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quant-ph9905019.txt |@word represent:2 partial:7 consider:4 remarkable:2 interference:4 magnetic:12 results:6 leads:1 roy:1 scalar:3 grateful:1 edu:1 primes:1 hψ:1 ψcm:3 devoted:1 whose:1 b268:1 depend:4 chinese:1 involve:3 29b:1 29a:1 charge:25 those:3 must:1 b182:1 very:2 rise:1 wave:18 probability:1 valued:8 chan:1 affect:1 emphasized:1 difference:1 exact:5 condition:10 obvious:2 solves:1 level:7 cause:2 gui:1 tanh:3 solution:20 large:1 solved:9 convenience:1 vector:6 phase:1 dealt:1 small:2 relation:5 a124:1 degeneracy:11 force:1 sukhatme:1 sin2:9 cosh:1 approximation:4 second:13 interval:1 further:2 zq:7 even:3 established:1 what:1 abc:5 appear:4 section:18 dr2:1 brief:1 expressed:1 current:2 zaslow:1 paragraph:1 above:10 boundary:2 deal:4 new:5 net:1 principal:1 method:2 body:12 condensed:1 2µa:1 lee:1 2kr:3 respectively:2 guangzhou:1 component:2 here:12 china:4 separation:1 address:1 directions:1 equations:4 eikr:1 logarithmic:3 differential:3 box:1 study:8 studied:6 allows:1 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quant-ph9905020.txt |@word gw:1 trigonometric:1 roy:3 ge:1 commute:1 2c2:1 broader:1 parameterization:1 ros:2 reˇ:1 spector:1 const:1 mutatis:1 bx2:1 intensive:1 quasi:11 does:1 infinitesimally:1 stable:2 mutandis:1 anharmonic:1 conjecture:1 confirmation:1 permissive:1 very:2 subject:1 wave:2 every:1 exact:1 condition:1 kukulin:1 immediately:1 hamiltonian:4 solution:1 large:3 discrete:1 differential:2 small:2 heading:1 degeneracy:2 sturm:1 oscillation:1 cond:1 kato:1 discover:1 further:2 odd:2 zr:1 linear:1 even:5 what:1 appear:2 new:3 filled:1 satisfy:1 confluent:1 respectively:1 l1:1 component:2 path:1 strong:2 equations:1 appears:1 change:1 extreme:1 roychoudhury:2 shift:4 inspired:1 maioli:1 resulting:1 pick:1 changes:1 varshni:2 via:1 besides:1 family:1 merely:2 explained:1 private:1 decrease:2 viz:1 unit:1 use:1 asymptotic:2 prove:1 remains:4 contains:1 permitted:1 few:2 therefore:1 bender:8 scope:1 nagarajan:1 subcritical:1 more:3 formally:1 hermitean:4 becomes:2 operators:1 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quant-ph9905023.txt |@word tˆq:1 concept:6 consider:5 springer:5 squared:2 lack:1 alternatives:1 results:8 leads:3 extrapolated:1 generalize:1 computation:1 expressions:4 reˆ:1 issues:3 restrictions:1 devoted:1 whose:1 clarification:2 concerned:1 tˆab:42 acting:4 pˆn:1 tween:1 uniqueness:4 compensate:2 weyl:1 those:5 grabowski:3 under:9 include:2 presentation:3 sent:1 eliminate:1 case:22 provides:1 straightforward:2 orthogonal:2 very:3 could:3 later:2 none:4 choice:2 isomorphism:8 traced:1 emphasized:2 difference:2 semibounded:1 immediately:1 presented:1 did:1 unregulated:1 proposals:2 applicable:2 t0:1 discrete:1 pˆ3:1 pˆ2:2 palao:5 guiding:1 indices:18 eigenvalues:3 path:1 der:2 proof:2 degeneracy:4 possibility:2 application:1 recourse:1 sion:1 english:1 direct:10 sign:2 jump:2 located:1 second:5 perspective:1 pass:1 further:6 defines:4 quite:1 canonical:2 even:9 will:15 what:5 essence:1 appear:2 rate:2 clock:3 section:10 symbolically:1 mg:2 current:1 version:2 localized:1 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quant-ph9905024.txt |@word since:2 consider:5 show:2 buzek:1 sent:2 leads:2 course:1 paper:2 including:1 fidelity:3 still:1 row:1 note:2 group:4 violate:1 how:1 true:1 regarded:1 relativity:2 had:1 ox1:1 should:2 b1:6 only:6 behave:2 copies:6 mail:2 must:1 local:1 into:1 columns:1 placed:1 divides:1 makes:3 non:5 his:3 motivated:1 dk:1 orthogonal:2 dependent:3 dg:2 zurek:2 nonorthogonal:1 famous:1 probability:5 cannot:4 try:1 entangled:3 they:1 oxford:2 now:2 him:1 condition:3 like:1 places:4 particle:2 university:1 arxiv:1 guo:5 alice:9 lett:3 infer:1 large:3 sufficiently:1 yields:1 she:6 arbitrary:1 disregard:1 found:1 2n:2 works:1 macchiavello:1 require:1 proof:2 constraints:2 subset:1 guessing:1 lucien:1 set:2 inputs:2 violated:1 successfully:4 some:4 idea:2 hillery:1 up:1 second:1 been:1 however:1 cloning:10 read:1 measure:1 quantum:10 laboratory:1 indistinguishability:1 guess:1 special:2 p0:2 project:1 shown:2 throughout:1 lead:3 space:2 define:1 furthermore:2 measurements:4 rev:4 overlap:1 whole:1 succeeds:1 replacing:1 state:12 does:3 various:1 correctly:1 between:1 shared:1 particles:1 conditions:1 prob:1 demonstrated:1 either:1 inevitably:1 measures:3 recently:2 nature:3 bl:10 bn:18 each:2 communicate:4 use:1 bk:1 clarendon:1 succeed:1 corresponding:2 groups:2 output:6 put:1 shows:1 argument:2 hand:1 table:4 hilbert:2 massar:1 thank:1 a1:7 pairs:4 arrive:1 her:1 constraint:5 column:8 many:3 could:4 vectors:2 equal:1 contradiction:1 david:1 produce:1 place:2 ox:2 hence:1 divincenzo:1 bob:22 lth:2 onto:4 road:1 first:1 deterministic:1 sure:1 although:1 prepared:1 bell:2 guaranteed:1 b2n:3 imagine:2 number:3 bruss:2 due:1 down:1 pair:1 appropriate:1 ab:2 references:1 bα:2 written:1 actually:1 establish:2 relating:1 linearly:7 take:1 given:2 necessarily:1 smaller:1 proceed:1 would:2 basis:2 probabilities:1 measured:1 there:2 approximate:2 least:1 process:1 restricts:1 much:1 call:3 therefore:1 way:1 ph:3 perfectly:3 behaved:1 possible:6 more:2 wants:2 conditional:1 imperfect:1 knows:1 successful:1 happen:1 smolin:1 p1:2 about:1 but:2 cloned:8 repeated:2 authors:1 clones:4 projective:1 cases:3 careful:1 producing:2 than:12 those:2 he:8 case:3 topic:1 none:1 wootters:2 