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quant-ph9811069.txt |@word logarithms:1 concept:1 sci:1 consider:2 global:1 results:2 roy:2 proposition:8 computation:4 consists:2 row:3 inverse:1 referring:1 deterministic:1 factoring:2 answered:1 γi:12 does:5 th:2 ti:2 analogous:1 crest:1 norm:4 hill:1 string:1 straightforward:3 rise:2 choice:1 print:1 every:6 ma:1 papadimitriou:1 condition:30 school:2 obvious:1 hamiltonian:2 turns:4 t2:9 t1:9 discrete:2 vector:3 noted:1 configurations:18 deutsch:11 second:2 abbreviates:1 concludes:2 dynamics:1 machines:49 canonical:1 even:1 aim:3 what:4 plays:1 stands:1 trivial:1 section:10 transforms:1 networks:1 cell:6 above:9 new:1 consisting:9 satisfy:4 edited:2 respectively:4 here:2 canonically:1 represented:7 consideration:2 along:3 appears:1 change:1 obtained:2 search:1 tapes:3 studied:1 approaches:1 contradiction:1 published:1 usually:1 explain:1 uniquely:5 formulated:2 useful:1 projection:2 classification:1 plenum:1 summation:6 tools:1 unit:3 alamitos:2 prove:3 positive:2 contains:2 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quant-ph9811070.txt |@word partial:3 consider:4 remarkable:1 results:2 leads:2 commute:6 gc:2 kato:4 perturbations:4 reasoning:1 γx:1 depend:3 calculate:1 subjected:1 equivalence:2 simplify:1 charge:1 program:1 under:8 ωt0:1 p2:3 straightforward:1 orthogonal:2 very:1 than:3 rise:4 translations:1 account:1 seemingly:2 wave:2 lecture:1 sheds:1 difference:2 condition:3 four:1 obvious:2 hausdorff:1 hamiltonian:37 did:1 turns:1 notes:1 t2:1 solution:5 t0:49 large:1 admissible:1 pˆ2:9 phase:1 indices:6 relation:5 optics:1 smaller:1 force:1 consistent:1 estimates:1 literature:1 sign:3 second:5 evaluated:3 follow:1 dynamics:4 estimated:1 selfadjointness:1 canonical:4 spectral:1 established:1 stands:1 rate:1 incompatible:1 giving:1 trivial:1 specification:1 analogously:1 en:6 fifth:1 goes:1 suppose:3 filled:1 satisfy:4 degree:1 respectively:3 here:13 behaviour:6 canonically:2 simon:1 separation:1 relaxation:1 path:1 november:1 aχ:1 equations:1 appears:1 change:2 box:27 spite:2 covers:1 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quant-ph9811071.txt |@word since:1 radiation:1 results:1 rest:1 known:1 relation:13 using:1 alternative:1 d2:2 reasoning:1 york:1 group:1 generator:1 field:1 pˆi:4 commutators:2 photons:1 pˆj:8 seems:2 hall:1 going:2 transformed:1 choose:2 transformation:4 momentum:5 means:2 de:2 dt2:1 finding:2 preprint:1 cannot:2 ˆi:5 interesting:1 nov:1 accepted:1 prentice:1 dq:14 school:1 particle:1 presented:1 always:1 university:2 arxiv:1 solution:1 solved:1 vector:1 louis:1 qi:3 identifies:1 qj:1 abbassi:1 classical:1 frame:1 related:1 identified:1 see:1 result:3 impossible:1 quantum:4 iran:1 operation:1 employment:1 satisfies:1 canonical:2 commutation:8 lead:1 section:2 trivially:1 favour:1 find:1 particles:12 written:1 above:2 between:4 new:5 ˆj:7 boost:1 wiley:1 recently:1 theory:1 fondation:1 however:1 here:2 how:1 reason:1 free:1 although:1 based:6 annales:1 originates:1 box:1 