1 common:2 fixed:1 set:11 bounds:1 relative:2 depends:2 φex:4 satisfying:2 ωk:2 state:13 smallest:1 hopefully:1 invariant:2 boundary:3 caves:1 petz:1 terms:1 extend:1 comp:1 however:1 comm:1 group:1 relying:1 essentially:1 last:1 uncertainty:1 equal:1 fulfilled:1 hω:15 colloquium:1 gibbsian:1 uni:1 estimation:1 expression:1 comes:1 unitarily:1 ch:3 conclude:1 reasons:1 leipzig:3 dimensional:2 assertions:1 dependent:1 respect:6 particulary:1 armin:1 coarse:1 pj:13 pk:4 ph:1 algebras:5 define:1 defect:1 observe:1 xxi:1 general:1 case:1 myself:1 narnhofer:4 will:2 property:1 mexico:1 von:2 thus:1 ii:4 reads:2 different:2 perform:1 concavity:1 quant:1 gibbs:1 modification:1 finite:4 subalgebra:7 difficult:1 mutual:2 publ:1 identity:2 eigenvectors:1 task:1 off:1 analysis:1 without:1 sets:1 entry:1 dimension:1 λp:1 being:1 determinate:1 λk:1 λj:2 disturbance:1 density:8 similarities:1 add:1 setting:1 extends:1 lett:1 easy:1 theorem:3 input:9 bifurcating:1 real:2 measurement:1 possible:1 press:1 using:1 unique:1 mod:1 like:2 identifying:1 follows:2 performing:2 output:6 works:1 reduced:3 terminology:1 accessible:4 reidel:1 because:1 neumann:2 examples:2 convex:20 proofs:2 manipulations:1 decomposition:7 refer:1 rep:1 equivalent:1 isomorphy:1 universit:1 commutative:2 gained:1 mutually:1 theory:2 inclusion:1 levitin:1 communication:2 into:1 within:1 functional:4 hermitian:3 references:1 elementary:1 often:1 span:1 support:1 there:2 question:1 long:1 start:1 call:2 treat:1 function:5 elsewhere:1 form:1 but:3 gain:1 implies:1 trying:1 true:2 compute:1 whether:1 la:1 up:2 ur:1 below:1 ωj:3 called:6 eigenvector:1 recalling:1 mechanics:1 taylor:1 computing:1 defined:1 abstract:1 describe:2 texts:1 denote:1 peres:1 inf:4 defines:4 functions:1 no:1 other:1 mathematics:1 thirring:2 generated:1 4z:3 assume:1 unital:5 together:2 graining:1 equivalently:1 weights:1 original:1
|
quant-ph9701015.txt |@word code:9 consider:1 results:1 illustrated:1 entropy:3 expressions:1 whose:2 terms:1 knill:1 subjected:1 vs:2 send:1 environment:2 finally:3 those:2 under:1 analogous:3 include:1 sent:6 division:1 random:4 string:1 straightforward:1 orthogonal:3 splitting:1 every:1 telling:1 matrices:2 transmission:5 notes:1 fewer:2 occurs:1 deals:1 discrete:2 erasures:3 section:3 optics:1 noted:1 upper:5 smaller:1 mceliece:1 rate:8 pass:1 further:1 theory:5 even:2 what:1 errors:5 assistance:1 dephasing:2 decoding:3 errorcorrecting:1 above:2 nonadditivity:1 shared:1 contributes:1 contrast:2 hash:2 notions:1 respectively:4 teleportation:2 here:2 diagonal:1 operating:1 excess:1 alone:3 ensembles:1 obtained:2 sending:5 incoming:2 sender:5 institute:1 study:1 allows:1 amount:1 resulting:1 schumacher:5 hospitality:1 bob:9 followed:1 bounds:3 vii:1 welch:1 apply:1 total:1 establish:1 unit:1 use:12 additive:2 asymptotic:6 usa:1 army:1 remains:2 positive:8 distinct:1 classically:1 