input:3 showed:3 was:1 equation:2 terms:1 bounds:1 us:4 will:7 assume:2 suppose:2 qcm:2 uk:2 ckl:1 following:2 making:1 property:2 gisin:4 mechanics:1 correspondence:1 ac:2 sometimes:2 guesses:2 do:1 ai:2 abstract:1 measurement:3 share:1 them:1 general:3 states:16 say:2 assumptions:1 duan:5 unlikely:1 further:1 motivating:1 nth:1 made:1 any:4 again:2 different:1 a57:1 zero:4 no:6 little:1 make:1 when:3 off:1 parks:1 tells:1 machine:4 application:1 run:1 other:5 quant:3 machines:1 respects:1 mixtures:1 department:1 instead:1 φk:2 showing:1 conclude:1 independent:4 used:1 wrongly:1 see:2 though:1 may:5 clone:6 after:1 what:1 3pu:1 less:1 most:1 a2:8 prepares:1 acknowledgements:1 probabilistic:5 ekert:1 single:1 times:1 inferring:1 attempt:3 faster:6 succeeded:1 nevertheless:1 light:6 clear:2 locality:1 stronger:1 know:1 write:1 very:1 signalling:7 physics:4 dimension:1 fact:2 realised:1
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quant-ph9905025.txt |@word consider:3 remarkable:1 illustrates:1 caused:1 magnetic:2 splitting:4 generalize:1 cooperative:7 consists:2 hole:5 causes:1 technique:2 passage:7 intensive:1 γi:1 those:2 th:1 γa:2 include:2 letokhov:1 applied:2 doped:1 amplitudes:1 very:2 frequencies:8 tanθ:1 induce:2 results:2 resonant:6 affect:1 swapping:1 hamiltonian:1 positions:1 proposals:1 itamp:1 t1:1 large:4 small:5 optics:2 noted:1 lloyd:1 upper:1 smaller:1 force:2 oscillation:1 deutsch:1 pulse:7 ωab:5 past:1 second:1 populating:1 rectangular:1 even:3 3z:2 abb:1 nano:1 selected:3 dephasing:4 centers:2 current:2 above:8 new:3 3a:1 qbits:2 method:1 filled:1 y2:1 condensed:1 transparency:1 ibid:2 respectively:4 here:5 atoms:32 desired:2 asymmetry:1 focused:1 groups:1 relaxation:7 σac:2 σab:2 along:1 strong:1 equations:1 appears:1 knowledge:1 obtained:1 search:1 involved:1 studied:1 allows:1 reports:1 suggests:1 simultaneous:1 resulting:3 resonance:6 implement:2 narrow:4 studies:1 cancellation:1 york:2 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quant-ph9905027.txt |@word code:29 consider:3 rev:1 desirable:1 results:12 four:2 comments:1 computation:17 projective:1 contributions:1 causes:1 c0:10 referring:1 knill:3 show:1 tr:2 finally:1 critical:1 preserved:1 kwong:1 resources:1 case:7 amplitudes:2 string:2 straightforward:1 very:6 rise:2 differently:1 every:1 additional:1 remarks:1 affect:2 associated:2 difference:1 condition:1 entire:1 incoherent:1 level:10 altering:1 turns:4 solution:1 fewer:1 large:7 solved:1 small:3 noted:1 measuring:8 averaged:1 undoes:1 29th:1 zd:3 α2i:2 consistent:1 za:8 zb:12 zc:8 rate:13 value:2 recursiveness:1 cat:2 odd:12 eigenspaces:1 theory:2 even:20 what:3 errors:27 appear:1 iterating:1 giving:3 sum:7 bc:3 consequent:1 reminiscent:1 consistently:1 anywhere:1 above:14 resilient:1 new:6 method:7 full:1 bravyi:1 respectively:2 equals:1 here:10 desired:11 them:1 represented:1 appears:2 change:3 obtained:7 division:1 suitably:1 shift:1 studied:1 allows:2 expression:1 leaving:2 accomplished:1 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quant-ph9905029.txt |@word teich:1 partial:3 guang:1 chinese:1 show:2 supported:1 obtain:1 hgs:16 roy:2 already:1 relation:1 thanks:1 nbss:1 using:4 understandable:1 japan:1 expressions:1 find:3 before:1 write:1 partially:1 based:2 just:1 sciences:1 interesting:1 plot:2 olya:3 glogower:2 mη:1 decreases:2 gen:3 forms:1 lower:1 only:3 other:1 those:1 must:1 take:1 real:7 non:9 l83:1 jing:1 gallardo:1 mβ:6 db:1 comparing:1 increases:4 fan:3 lett:2 they:4 prof:2 dv:1 integer:3 now:2 discuss:1 mod:5 liu:1 like:1 immediately:1 bn:6 always:2 arxiv:1 orthonormal:1 investigate:2 europhys:1 mode:2 arbitrary:1 joshi:3 about:1 difficult:1 help:1 mean:2 set:1 methods:1 classical:7 generation:1 consistent:1 hypergeometric:13 some:1 related:5 maximum:2 equivalence:1 zero:1 value:2 quantum:5 laboratory:1 soc:2 eq:6 really:1 provided:1 shown:1 satisfying:3 interacting:1 space:1 electromagnetic:2 section:3 rev:6 symmetric:1 increase:1 state:20 above:1 between:3 barranco:1 values:3 email:1 themselves:1 foundation:1 recently:3 lee:1 complementary:3 equivalent:4 guess:1 here:1 atoms:1 am:1 following:2 binomial:5 china:2 interpolate:2 although:1 bs:15 article:1 because:1 properties:11 science:1 obtained:1 both:1 essentially:3 would:1 limits:1 institute:1 study:2 studied:4 discussed:1 equal:2 wang1:1 variance:5 introduced:7 first:1 reduce:2 intermediates:1 cn:1 probability:7 conclude:1 number:12 aphy:1 negative:12 dimensional:1 hermitian:4 written:2 references:1 matsuo:1 operator:8 math:4 ps:7 given:3 necessarily:1 reference:1 iphy:1 prove:1 introduction:1 positive:1 eqs:1 there:3 three:7 been:1 next:1 their:3 intermediate:9 call:1 calculations:1 certain:1 pj:1 torre:1 ph:1 national:1 possible:1 fig:4 function:2 hahn:5 corresponding:1 grant:1 form:2 θm:9 academy:1 cos:1 but:1 coherent:4 optical:1 pnm:3 authors:1 known:1 sun:1 than:2 coefficients:3 nbs:9 case:2 commun:1 pacs:1 variances:3 work:1 2πm:1 up:3 us:1 promotes:1 will:2 clarified:1 minimum:2 limit:4 identical:4 investigating:1 distribution:5 taking:1 stoler:2 point:1 beijing:1 ac:1 larger:2 constant:1 saleh:1 close:1 defined:8 hnm:1 abstract:1 vk:1 thus:1 xiao:1 according:1 states:35 discussions:1 single:2 barnett:7 acknowledgment:1 numbers:2 degenerate:2 sense:1 claimed:1 seen:1 seem:1 formalism:5 identities:1 sasaki:3 constructed:1 agarwal:1 different:8 susskind:2 author:1 distributions:5 make:1 when:1 detail:1 note:1 field:2 setting:2 quant:1 generalized:7 inµ:1 opt:8 acta:1 puri:1 finite:1 parameter:1 pan:1 conclusion:2 independent:3 literature:1 peaks:3 may:1 max:1 after:2 them:1 polynomials:5 bss:3 phase:38 remark:2 pegg:4 pss:1 fu:5 adopt:1 well:1 having:1 lη:1 yang:1 so:1 exp:2 mechanical:1 definitions:1 maxima:1 physics:3 order:2 fact:3 usual:1