both:1 about:1 derivation:2 most:1 golshani:1 according:1 o:1 motion:1 addition:1 massive:2 published:1 hence:1 suitable:2 consequently:1 cˆ1:1 outlook:1 symmetry:1 number:1 references:1 operator:9 proved:1 readily:1 transformations:2 prove:1 introduction:1 there:1 system:2 been:1 linear:1 therefore:3 generators:1 ph:1 speaking:1 gives:2 function:1 hc2:1 direction:2 form:1 operators:7 photon:3 but:2 jordan:2 authors:1 tehran:1 c2:7 translation:1 algebraically:1 dt:30 must:1 dtj:1 pacs:1 la:1 equation:1 work:1 dept:1 infinitesimal:1 dqj:9 following:2 problem:2 property:1 poincare:1 mechanics:2 constant:3 give:1 abstract:1 am:1 argument:1 ii:2 pˆ:2 our:1 hamiltonian:1 any:2 shojai:1 lie:2 no:1 generally:2 note:1 sciences:1 valid:3 quant:1 department:1 massless:10 parameter:1 heisenberg:1 independent:1 broglie:1 altered:1 algebra:2 hδij:2 time:1 derived:1 commutator:3 qˆi:1 position:7 ballentine:1 unless:1 light:1 well:1 deal:1 mechanical:1 coordinate:2 velocity:6 physics:1 fact:2
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quant-ph9811072.txt |@word our:3 horne:3 particularly:1 consider:1 show:5 violation:9 able:1 over:2 existing:1 course:1 paper:4 through:2 inconsistent:1 nonfactorizable:2 go:1 inference:1 satisfies:1 still:1 trivial:1 its:1 paradoxes:1 before:3 finally:1 based:1 system:2 parameters:1 golshani:1 inconsistency:2 true:1 relativity:3 should:1 state:10 mathematically:1 source:3 only:3 going:3 systems:3 theorem:5 stochastic:4 variables:1 reality:1 above:1 get:1 implicitly:2 bˆ:3 functional:1 famous:1 p12:18 cannot:2 orientations:3 mention:1 press:2 using:4 nov:1 years:1 condition:16 treating:1 school:1 replacing:1 particle:6 level:1 always:1 university:2 arxiv:1 factorizable:1 realistic:5 inequality:8 each:2 relation:3 nonlocality:1 side:1 gerlach:2 mathematical:1 application:1 multiplying:1 often:2 classical:5 people:1 imposing:1 there:3 violated:2 conditional:6 some:1 measurable:1 detection:2 argued:1 imply:1 decays:1 plenum:1 result:3 measurement:1 quantum:17 terms:1 violates:1 special:3 even:2 bility:1 shown:3 inequalities:4 apparatus:2 temptation:1 shimony:3 since:1 rev:1 integration:1 denotes:1 particles:5 when:2 written:1 version:1 decomposition:2 goes:1 between:4 incompatibility:6 new:1 receiving:3 conditions:1 kluwer:1 independence:8 edited:2 iran:4 theory:7 respectively:3 here:2 standard:1 how:1 york:1 directions:2 detecting:1 hand:3 axioms:2 bz:1 takes:2 box:4 definition:4 integrating:1 derivation:1 jarrett:1 ˆb:55 institute:2 cox:1 am:2 density:1 dependence:1 o:4 compatible:1 probable:1 hopkins:1 duced:1 no3:1 opinion:1 studies:2 think:2 experimental:2 first:1 concluded:1 ch:10 spatially:1 probability:17 bell:17 into:2 johns:1 powerful:1 number:1 predictions:3 sixty:1 right:1 references:1 stern:2 apply:1 total:1 necessarily:2 van:1 additional:3 aˆ:7 introduction:4 observes:1 doesn:2 due:2 relations:1 detected:2 their:2 sin2:2 der:1 therefore:5 equation:1 peaceful:3 ph:1 theoretical:2 possible:2 more:1 separated:1 obtained:1 correlations:1 form:2 