noisy:2 achieving:1 more:5 separated:3 optimizing:1 sharing:1 formally:1 knows:1 outputs:1 pairs:3 flag:1 particular:2 known:11 iii:1 must:3 high:1 springer:1 ibm:1 science:1 remain:2 rains:2 values:2 stabilizer:1 following:2 trans:1 example:1 proof:1 compare:1 preserving:1 share:1 involve:1 effectively:1 performed:1 sense:2 spanning:1 times:2 conversely:1 occur:1 information:23 redundancy:1 end:2 syndrome:2 carriers:2 rather:1 distinguishable:1 rosen:1 feature:1 nontrivial:1 pure:4 optimal:2 brassard:1 map:1 mar:1 blocks:1 communicating:1 may:4 max:2 clone:1 after:1 mapping:3 data:2 parallel:2 realized:2 natural:1 third:1 purification:1 complexity:1 sect:1 allow:1 words:2 erasing:1 help:1 office:1 noteworthy:1 indeed:1 over:4 course:2 enumerators:1 paper:1 through:8 existence:1 fidelity:5 ieee:1 its:2 before:1 perfect:3 tending:1 derive:1 thank:1 exact:2 presence:1 exhibits:1 previously:1 detected:1 systems:2 superoperators:1 main:1 might:1 split:1 maximal:2 them:3 someone:1 greater:5 thereby:1 practice:1 tails:1 effects:1 they:1 identically:1 1b:1 now:2 nor:1 2t:1 represents:1 february:1 iff:1 transmitted:2 each:7 accommodated:1 higher:1 side:1 inputs:2 series:1 eg:1 reduce:1 related:2 deterministically:1 used:5 measure:1 quantum:67 out:1 divincenzo:2 shown:4 fundamentally:1 space:2 since:2 rev:6 holevo:2 research:3 increase:3 denoted:1 lecture:1 adaptive:1 receiving:3 correct:5 shows:2 foundation:1 earlier:1 linear:3 retrieved:1 differ:1 possibility:2 standard:1 completely:2 besides:1 jozsa:2 additional:1 definition:3 depolarizing:9 interaction:1 could:2 messages:2 david:1 conducted:1 hence:1 supplemented:1 think:1 first:2 initial:1 features:1 probability:15 encoding:2 coding:2 number:3 preservation:1 channels:21 instances:1 employing:1 construct:1 another:2 impossible:2 precisely:1 open:1 size:4 passes:1 given:6 heads:1 exists:1 indicate:1 unknown:2 system:3 least:3 heights:1 1a:1 their:3 intermediate:2 john:1 bits:3 recovered:2 exactly:5 part:1 superoperator:4 simulate:3 copy:1 bennett:4 than:5 begins:1 perfectly:2 determines:2 unfortunately:1 prevent:1 zero:4 kraus:1 states:14 depolarization:1 contrary:1 amplitude:3 were:1 cloning:2 fashion:1 decoded:1 epr:2 correction:5 modern:1 argument:2 crossover:1 case:3 need:2 seem:1 recover:1 any:11 elsewhere:1 latency:1 strength:3 mappings:1 able:3 instance:2 generalized:1 transmit:4 channel:72 multiple:3 fundamental:1 trace:1 though:1 who:1 but:6 phase:12 coin:1 precludes:1 dummy:1 sometimes:1 coincides:1 possesses:1 definitely:1 combinations:1 typically:2 assisted:3 operations:1 emerging:1 shot:2 show:3 charles:1 purely:1 spaces:1 encoded:1 threshold:1 q1:3 q2:22 retransmission:1 dividing:1 paralleling:1 state:16 should:1 transmitting:1 only:3 explicitly:1 local:1 thresholds:1 do:2 erasure:26 establishes:2 quantph:2 unassisted:1 joint:2 watson:1 cannot:4 closely:1 despite:1 dv:1 copying:1 