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quant-ph9905030.txt |@word consider:5 maximum:1 crucial:1 magnetic:2 varying:1 truncated:4 results:2 ds:1 leads:3 subtle:1 edu:1 follow:1 expressions:1 phonons:2 seemed:1 whose:3 certainly:2 hold:1 calculate:1 zone:1 collisions:1 subjected:1 tr:4 ts:10 extraneous:1 finally:1 under:1 tg:6 nodes:5 cm3:1 tc:8 sound:2 conjecture:1 advantage:1 very:5 brownian:1 vt:3 conjectured:1 induce:1 wave:32 electron:1 balancing:1 experimentally:2 difference:1 encounter:6 splitter:3 t6:5 positions:8 t4:7 t5:1 t2:2 t3:3 t0:1 t1:4 large:4 vector:7 dealt:1 small:6 equation:1 configurations:1 prevent:1 force:4 tem:1 periodicity:1 exposed:1 dealing:1 consistent:2 sin2:1 measurably:1 second:3 equal:3 incidentally:1 further:1 even:2 what:4 disk:3 appear:1 apparatus:4 giving:1 section:4 decays:1 near:1 current:2 version:2 sideways:1 values:6 method:2 movement:1 satisfy:1 q1:2 outgoing:1 full:1 arb:1 spacing:1 eλ2:1 eλ1:3 atoms:1 refinement:1 tangent:2 separation:2 others:1 path:3 along:1 strong:1 respect:1 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quant-ph9905031.txt |@word partial:1 consider:1 remarkable:1 edu:1 calculate:1 daleo:1 spin:1 nonlocal:4 finally:2 include:1 alternating:2 very:2 translations:1 geometrical:1 reordering:1 difference:1 fractal:1 presented:3 consequences:1 ecnicas:1 t0:1 t1:1 large:4 small:9 eigenvalues:1 possibility:1 strongly:1 sin2:1 sign:8 second:1 cost:1 evaluated:1 further:1 chem:1 odd:13 theory:1 even:8 index:3 what:1 appear:1 brackets:1 sum:7 drifting:1 labeled:1 uniform:4 above:2 new:2 net:1 increasing:1 boost:1 respectively:1 realizations:1 b2s:2 here:6 departamento:1 excess:1 consideration:1 equations:2 appears:1 change:9 extreme:1 obtained:1 involved:1 study:1 studied:1 leaving:1 suggests:1 amount:2 action:1 indeterminacies:1 br:1 consejo:1 summations:1 prefer:2 a2s:2 summation:2 use:1 would:5 prove:1 remains:1 positive:1 contains:1 negative:1 few:1 therefore:2 taken:1 torre:2 type:5 until:1 introducing:1 becomes:1 opposing:1 normalized:1 particular:1 stanley:1 cases:1 iτ:4 evolves:1 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quant-ph9905033.txt |@word partial:1 caused:1 hinrichsen:1 leads:3 preserves:1 depend:1 calculate:5 pˆi:6 pˆj:3 quasi:1 γn:2 th:1 case:5 2γn:4 string:1 straightforward:2 very:2 sufficient:1 wave:6 electron:6 experimentally:2 difference:1 brihaye:1 level:5 evaluation:3 maggiore:1 solved:2 math:1 small:3 eigenvalues:1 mangano:2 degeneracy:3 upper:7 smaller:2 force:1 approximation:1 fold:2 canonical:1 appear:2 section:1 near:1 3i:1 above:1 ˆi:1 ground:1 method:7 ek0:3 degree:2 here:8 diagonal:2 ansatz:1 xα:1 table:1 change:2 obtained:3 great:1 suitably:1 shift:5 leaves:1 studied:7 leaving:1 products:1 action:1 york:1 useful:1 9n:1 summation:1 apply:1 planck:1 derivatives:1 use:1 takes:3 would:4 prove:1 remains:1 positive:1 charge:1 next:1 ψk:1 nucl:1 associated:2 theoretical:5 operators:3 corrected:1 odinger:7 normalized:2 particular:2 cases:1 iii:2 must:1 high:1 account:1 deformed:2 gabriel:1 equation:7 work:2 oscillator:12 modified:6 remain:1 values:3 splittings:5 following:6 fulfill:1 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quant-ph9905034.txt |@word limited:3 desirable:1 four:2 controversial:2 sch:1 whose:1 replacements:1 calculate:1 presents:1 under:3 divergent:1 experimentally:2 school:2 solution:5 correct:5 convenience:1 vector:1 indices:1 wronskian:9 force:1 estimates:1 direct:1 approximation:22 second:5 qualitatively:2 estimated:2 4x2:1 even:3 picoseconds:1 above:10 new:7 ˆj:1 coefficient:11 agreement:3 κi:13 κj:11 mechanisms:2 never:1 equals:1 here:8 atoms:1 reported:1 κr:3 obtained:7 suitably:1 study:5 changed:1 approaches:3 ignoring:1 studi:1 suitable:2 changes:10 joshua:1 slices:1 explained:3 highly:1 total:8 experimentation:1 plot:5 would:3 jaekel:1 type:1 separates:1 inhabited:1 must:9 mm:3 work:4 mi:1 cancellations:1 theories:1 mv:3 example:1 give:1 relativistic:2 generically:1 indicates:1 times:4 absolute:2 celoria:1 provide:1 how:2 significance:1 ordinary:2 description:1 replacing:1 after:4 predicated:1 meaningful:2 constants:1 worst:1 order:7 interpretation:1 eigen:3 over:10 affect:3 fit:2 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quant-ph9905035.txt |@word consider:8 caused:1 global:2 disper:1 correo:1 catalina:1 follow:1 concerned:1 send:1 γt:17 finally:2 preserved:1 th:1 under:6 td:3 sent:3 g2:1 orthogonal:2 very:6 account:1 resonant:2 experimentally:1 condition:2 leads:1 disturb:1 vibrational:1 hamiltonian:1 proposals:1 large:4 science:1 small:2 optics:2 equation:1 upper:5 zero:1 traveling:1 manipulating:1 dynamics:3 ρn:6 odd:4 even:7 established:2 what:1 expressed:2 experiment:1 above:6 acknowledgments:1 evolving:1 respectively:3 modify:1 here:2 atoms:24 reported:1 ramsey:6 dora:1 possibility:6 address:3 path:1 along:4 wait:1 obtained:1 sending:1 search:1 davidovich:2 involved:2 larger:1 allows:1 conveniently:1 changes:2 via:1 followed:1 projection:3 highly:1 apply:2 use:2 takes:1 