both:1 quantities:1 formulate:1 prediction:1 because:1 normalized:1 tehran:4 cases:1 spin:2 than:2 p2:20 states:2 p1:20 applying:1 showed:1 pacs:1 originally:1 work:1 see:1 axiom:3 reproduce:2 tensor:1 miller:1 following:1 demonstrate:2 problem:2 outcome:4 root:1 called:3 characterizing:1 proof:1 mechanics:13 merwe:1 vector:1 associated:1 attribute:1 abstract:1 thus:3 pro:1 denote:1 involve:3 clauser:3 assumptions:3 dλ:8 want:1 formulation:1 claimed:1 follows:1 formalism:1 technology:1 physical:4 different:1 conjuction:1 locality:17 analyzers:2 dλρ:3 generally:1 sharif:1 write:1 sciences:1 parts:2 quant:1 uncertainty:1 department:2 mathematics:2 gets:1 parameter:4 conclusion:1 independent:1 product:2 used:7 tried:1 haven:1 opposite:1 models:1 reached:1 what:2 collection:1 singlet:6 deriving:1 most:1 important:3 selleri:1 but:5 demonstrating:1 pair:1 ballentine:4 algebra:1 data:3 sides:1 types:1 sub:1 other:2 prove:1 cause:1 factorized:1 warranted:1 considered:2 space:1 rule:1 academic:1 without:1 so:2 baltimore:1 components:1 mechanical:2 model:13 physics:5 having:2 fact:1 left:1
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quant-ph9811073.txt |@word consider:4 switched:1 global:1 results:1 gy:2 existing:1 generalize:1 computation:10 edu:1 gn:2 adjustment:3 gk:6 gj:1 increase:1 amplification:1 depend:1 knill:5 concerned:1 technique:13 send:1 finally:2 restriction:1 those:5 th:7 include:1 resources:2 applied:3 amplitudes:6 advantage:3 g0:1 far:2 equivalent:2 choice:2 unstructured:1 tradeoffs:1 worst:2 reordering:1 entries:1 mixing:12 difference:1 matrices:23 høyer:4 condition:2 entire:1 gov:5 swapping:1 level:1 cosine:1 fewer:2 large:2 item:5 vector:2 small:4 application:1 smaller:1 concise:1 dealing:1 direct:3 sign:3 approximation:3 second:3 cost:2 invocations:1 further:1 implemented:21 even:4 will:24 errors:1 appear:1 iterating:2 giving:2 section:13 selected:2 http:5 labeled:1 expressed:1 networks:1 access:1 abs:5 concisely:2 d0:1 above:2 basic:1 new:1 method:5 implementable:3 satisfy:1 full:1 exchange:1 respectively:1 applies:1 here:5 ranges:2 desired:18 selective:1 operating:1 bj:3 represented:4 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quant-ph9811074.txt |@word represent:1 concept:3 partial:1 consider:2 limited:1 crucial:5 rob:2 separates:2 reversibility:4 results:7 nato:1 leads:3 commute:1 shimony:1 consists:2 sci:1 moon:5 localized:2 restrictions:1 excludes:1 certainly:1 violate:1 equivalence:1 should:4 acting:2 ψj:5 environment:1 superficially:1 finally:1 device:2 those:2 whatsoever:1 under:7 include:2 p2:2 global:1 takes:1 orthogonal:12 far:3 than:3 conditions:2 stipulate:1 focus:1 corollary:5 p1:2 every:2 minded:2 irreversibility:1 advised:1 mixing:1 experimentally:1 emphasized:9 difference:2 exact:1 condition:9 induced:1 obvious:1 incoherent:2 appart:1 presented:4 cause:1 notes:1 applicable:1 fewer:1 admissible:1 coincidences:3 unproblematic:1 demonstrated:3 indices:1 shows:3 noted:1 upper:1 occurrence:5 discriminates:15 miller:1 consistent:2 direct:2 