conjunction:3 him:1 reveal:1 processes:1 arxiv:1 requesting:1 fuchs:2 prevents:1 including:1 fixed:1 set:1 computed:3 fair:1 achieved:1 physically:2 generally:1 national:1 maximum:5 relative:3 see:4 sec:1 result:1 enhanced:1 discussions:1 disturbing:1 analog:1 capacity:39 pattern:1 positivity:2 symmetric:2 qubits:22 enough:2 between:11 available:1 superadditive:1 recently:1 ability:1 receivers:3 initially:1 however:2 equals:1 disturbance:1 both:4 realizable:1 grassl:1 many:1 distinctively:1 equal:6 0b:1 σz:2 0a:1 receiver:8 exceeds:1 qubit:15 safely:1 arbitrarily:1 among:1 supply:1 simple:5 wootters:2 asymptotically:3 corresponds:1 represented:1 erased:7 uncorrected:1 described:5 second:1 basis:4 three:3 been:7 whom:1 faithfully:1 erases:2 ph:7 fig:6 sufficient:2 locations:3 observers:3 coherent:6 external:1 general:4 spin:1 protocols:3 applied:1 replaces:2 pacs:1 plain:1 reliable:3 tolerate:1 evaluated:1 will:2 teleport:1 while:2 suppose:1 error:11 report:8 situation:3 twoway:1 opt:1 unitary:1 laflamme:1 memoryless:2 thus:3 non:5 iv:1 ii:1 good:2 vanish:3 increased:1 binary:3 different:1 combination:3 grant:1 supported:1 large:4 lett:2 same:5 randomization:2 complex:1 quant:7 arguments:2 pauli:1 interpolation:1 independent:3 extended:1 hand:4 uses:5 entanglement:7 additivity:1 implements:1 lower:3 center:1 pellizzari:1 charlie:3 well:1 patterns:3 without:3 greatest:3 simulated:1 dimension:1 know:1 protocol:1 popescu:1 less:1 being:2 storage:2 resp:1 actions:1 detail:1 stored:1 purified:1 eigenstates:1 adding:1 nǫ:2 candidate:1 density:4 mathematically:1 source:1 treatment:1 input:13 remaining:2 ought:1 identical:1 nielsen:2 capacities:16 possible:1 cf:7 entangled:3 distillable:1 using:3 bit:3 correcting:3 mod:1 necessary:1 helpful:1 sizes:2 exploiting:1 already:1 alice:6 serves:1 sized:1 communications:1 yields:1 arbitrary:2 output:10 signal:1 shor:2 therein:1 qec:21 because:7 often:1 classical:44 sequence:1 conditional:1 some:2 back:1 examples:1 convex:1 intact:5 happens:1 provided:1 vol:1 dimensions:1 undisturbed:1 support:1 broad:1 measurements:3 per:2 does:3 provides:1 tends:1 pec:7 measuring:1 measures:1 shadow:1 processing:1 communicate:1 although:1 renders:1 hilbert:2 bz:1 simpler:1 would:3 introduces:2 informing:1 probabilities:2 range:3 mixed:8 slightly:1 block:6 seeing:1 follows:2 h2:1 communication:14 into:8 bound:4 appropriate:1 ussr:1 references:1 rounds:1 beth:1 log:2 measured:1 strictly:2 there:3 question:2 start:1 way:13 forward:6 was:2 tight:1 complete:1 smolin:5 rumsey:1 preparations:2 encoder:2 construction:1 decoder:2 unreliable:1 he:1 info:1 made:2 versions:1 whether:3 noiseless:6 transmits:1 yorktown:1 theoretical:1 below:1 limit:4 define:1 similar:3 associated:1 defined:4 toss:1 describe:1 denote:1 transm:1 single:7 reliability:2 exist:4 inf:1 formalism:1 distributions:1 mutual:4 codes:8 faithful:3 no:17 amounts:1 ekert:1 when:5 vanishes:1 ny:1 other:4 test:1 cloned:1 kinds:1 separate:1 symbol:1 allowing:2 dephased:4 gap:2 needed:1 matrix:3 practically:1 physics:2 berlin:1 rule:1 notion:1 impossibility:1 time:1 backward:2 probl:1 strings:1 coherently:1