would:1 probabilities:1 hilbert:1 few:1 approach:1 therefore:1 fixed:1 until:2 today:1 more:1 1µs:1 operators:1 odinger:18 reversible:1 normalized:1 particular:1 known:2 conditioned:1 ρa:1 evolves:5 keeping:2 crosses:1 ma:1 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quant-ph9905036.txt |@word partial:2 consider:6 results:3 four:1 roy:2 commute:1 lewenstein:1 obtaining:1 follow:1 increase:1 graph:1 concerned:1 nonlocal:1 present:2 under:2 ta:5 case:20 belonging:1 very:1 rise:1 account:1 choice:2 every:3 anonymous:1 entries:1 matrices:9 condition:7 trj:3 trm:1 turns:1 try:3 trx:2 upper:1 work:1 direct:1 hillery:1 second:2 further:1 machines:9 even:2 section:10 indian:1 above:8 consisting:1 satisfy:2 ρad:3 respectively:9 here:10 understanding:1 b2i:1 address:2 represented:4 along:2 equations:5 obtained:5 institute:2 changed:1 published:1 plotted:1 projection:1 4a2:1 seven:1 decrease:2 apply:4 unit:1 use:1 proceed:1 would:1 remains:2 positive:4 negative:3 next:3 ψi:14 m1:16 therefore:2 taken:4 type:4 more:1 sharing:1 composite:3 becomes:3 ρxy:2 normalized:2 known:1 cases:4 keeping:1 ρi:2 equation:8 ρj:5 mi:4 remain:1 values:11 following:13 making:1 f1:4 f2:4 f3:4 figure:10 give:1 process:4 india:4 states:22 dm:2 numbers:2 want:1 allowed:1 hyperbola:3 caption:2 discussion:1 acts:2 orthogonality:2 machine:47 how:4 pure:8 optimal:17 simplicity:1 product:3 may:4 max:6 after:7 space:1 tangling:1 explored:1 fi:1 unentangled:1 correspond:1 λ2x:7 λ2y:14 so:12 keeps:1 representation:1 bipartite:6 operations:17 six:1 eigen:1 produces:2 over:1 satisfied:11 paper:1 statistical:1 mentioned:3 fidelity:1 still:1 its:3 before:2 derive:1 manuscript:1 acknowledge:1 bandyopadhyay:2 decreases:1 better:3 anirban:1 mail:3 schmidt:1 dad:4 non:14 greater:1 seeking:1 numerically:3 mention:1 instead:1 now:13 discuss:1 term:3 always:1 university:1 orthonormal:1 each:5 found:1 macchiavello:1 side:3 constraints:3 subsystem:3 disentanglement:12 quantum:1 our:6 operation:12 special:1 out:8 divincenzo:1 shown:7 matrix:8 factors:7 since:2 rev:7 looking:1 re:2 m0x:2 performs:1 got:2 issue:1 occurs:2 shows:3 earlier:2 linear:1 reason:1 put:2 universally:4 unresolved:1 keep:1 introduction:1 isotropic:1 first:4 separable:9 dxy:8 redefine:1 xy:10 2a2:2 2a3:2 directly:2 blank:1 given:17 reference:1 similarly:1 unitarity:1 system:4 their:1 1i:3 1j:4 gives:1 asymmetric:7 continuous:1 authors:1 copy:1 than:10 kind:2 perfectly:1 accordance:1 fuchs:1 namely:1 buzek:1 footnote:1 unchanged:1 mind:1 curves:1 say:6 kara:1 close:1 any:14 lie:1 subsystems:5 bengal:2 note:4 mix:2 ideal:2 broadcasting:1 take:3 spectral:1 trace:1 shall:2 decreasing:1 most:5 pair:2 analytically:1 class:1 considered:2 clear:2 order:1 left:3 physics:2 sum:1 quantity:2 phenomenon:2 relation:3 find:3 terno:3 kar:3 should:1 only:5 version:1 factor:9 local:29 oct:1 mixture:1 get:4 express:1 cannot:1 words:1 arranged:1 disentangling:32 regarding:1 transposition:2 arxiv:1 common:1 requirement:2 set:1 constructing:1 exists:3 achieved:1 maximum:14 see:7 college:1 cloning:7 unaltered:1 optimum:1 satisfies:1 symmetric:3 state:28 µi:6 between:1 isical:2 conditions:23 recently:2 nature:1 qubits:12 bose:1 come:1 both:3 ρent:5 taking:1 equal:5 against:1 0j:3 uni:1 qubit:13 0i:3 among:1 point:1 corresponds:1 satisfaction:4 maximize:1 associated:2 described:2 basis:1 west:2 locally:2 three:11 been:2 ai:2 reduction:16 much:1 applying:8 ph:3 universal:20 corresponding:7 m1j:12 demand:1 maximally:3 former:1 those:1 applied:3 semidefinite:1 look:1 pacs:1 value:21 rectangular:3 will:15 suppose:1 error:1 situation:2 real:2 a22:2 unitary:6 thus:5 surprisingly:1 ii:3 middle:1 im:8 ernet:1 different:2 verified:1 same:5 quant:3 arguments:1 difficult:1 independent:1 used:2 numerical:1 effect:1 hand:3 uses:2 entanglement:1 a2i:1 totally:2 identity:1 acknowledgement:1 well:1 without:1 calcutta:2 ekert:1 comprise:1 usual:1 ρbd:7 less:4 being:5 λy:14 λx:14 obtain:1 transforms:1 λj:4 previous:2 thankfully:1 density:15 seems:1 belongs:2 transformed:1 lett:8 theorem:3 input:1 transformation:2 identical:4 exploiting:1 mor:3 possible:5 department:3 entangled:12 sanpera:1 using:14 imposed:1 particle:3 follows:2 isotropy:4 separately:2 arbitrary:5 revision:1 reduced:15 deal:1 some:3 b4:12 b1:12 b2:10 b3:10 provided:4 ηx2:18 comments:1 does:2 particles:1 bd:2 disentangle:3 bi:2 broken:3 ηmax:14 ηj2:1 hilbert:1 bz:1 takes:1 comparison:2 constraint:1 tracing:4 discussed:3 summarise:1 mixed:2 road:3 own:1 into:2 m0j:15 ηj:18 ηi:4 copies:4 references:1 parties:8 operator:1 disentangles:1 ηy:46 ηx:31 there:3 question:2 describes:1 m0:42 north:1 form:3 phenomena:1 smolin:1 regard:1 but:5 attainable:1 line:4 made:2 uy:2 ux:2 intuitive:1 horodecki:6 whether:2 bounds:1 us:2 uj:5 problem:1 bruß:1 ac:2 ordered:1 ad:2 up:1 defined:3 certain:1 abstract:1 general:8 peres:4 single:4 exist:3 check:1 physical:1 functions:1 disentangled:10 no:5 whereas:2 when:4 other:6 test:2 mathematics:3 conclusion:1 dhom:1 denote:1 a1:8 a3:8 a2:5 implies:3 ghosh:1 required:1 curve:5 together:2 notion:1 impossibility:1 signalling:1 starting:1 original:1
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quant-ph9905037.txt |@word limited:1 emch:2 partial:1 consider:1 represent:3 eaires:1 ψ1r:2 alternatives:1 results:1 four:2 ψ1i:1 scalar:8 commute:13 generalize:2 go:1 compact:1 preserves:3 hold:2 equivalence:1 tr:13 charge:2 those:5 th:1 fermionic:2 p2:2 belonging:2 comm:1 straightforward:1 orthogonal:11 very:1 springer:1 choice:1 every:6 matrices:25 condition:5 hamiltonian:9 turns:1 solution:1 discrete:2 vector:1 dealt:1 indices:1 eigenvalues:8 degeneracy:2 concluded:2 direct:2 likely:1 further:1 ωt:3 quite:1 canonical:6 even:7 invertible:3 brackets:1 section:3 birkhoff:1 goes:1 new:7 construction:1 ever:1 satisfy:1 full:1 degree:1 never:1 here:8 possibility:1 groups:3 exponent:1 represented:4 standard:13 appears:1 ensembles:1 antisymmetric:7 sjs:1 vectors:4 allows:1 erateurs:1 espace:1 products:5 poisson:6 fourier:1 makes:2 options:1 involves:1 york:3 formulated:1 useful:2 projection:5 logically:1 1st:1 apply:1 total:1 unit:10 would:3 probabilities:2 positive:5 contains:1 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quant-ph9905043.txt |@word now:1 measurements:1 consider:1 rev:6 magnetic:9 global:7 dynamic:2 results:1 existing:1 leads:1 commute:1 ciar:1 computation:3 expressions:1 faster:1 2r1:1 sch:2 semiconductor:1 inverse:2 irrelevant:2 technique:2 environment:2 critical:2 device:2 present:1 under:3 andreev:1 tb:2 swap:2 case:4 sherbrooke:2 risk:1 straightforward:1 very:2 wave:10 blockade:1 electron:3 worst:1 difference:2 matrices:2 condition:1 level:1 nostrand:1 frozen:1 small:8 accumulation:1 degeneracy:2 smaller:1 force:2 zi:1 oscillation:1 dealing:1 estimates:1 pulse:2 sign:1 approximation:1 rate:1 further:1 dynamics:2 estimated:2 employ:1 plays:2 advantageous:1 diag:1 axes:3 tsai:1 current:3 waiting:1 version:1 localized:2 above:3 new:1 nakamura:1 princeton:1 simultaneously:3 respectively:1 commercial:1 here:3 diagonal:1 desired:4 iσx:1 capacitor:2 groups:1 excess:1 active:3 along:1 strong:1 z1:2 change:1 box:1 property:1 shift:2 allows:1 leaving:1 amount:1 periodic:1 decoupled:2 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quant-ph9905044.txt |@word concept:3 consider:1 crucial:1 leads:2 generalize:1 edu:2 hole:3 pˆc:1 shanghai:1 finally:1 th:1 under:1 case:3 far:1 wave:18 bjorken:1 electron:2 condition:2 level:2 solved:1 consistent:1 prediction:1 sign:1 chen:1 qualitatively:1 even:3 what:1 appear:1 version:2 above:2 new:2 edited:1 ibid:1 respectively:1 equals:1 here:1 china:2 drell:1 equations:1 publisher:1 great:1 usually:1 uniquely:1 gordon:2 univ:1 takes:1 would:1 remains:1 negative:3 ψt:7 ψi:4 m2:5 ψc:2 more:1 becomes:1 company:1 odinger:1 correspondingly:1 cases:1 mc:2 ρi:1 science:2 equation:9 work:1 ρr:1 ρt:2 learn:1 following:1 meet:1 conformity:1 example:1 claim:1 give:1 process:1 relativistic:2 accept:1 states:1 collision:1 uckelberg:2 axis:1 nyu:2 located:1 criterion:1 pure:1 acta:1 hopeless:1 may:1 earlier:1 hence:1 physik:1 choice:1 stress:1 natural:1 2mc:1 st:2 green:1 decreasing:1 helv:1 essence:1 pointed:1 course:1 paper:1 existence:2 still:1 its:5 group:1 interesting:4 relativity:1 mail:3 repulsive:1 now:1 2p:1 always:3 university:2 transmitted:5 reasonable:3 weimin:1 2m:4 energy:7 ec:2 antiparticle:8 expect:1 quantum:6 eq:8 special:2 out:1 category:1 shown:4 since:3 rev:4 is6:1 looking:1 hill:1 theory:1 governing:1 quite:1 reason:1 york:2 recast:1 motion:1 place:1 exponentially:1 consequence:1 symmetry:2 guan:1 reflected:3 nova:1 another:1 comprises:1 precisely:1 eqs:1 behaves:1 reflectivity:2 needed:3 postulate:1 especially:1 explanation:4 part:1 determined:1 doubly:1 historical:1 were:1 well:1 say:1 need:1 any:1 jour:1 self:1 potential:1 sakurai:1 so:4 ˆp:1 electric:1 though:1 who:1 pair:1 measured:1 χt:1 kg:6 observation:1 clear:1 feynman:2 exp:7 physics:3 χi:2 show:1 supported:1 purely:1 find:1 iet:1 should:6 dvoeglazov:1 local:1 continuity:1 klein:9 get:1 ϕt:2 express:1 beam:1 ϕi:2 words:1 podolsky:1 qx:1 arxiv:1 redefined:1 fixed:1 qm:1 view:2 reveals:1 requirement:1 observer:1 see:2 result:1 sea:1 satisfying:1 importance:1 boundary:1 notice:1 positron:1 jt:4 however:3 jr:3 incident:4 ji:3 eˆc:1 essentially:1 qft:3 experimental:1 strongly:1 cn:1 point:4 seems:1 dimensional:1 respect:1 along:1 publishing:1 px:2 locally:1 been:1 pc:2 yan:2 basic:1 expected:1 ph:3 fudan:3 addison:1 corresponding:1 photon:1 coherent:1 understand:1 demand:1 c2:8 c4:2 p2:1 will:2 while:3 situation:1 coupled:2 iq:3 reads:1 same:1 selfconsistent:1 parts:1 quant:3 fill:1 difficult:1 v0:11 purpose:1 necessity:1 infinite:1 schr:1 epr:1 analysis:1 feshbach:2 components:1 english:1 very:1 guang:1 rosen:1 villars:2 preprint:3 ny:1 had:1 add:1 book:1 attractive:1 continuation:1 transformation:1 momentum:2 real:1 know:1 dirac:1 advanced:1 mod:1 acute:1 like:2 particle:9 follows:1 resorted:1 served:1 right:1 creation:1 understood:1 happens:1 mc2:7 proc:1 reaching:1 oscillating:1 wesley:1 mcgraw:1 imaginary:1 discussed:2 o:1 ψr:3 raised:2 h2:1 into:1 washington:1 nsf:1 acad:1 einstein:1 hep:1 there:1 question:1 long:1 describes:2 was:2 propagator:1 function:8 form:1 forming:1 jun:1 but:2 partially:1 wish:1 problem:2 poincare:1 mechanics:5 ac:1 ab:1 general:1 moves:1 inc:1 ni:5 paradox:8 no:3 when:3 schwinger:2 field:2 other:1 nat:1 department:2 operators:2 conclusion:1 explaining:1 superposition:1 zhou:2 important:1 ago:1 together:2 starting:1 original:1