|
quant-ph9701016.txt |@word represent:2 quarks:1 sci:1 consider:8 iǫ2:2 results:1 computation:3 edu:2 talks:1 poorly:1 devoted:1 whose:1 preserves:1 boghosian:4 calculate:1 deterministic:1 acting:5 factoring:1 tq:4 finally:1 humi:1 present:1 under:9 stochastic:3 analogous:2 include:1 worth:2 norm:1 ucsd:2 applied:1 amplitudes:3 hibbs:1 very:7 choice:1 electron:1 every:4 cellular:1 affect:1 difference:3 hamiltonian:1 irreducible:1 notes:1 solution:1 large:2 discrete:8 vector:6 small:4 eigenvalues:1 configurations:1 mn:2 force:1 cooperative:1 ψi:1 sign:1 second:2 street:1 enhancement:1 further:1 dynamics:8 implemented:2 theory:4 even:5 what:1 giving:1 sum:1 experiment:1 above:4 international:1 ground:3 ever:1 method:2 frisch:2 body:24 simultaneously:1 respectively:1 coveney:1 never:1 modify:1 here:3 agreement:1 desired:1 dimensionality:1 path:1 along:1 equations:5 appears:1 change:1 technical:2 study:2 vectors:4 accomplished:1 resulting:1 handful:1 permutation:1 action:1 automaton:8 involves:1 useful:2 gluons:1 extra:1 nonlocal:1 1st:1 total:6 unit:1 readily:1 use:5 figure:1 would:15 probabilities:2 contains:3 next:1 few:1 automata:7 noting:2 overhead:1 ψl:4 ip:1 taken:2 type:3 until:1 more:7 clever:1 abrams:1 becomes:2 operators:1 apparent:1 odinger:30 normalized:1 particular:2 effort:1 must:2 keeping:1 ma:1 ibm:1 science:4 equation:33 work:3 oscillator:1 tc:2 reviews:1 degrees:1 values:1 indicating:1 henry:1 making:1 arrive:1 example:7 reviewing:1 2lm:4 creutz:1 renormalization:1 indicated:2 give:2 calculation:4 sense:1 implementations:1 states:10 collision:23 numbers:8 allowed:4 analysis:1 tolerant:1 simple:6 scales:2 information:2 united:1 end:1 rather:4 imprecision:1 acts:2 algorithms:13 machine:1 how:3 nontrivial:1 94er40818:1 adjacent:1 parameter:1 ensemble:4 wolfram:1 mar:1 transforming:1 after:2 derived:1 f49620:1 plane:1 waves:1 cambridge:1 representations:1 wave:1 april:1 parallel:1 realized:1 natural:2 correspond:5 parameterized:4 element:1 their:1 perform:2 complexity:6 so:7 allow:2 farhi:1 increase:1 order:6 talk:3 typical:1 operations:6 restriction:1 office:1 schweber:1 over:2 despite:1 satisfied:1 years:1 discretization:1 paper:3 through:3 satisfies:3 still:1 inaccessible:1 its:1 discretizing:2 phillips:1 group:2 symmetry:1 acknowledge:1 interesting:2 lm:7 better:1 absence:2 complex:10 microscopic:2 systems:17 susskind:1 might:4 overcome:2 someone:1 return:1 hop:1 washington:1 fig:7 break:1 framework:1 effects:3 they:4 rotation:1 now:7 discuss:2 chromodynamics:1 eigenvalue:2 term:3 several:2 dirac:4 january:1 university:3 arrows:1 2d:6 mode:1 reasonable:1 each:26 2l:1 2m:8 2n:1 difficult:1 