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quant-ph9905045.txt |@word code:1 sci:1 magnetic:3 results:2 illustrated:1 roy:2 scalar:3 computation:1 involved:1 depend:1 alamos:2 program:1 ti:3 anharmonic:5 include:1 garden:1 very:1 frequencies:1 maas:1 figs:2 summarized:1 experimentally:1 difference:2 matrices:3 harmonicity:1 leads:1 school:1 hamiltonian:12 natl:1 t2:3 t1:2 small:1 eigenvalues:1 noted:1 oscillation:2 pulse:5 street:1 design:1 ter:1 implemented:4 spectral:1 richard:1 version:1 above:5 expresses:1 technology:1 increasing:1 implementable:1 margolus:1 chose:1 here:2 desired:2 selective:1 relaxation:3 along:1 implicit:1 obtained:1 institute:1 shift:1 study:1 larger:1 through:1 chemical:2 knill:2 usually:1 resonance:3 implement:2 studies:1 composed:1 scales:1 visible:1 flexibility:1 propagators:1 takes:1 would:3 army:1 laflamme:2 physics:1 cory:3 kinematics:3 therefore:1 theoretical:1 today:1 more:2 clearly:1 operators:1 under:3 particular:4 analogous:1 ma:3 science:4 challenge:1 work:1 oscillator:11 concepts:1 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quant-ph9905048.txt |@word represent:4 unavoidable:2 partial:1 consider:10 springer:2 interference:6 amplifier:6 results:12 chiao:1 leads:11 eds:1 quadrature:2 computation:4 consists:4 amplified:2 contributions:1 gr:5 whose:1 dimensionality:3 re:3 tw:3 plasmons:1 nonlocal:3 environment:2 absorbing:1 quasi:1 program:2 squeezing:3 γn:6 ti:1 eibl:1 stochastic:1 γa:11 applied:1 belonging:2 wjj:2 presently:1 advantage:1 orthogonal:7 barium:1 2re:1 assuming:1 keeping:1 induce:1 wave:4 p1:4 every:1 mattle:3 resonant:1 affect:1 difference:2 exact:4 cα1:1 condition:6 splitter:5 iw:4 obvious:1 swapping:1 pbs:9 presented:2 positions:1 solution:5 damped:1 large:6 convenience:1 vector:1 lever:1 shows:4 optics:3 der:1 vincenzo:2 configurations:13 prevent:1 strongly:2 sapienza:2 force:1 bessel:1 dealing:1 consistent:1 sin2:1 direct:1 pulse:2 cosh:1 rhomb:2 second:3 perspective:2 insertion:1 correlator:1 further:1 dynamics:8 requiring:1 click:1 linear:18 even:1 cee:1 nonlinear:8 adds:1 apparatus:3 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quant-ph9905053.txt |@word leighton:1 similarity:3 interference:3 magnetic:3 four:1 entropy:3 consists:4 integrity:1 marching:1 relationships:2 whose:5 u3:2 segments:2 contained:2 under:14 ontological:20 worth:1 divergent:1 connects:1 every:5 summarized:1 affect:3 bringing:1 school:1 internally:1 supports:2 solution:2 convenience:1 vector:8 succession:1 indices:1 enjoy:2 force:3 pragmatic:9 construed:1 consistent:4 direct:4 horn:1 approximation:7 elegant:1 second:11 attended:1 implemented:1 even:19 established:1 incompatible:1 specification:2 selected:1 above:12 new:23 increasing:3 ever:7 consisting:2 told:1 1997b:1 evolving:2 simultaneously:4 notions:1 presynaptic:7 never:4 here:26 atoms:3 feeding:1 tornado:2 represented:28 obtained:2 substance:1 distinctness:1 rests:2 leaves:3 changed:6 completely:7 reports:2 stressed:1 complicated:1 stipulated:1 spacetime:15 york:5 criticism:1 diameter:1 projection:7 rosenberg:1 discontinuous:6 explained:3 objectively:1 brought:3 moral:1 total:2 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quant-ph9905060.txt |@word epeau:1 sci:1 consider:6 pointing:1 results:6 leads:1 go:1 particles:37 depend:1 alamos:4 acting:4 ıa:2 spain:1 orthogonal:1 implicitly:1 untenable:1 every:2 summarized:1 four:23 swapping:2 presented:1 knight:1 eigenvalues:9 shows:1 ten:3 consistent:2 second:4 further:1 specker:4 even:2 will:4 incompatible:2 analogously:2 access:1 experiment:4 new:1 told:1 satisfy:3 edited:2 simultaneously:3 ibid:2 respectively:1 component:1 teleportation:2 possibility:2 address:1 luis:1 equations:2 appears:1 change:2 involved:1 popescu:1 allows:1 contradiction:1 published:2 opinion:1 andaluc:1 honor:1 composed:3 useful:1 projection:2 hardy:4 would:5 probabilities:2 positive:3 contains:1 negative:5 properties:5 call:1 therefore:5 a56:11 taken:1 type:3 today:1 more:1 separated:3 composite:5 trait:1 operators:16 ascribe:1 odinger:1 duplicating:1 particular:4 iii:1 must:5 account:1 work:2 labeled:1 itself:1 values:2 following:4 my:2 example:2 proof:12 boschi:1 predict:5 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quant-ph9905061.txt |@word logarithms:1 sci:1 consider:1 rev:5 magnetic:12 particular:1 results:8 leads:1 scalar:3 computation:5 equalized:3 expressions:1 weakly:1 issues:1 certainly:1 inverse:1 leung:1 γs:6 knill:2 technique:2 tr:4 acting:1 factoring:1 tq:1 environment:1 γi:6 compensate:1 those:1 under:4 sent:2 case:3 random:1 amplitudes:1 expressing:1 zhang:1 far:1 frequencies:1 wave:4 wishes:1 figs:1 summarized:1 experimentally:4 difference:1 correlates:1 ibm:1 four:4 school:1 incoherent:1 level:1 positions:1 t2:3 solution:5 large:1 discrete:2 vector:1 progress:1 lloyd:1 application:10 smaller:1 illustrating:1 receiver:1 direct:1 pulse:17 sign:3 zero:3 further:1 dynamics:9 implemented:7 b01:2 plays:1 combined:1 richard:1 incompatible:1 sum:1 associate:1 brief:1 expressed:1 henceforth:1 experiment:3 above:7 mosca:2 new:2 net:1 90o:1 colella:1 2kt:1 locked:1 processing:2 led:1 respectively:5 component:2 here:2 behaviour:1 desired:6 explore:1 selective:2 focused:1 excess:1 alone:1 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quant-ph9905062.txt |@word demo:1 horne:3 efficiency:1 consider:1 remarkable:1 correlation:2 violation:6 when:1 out:1 years:1 obtains:1 eds:1 experiments:1 through:1 thanks:1 computation:1 signs:1 threshold:1 captions:1 denotes:1 its:1 network:1 based:1 certainly:1 holistic:1 group:1 violate:4 lo:1 less:1 proposed:1 actually:1 presents:1 parts:2 only:1 potential:1 pasquinucci:1 systems:3 theorem:1 hidden:2 main:1 loophole:5 scientific:1 maximal:3 case:2 non:1 supported:1 consequently:2 advantage:1 entire:1 sums:1 possible:3 corresponds:1 entangled:3 closely:1 despite:1 integer:1 now:1 easily:1 february:1 increasing:1 indeed:1 like:1 presented:2 converge:1 admittedly:1 university:1 settings:20 huelga:1 large:3 qm:1 inequality:23 integrals:1 arbitrary:5 switzerland:1 found:1 2n:4 european:1 inspection:1 valid:1 2j:1 reproducing:1 www:1 arxiv:1 old:1 foundation:1 violated:2 correlations:1 some:1 lett:5 bechmann:1 b4:8 see:2 result:2 b1:16 b3:14 quantum:11 our:2 odd:1 violates:1 special:1 standard:1 happens:2 what:2 still:1 inequalities:5 lead:1 bernard:1 rev:8 yet:1 state:3 experiment:1 bruno:1 above:1 tends:3 dλ:1 αj:3 acknowledgments:1 demonstrated:1 shows:1 model:2 notice:1 asp:1 recently:1 theory:1 nature:1 importance:1 respectively:1 each:1 diagonal:1 here:1 bk:3 indices:1 reproduces:1 free:1 ratio:8 holt:2 refers:1 appears:1 motivation:1 deduced:1 bj:3 both:1 cos:5 improved:1 world:1 applications:1 many:5 could:2 similarly:1 according:1 minus:1 sensitive:1 a2:10 kwiat:1 consequence:1 fry:1 generalizations:2 other:1 βj:3 first:1 arbitrarily:1 ch:2 co:1 divide:1 bell:12 communication:1 into:2 asymptotically:1 clear:1 number:5 huttner:1 dimensional:3 variable:2 set:1 references:2 another:1 news:1 factor:1 li:1 considering:1 given:1 statistics:1 checked:1 her:1 basis:1 introduction:2 lower:1 suffice:1 there:4 been:3 does:2 however:2 assumption:1 popescu:1 basic:1 shimony:2 ph:2 unige:1 was:2 national:1 fig:1 function:3 software:1 corresponding:1 geneva:2 santos:1 local:2 deviations:1 larger:1 particular:1 known:2 evidence:1 spin:2 than:1 present:1 partially:1 applied:1 detection:4 whether:1 science:2 work:2 us:1 aim:1 experimental:1 below:1 limit:1 walther:1 following:4 tmr:1 closing:1 outcome:1 example:1 stimulating:1 gisin:6 mechanics:2 planar:1 saturate:1 b2:16 figure:1 computing:1 spiller:1 abstract:1 aj:6 generalization:5 equal:1 states:2 discussions:1 examine:1 smaller:2 numbers:4 turns:1 close:1 clearly:1 physical:1 information:2 generalizes:1 any:3 worldview:1 locality:1 analyzers:2 s2:1 generally:1 feature:1 s4:1 note:2 necessary:1 setting:4 quant:2 generalized:4 largest:1 significant:1 detector:1 finite:1 lhv:1 sin:4 conclusion:1 independent:2 product:1 exactly:1 http:1 description:1 opposite:1 may:1 numerical:1 shown:1 singlet:2 a1:10 most:2 a3:9 important:2 a4:5 letter:2 entanglement:3 data:1 sides:1 appear:1 profited:1 realized:1 short:1 considered:1 chsh:8 clauser:3 no:1 well:1 s3:1 sn:1 allow:1 lim:1 swiss:2 n2:2 pearle:1 physics:4 original:1 usual:3
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quant-ph9905063.txt |@word limited:1 crampton:1 consider:3 gp:5 magnetic:10 particular:1 splitting:12 leads:1 per:1 restated:1 intricate:1 follow:1 expressions:1 contributions:2 whose:1 depend:4 calculate:2 graph:3 finally:4 those:1 excluded:1 include:2 hill:1 fax:1 supported:1 very:1 polarization:5 wave:3 electron:13 valdes:1 overcomes:1 experimentally:1 difference:3 condition:2 uehling:1 level:7 bn:2 make:3 hyp:10 solved:1 differential:1 small:2 gauge:3 work:2 dealing:1 sign:1 approximation:3 second:5 value:6 further:2 even:3 what:1 nonlinear:8 sum:1 d3:2 experiment:1 diaz:1 3n:1 above:3 3c:1 net:1 contributes:2 method:1 exercise:1 splittings:2 satisfy:1 respectively:1 component:1 here:2 atoms:7 ramsey:1 address:1 represented:1 κp:3 box:1 shift:23 introductory:1 studied:1 loop:1 studies:1 rafael:1 recursion:1 total:3 unit:1 use:2 charge:1 would:1 iev:1 contains:2 predictions:1 next:2 few:1 ψn:1 m2:9 taken:4 care:1 bethe:3 more:1 binding:5 operators:1 eν:5 normalized:1 excellent:1 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quant-ph9905066.txt |@word aln:1 partial:1 consider:4 scalar:1 consists:1 2ie:4 depend:1 analytic:1 tr:10 squeezing:13 under:2 fax:2 orthogonal:1 very:1 3aa:1 choice:2 reordering:1 difference:2 condition:8 dim:5 irreducible:3 convenience:1 vector:11 eigenvalues:2 anal:1 upper:2 smaller:1 tel:2 ten:1 japanese:1 zero:1 irreducibility:2 odd:5 selfadjointness:1 theory:2 even:3 appear:1 d2:2 section:3 3i:1 above:2 overcomplete:1 3a:1 method:2 satisfy:2 simultaneously:2 respectively:3 l20:4 te0:9 const:2 change:2 obtained:3 remark:2 zm:1 shift:1 vectors:4 commonly:1 simultaneous:9 action:2 makes:1 uniquely:1 schur:1 projection:1 masahito:2 unitary:5 apply:1 orderings:1 unit:5 prove:2 covariant:1 positive:4 saka:1 properties:2 call:1 therefore:9 associated:9 type:7 more:3 becomes:1 operators:13 known:4 cases:1 hold:2 springer:2 valued:3 science:1 equation:3 ρm:1 fock:1 following:7 mz:3 calculation:1 neglected:2 states:27 indicates:3 minimum:4 νa:1 numbers:1 sense:2 tan:1 conversely:1 e2t:7 means:4 utilize:1 orthogonality:1 located:1 optimal:3 parameter:3 obius:2 map:1 product:1 algebra:15 may:4 ζl:7 mapping:1 applications:1 plane:6 ζv:1 faculty:2 fh:2 wave:2 2l0:5 natural:1 λv0:1 sp:1 su:27 bunkyo:1 sl:1 representation:12 order:1 se:10 holds:2 eigen:3 over:1 satisfied:3 paper:3 statistical:1 existence:2 satisfies:5 ieee:1 its:2 derive:7 group:1 ln:8 2e0:2 affine:2 boson:10 forms:1 parts:1 choose:5 mail:2 them:2 combination:2 trh:2 bound:3 2p:1 they:1 hands:1 now:6 discuss:2 nor:1 eigenvalue:24 equality:1 university:3 2e:1 inequality:4 l2:8 2a:2 l0:52 2l:15 2n:11 side:2 2k:10 subset:1 displacement:2 related:8 frequency:1 measure:6 quantum:3 operation:1 