differential:1 fairly:4 24l:1 energy:3 idea:2 related:1 challenges:1 entering:1 quantum:77 operation:1 out:2 divincenzo:1 shown:1 matrix:15 space:18 restricted:1 since:2 rev:5 research:3 particles:29 collisions:1 contained:1 multiply:1 millions:1 shows:1 stat:1 foundation:1 performing:2 linear:1 interactions:5 free:5 standard:3 completely:1 statistics:1 complicated:1 york:1 jozsa:1 definition:1 pairs:1 interaction:7 determining:1 could:4 computers:6 david:2 motion:3 introduction:1 int:1 exponentially:3 incorporated:1 removing:1 think:1 first:11 industrial:1 probability:3 variables:3 number:23 restrict:3 instances:1 gases:4 another:1 4d2:1 carry:1 size:4 given:11 cartesian:1 integrals:1 advect:1 unitarity:3 hydrodynamics:1 mcgrawhill:1 system:39 least:1 indicate:2 quadratic:3 advection:3 1d:5 bits:16 unpublished:1 gives:3 continuous:2 accurately:1 sizable:1 part:6 simulate:13 authors:1 x2:4 representing:1 than:7 reflection:1 wide:1 impractical:2 princeton:3 behaved:1 measured:1 matter:1 individual:1 amplitude:6 were:2 result:1 boston:4 correction:1 nonabelian:2 argument:1 manner:1 exchanging:1 seen:2 occupied:3 any:7 ax2:1 note:4 instance:1 potential:14 square:1 take:4 performance:2 mit:1 begin:2 multiple:4 opposite:1 bruce:1 who:2 extending:1 boltzmann:2 advects:1 pair:4 acknowledgements:1 probabilistic:1 class:5 eigenfunctions:2 found:1 takes:1 considered:3 later:2 physica:1 doe:2 traditional:1 feynman:4 points:4 principle:1 exp:1 mechanical:2 velocity:2 physics:1 fact:2 sector:10 incorporate:3 shor:1 particularly:2 show:1 supported:2 speedup:2 rotating:1 iǫ:1 theories:1 gauge:2 fermions:2 d2:3 find:3 occupation:3 simulating:6 parameters:3 much:1 should:1 only:13 explicitly:2 believing:1 factor:5 local:6 oct:1 achieve:2 dn:1 abelian:1 his:1 dependent:1 air:1 simplest:1 overall:2 fluid:1 new:3 lattices:4 alexander:1 evolution:3 continuum:9 conditions:1 arxiv:1 hydrodynamic:1 including:2 fixed:3 discussing:1 rivet:1 satisfy:2 set:5 constructing:1 national:1 correlations:1 emergent:1 relative:1 see:7 computer:24 succi:3 close:1 kinetic:1 incorporating:1 eres:1 phases:3 satisfying:1 interacting:8 ways:1 nuclear:1 currently:1 definite:1 sites:12 state:21 determined:1 various:1 permutes:1 correctly:1 between:7 invariant:3 before:1 approach:1 available:2 restricting:1 recently:1 reproduced:3 spacing:1 attention:2 however:7 wt:2 no:1 analyzed:1 amer:1 suggested:3 both:1 σi:1 prescription:1 σn:1 tractable:1 many:27 according:1 contract:1 propagation:1 figures:1 context:1 highlights:1 expense:1 jersey:1 unclear:1 nonrelativistic:8 reasons:1 acted:1 corresponds:3 insist:1 dimensional:7 constant:1 november:1 conference:2 pp:1 described:8 basis:5 addition:1 due:2 been:1 pc:1 describes:2 interest:5 certain:1 combine:1 ph:6 define:3 bmb:1 interparticle:4 direction:3 corresponding:4 lga:9 gas:32 essentially:1 coherent:1 understand:2 external:5 systematic:1 