out:1 shown:3 space:12 since:4 rev:1 holevo:1 denotes:3 re:6 conclusions:1 rational:1 denoted:2 electronics:1 ref:1 math:1 linear:10 localization:1 derived:2 e0:29 definition:2 similarly:1 moment:2 unitarity:3 int:2 hence:6 first:1 origin:1 xn:2 hλ:3 sakaguchi:2 ez:2 number:10 zρ:2 construct:3 another:4 impossible:2 1p:2 given:2 µab:1 rewritten:1 width:1 ordering:4 adjoint:14 system:10 relations:38 their:1 ordered:2 structures:2 2aa:2 pittsburgh:1 part:2 than:1 coefficients:2 kind:3 holland:1 second:2 annihilation:26 determined:1 were:1 lowest:1 zz:2 generality:1 arg:1 turned:1 spectrum:1 any:3 lie:7 convenient:1 latter:1 note:1 k0:2 generalized:3 spectral:1 converse:1 trace:1 opposite:1 systems:1 algebraic:6 pair:1 class:1 calculated:2 exp:31 left:2 fukui:3 spaced:1 show:12 spaces:1 relation:24 solutions:1 trivial:2 aρ:1 q2:5 based:1 parameters:10 state:13 should:3 lemma:1 only:5 generators:2 circle:2 abelian:1 viewpoint:3 get:5 dz:7 closely:1 normalizable:1 qp:14 arxiv:1 investigate:5 daubechies:2 shi:1 kernel:4 set:4 λe:1 creator:1 packet:2 depends:2 ikp:2 sec:3 eliminating:1 japan:2 satisfying:2 commutation:5 siam:1 symmetric:1 written:2 various:3 wavelet:2 between:9 neither:1 conditions:3 triplet:10 rims:1 jp:2 however:4 ρzz:1 ker:6 both:3 uncertainty:5 casimir:2 estimation:2 otherwise:1 simple:1 harmonic:1 represented:1 anti:8 wider:1 moreover:4 selfadjoint:1 pp:1 e4q:1 commutative:1 basis:4 addition:2 three:1 defined:7 cauchy:2 interpret:1 basic:1 pk:1 ph:1 define:9 corresponding:6 concerning:1 hayashi:2 coherent:10 systematic:1 denote:1 those:2 case:24 value:2 will:13 while:2 error:1 squeezed:20 investigating:3 property:2 iy:1 cons:1 attains:1 iq:2 ip:3 thus:4 non:10 itself:3 im:4 eigenfunction:2 different:2 belong:1 problems:1 same:6 unity:1 complex:5 quant:1 proved:1 investigated:2 hand:3 v0:17 a2b:1 nl:1 identity:1 eigenvectors:7 lower:3 center:1 well:3 analysis:2 without:1 howe:1 position:4 dimension:2 usual:1 proposed:1 half:4 bµ:3 λa:1 correspondences:1 paul:1 eigenstates:1 previous:1 density:2 regarded:1 signals:1 belongs:4 transformation:1 momentum:4 real:2 aspects:1 around:1 easily:2 vacuum:2 using:3 loss:1 like:1 signal:1 e02:2 continue:1 reduced:1 parity:2 because:13 lectures:1 creation:15 self:13 choosing:1 respect:5 resolutions:1 scale:1 dense:1 a13:1 normal:23 does:3 proc:2 measuring:1 kyoto:4 equivalent:1 wavefunctions:1 symp:1 yuen:1 imaginary:1 hilbert:3 about:1 extension:18 discussed:4 wavelets:3 range:2 extensions:1 mean:1 perelomov:1 22k:1 into:1 h1:3 isomorphic:1 phase:4 hermitian:2 right:2 references:1 determine:1 operator:43 next:7 there:7 transform:1 normality:2 iq2:1 start:1 sections:2 function:10 north:1 complete:1 form:1 regard:1 but:4 introduction:1 hk:6 contradictory:1 true:1 utilizing:1 characteristic:3 inside:1 problem:11 similar:6 called:3 eigenvector:16 aa:11 ac:2 ab:7 constant:2 povm:13 abstract:1 measurement:10 doesn:1 general:3 engineering:2 av:3 dζ:2 dη:3 formalism:2 constructed:1 functions:3 completeness:1 no:2 nb:13 when:4 other:4 electrical:1 investigations:1 department:2 mathematics:1 sufficient:1 calculating:1 time:2 uniformly:1 generated:1 important:1 ξl:2 structure:3 implies:2 pseudo:1 4l:3 attaining:1 4k:1 4i:1 observables:1 4e:2 resolution:1 8th:1
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quant-ph9905067.txt |@word replacing:1 limited:1 concept:1 todays:1 consider:7 remarkable:1 represent:1 rev:8 results:6 computation:1 consists:1 follow:1 expressions:2 gk:1 content:1 depend:1 calculate:3 rayleigh:2 shall:4 finally:3 squeezing:10 those:2 under:7 kλ:4 anharmonic:2 p2:1 random:1 comm:1 straightforward:1 md:1 very:2 frequencies:1 multi:8 wave:1 ankara:1 condition:1 tri:1 disturb:1 reciprocal:1 dij:1 hamiltonian:8 knight:1 proposals:1 solution:1 standards:1 vector:3 small:1 eigenvalues:3 optics:8 application:3 strongly:2 10f:1 direct:2 pulse:1 cosh:2 approximation:9 second:3 dordrecht:1 bilkent:2 further:1 dynamics:3 canonical:1 even:6 established:1 nonlinear:1 stands:1 giving:1 section:6 selected:1 brief:2 expressed:1 ˆa:2 above:8 destroyed:1 new:3 method:3 contrast:1 counters:1 ozg:1 full:1 simultaneously:1 evaluating:1 degree:2 respectively:2 modify:1 here:12 pumping:1 ranges:4 reported:1 merlin:1 pub:1 peˇrina:2 active:6 consideration:2 appropriate:1 standard:1 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quant-ph9905068.txt |@word limited:1 concept:1 consider:1 secondly:1 interference:2 lack:2 dynamic:2 results:11 leads:2 entropy:1 overlap:4 localized:1 seemed:1 whose:1 const:1 deterministic:16 nonlocal:1 finally:1 preserved:1 th:1 under:2 pˆy:1 stochastic:2 analogous:1 ingredient:1 belonging:1 global:1 very:3 implicitly:1 springer:1 choice:1 lyapunov:1 mixing:1 experimentally:1 condition:1 abandoned:1 randomness:4 level:1 positions:2 applicable:1 t0:27 large:1 solved:1 detected:1 small:1 eigenvalues:2 originally:1 concluded:3 zn:3 zi:1 prediction:2 elegant:2 zero:1 invention:1 further:2 dynamics:13 even:1 established:1 ohne:1 nonlinear:1 apparatus:1 expressed:1 experiment:3 absolute:1 above:3 new:2 connected:2 journal:2 contrast:3 christian:1 excludes:1 respectively:2 here:3 agreement:1 behaviour:4 separation:3 grundlagen:1 alone:1 consideration:1 along:7 strong:1 equations:3 z1:1 change:1 deduced:1 obtained:2 chaotic:11 technical:1 shift:3 studied:2 allows:3 approaches:1 example:1 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