x2i:2 plasmas:1 irrelevant:1 those:2 reverse:1 case:5 divisions:1 exponential:4 kogut:1 excited:3 will:19 while:2 behavior:5 error:1 situation:1 graphed:1 unitary:5 coupled:1 vi:1 simulations:2 thus:6 site:13 probabilistically:1 iv:2 numerical:3 need:2 im:1 march:1 conserve:3 different:1 d11:1 grant:1 generic:1 make:1 problems:3 same:5 clearly:2 unity:1 parts:1 quant:6 φe:1 conversations:1 finite:2 higher:1 development:8 independent:2 jeffrey:1 used:6 solved:1 trajectories:1 effect:1 hand:1 moment:1 moving:7 purpose:3 potentials:1 2dq:1 recent:2 scaling:1 schr:30 center:1 possibly:1 obstacles:1 well:3 ccs:3 concrete:2 de:3 components:1 simulated:4 position:2 model:5 laboratories:2 dimension:6 left:2 benzi:1 just:3 less:1 being:2 when:4 positions:2 eigenstates:3 adding:2 preprint:7 conclusions:1 point:5 pupt:3 lattice:64 transformed:1 lett:1 hasslacher:2 mod:2 transformation:1 momentum:1 build:1 real:2 psi:2 aspects:2 easily:1 rules:2 possible:8 harmonic:1 test:1 increases:3 press:1 using:7 bit:6 helpful:1 nsf:1 theor:1 necessary:1 like:1 particle:39 permuting:1 velocities:1 extremely:2 isotropy:1 continue:1 steps:3 sparse:1 arbitrary:10 fault:1 essential:1 lallemand:1 accessible:3 parity:2 because:6 methods:2 classical:26 interact:3 some:4 back:1 bounce:2 pσ:3 nonetheless:1 home:1 peter:1 diagonalizing:1 ψr:4 scale:1 describing:1 dimensions:5 affects:1 measurements:2 per:2 track:1 eliminate:1 assuming:1 considering:1 scientific:2 power:1 performed:2 sixth:1 wavefunctions:1 instantiation:1 expansion:1 bu:4 step:8 inherent:1 contracts:1 francis:1 hilbert:8 meyer:3 comparison:1 about:2 usa:2 most:2 freedom:1 capable:1 discussed:10 o:3 simulation:6 remains:1 range:1 d69:1 obeys:1 act:2 graphically:2 therein:1 conserving:2 computational:6 presence:2 into:4 numerically:2 billions:1 phase:9 appropriate:1 right:2 references:2 determine:1 operator:4 physical:5 utility:1 schrodinger:2 rows:1 additional:1 distinctions:1 there:13 approximate:1 long:3 joseph:1 bosons:1 way:3 series:1 forward:2 conceivable:1 was:8 naturally:3 function:7 complete:1 phenomena:1 qcd:3 but:1 principles:1 proportionally:1 delta:4 line:1 fg02:2 lloyd:3 october:1 applying:1 pointlike:1 understood:1 whether:1 up:2 us:8 theoretical:1 limit:9 problem:1 similar:5 mechanics:5 taylor:4 associated:6 conserves:1 defined:7 minutes:1 universal:1 describe:4 metals:1 general:11 single:18 associating:1 formulation:2 constructed:2 completeness:1 graphs:1 ekert:1 generally:1 other:5 department:3 mathematics:1 genericity:1 conclusion:1 briefly:2 may:3 models:25 subspace:3 vertex:1 fc02:1 important:1 massachusetts:1 suited:1 included:1 fermi:2 needed:6 nondeterministic:1 ago:1 independently:1 faster:1 algorithm:2 assume:2 pomeau:2 columns:1 working:1 rule:18 mass:4 situations:1 time:26 far:1 serious:1 decoherence:2 starting:1 having:1
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.