feasibility:1 discriminated:3 second:1 rigorous:1 further:2 click:1 ionized:1 linear:3 even:3 will:10 what:4 plays:1 stands:1 sun:1 section:10 equipment:1 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quant-ph9811075.txt |@word consider:2 rev:12 riesenfeld:1 focus:2 integration:1 consists:1 expressions:1 inverse:5 depend:1 calculate:1 alamos:2 tt:2 tq:8 tm:6 lewis:4 alberta:1 division:1 results:1 prog:3 husimi:1 nieto:4 condition:4 2κe:2 hamiltonian:12 did:1 υd:1 michael:1 solution:5 differential:2 υt:1 miller:2 consistent:1 go:1 second:4 substitute:1 linear:1 employ:1 nonlinear:2 invertible:1 t2n:1 giving:1 section:6 above:2 new:7 method:3 satisfy:2 respectively:2 here:4 korsch:1 groups:1 aid:1 path:1 equations:46 change:7 obtained:4 buch:1 rdr:1 study:1 studied:5 soliani:1 drt:1 commonly:1 products:1 suitable:1 involves:1 ˇh:2 emerge:1 via:3 kerner:1 apply:4 derivatives:1 use:1 proceed:1 would:1 levine:1 eυ:2 positive:2 mexico:1 next:4 comparing:2 therefore:2 calgary:2 type:4 theoretical:1 possible:1 more:1 becomes:3 operators:7 under:3 odinger:47 eν:5 particular:1 known:1 cases:1 circumstances:1 keeping:1 isomorphism:1 ma:1 permits:1 equation:51 work:1 oscillator:4 remain:1 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quant-ph9811076.txt |@word partial:1 consider:2 gp:25 hats:1 particular:3 results:2 gx:25 four:1 follow:1 expressions:6 research:1 worked:1 gi:7 depend:1 calculate:3 alamos:2 tq:7 finally:3 tm:6 squeezing:1 preserved:1 alberta:1 analogous:1 equalities:1 division:1 g2:1 advantage:2 wave:1 putting:1 nieto:7 matrices:1 groups:1 annihilated:1 hamiltonian:2 did:1 irreducible:1 tanh:2 michael:1 solution:3 gop:4 convenience:2 vector:1 correct:1 wronskian:2 zk:2 miller:2 sin2:1 cosh:12 second:6 primes:1 substitute:1 canonical:1 employ:1 t2n:1 section:12 find:5 ˆc:3 fortschritte:1 above:1 new:2 ˆj:3 ground:2 method:2 ˆn:1 satisfy:7 full:1 respectively:6 here:3 sandberg:1 xξ:1 sinh:10 others:1 equations:32 obtained:4 wesley:1 until:1 studied:1 drt:1 g2x:1 p2:2 products:5 published:1 action:2 placing:1 cˆ2:2 involves:1 regardless:1 requiring:1 prefer:1 unitary:1 apply:1 should:2 establish:1 linearly:1 derivatives:2 use:8 proceed:2 working:2 commun:1 e1:3 objectives:1 mexico:1 next:1 comparing:1 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quant-ph9811077.txt |@word concept:1 reversal:2 seeing:1 being:3 fitch:1 observed:1 nτ:3 results:1 eds:1 experiments:1 through:1 wolf:1 109b:1 mentioned:1 letters:1 asymmetry:1 find:2 eigen:1 caldirola:1 particles:1 trying:1 probability:1 decay:7 energies:1 scenario:1 original:1 seems:1 complex:1 should:1 thermodynamics:1 only:2 other:3 systems:1 under:1 hidden:1 main:1 into:2 real:1 do:1 non:1 motivated:1 greater:1 quantph:1 gellmann:1 possible:1 pions:2 beam:2 reprint:1 indicative:1 they:1 press:1 integer:1 dt:1 now:2 christenson:1 like:1 term:1 reading:1 unlike:1 particle:2 hamiltonian:1 university:1 δt:1 arxiv:1 applicable:2 consisting:1 try:1 discrete:1 academic:1 either:1 arrow:4 h11:1 small:1 reduces:1 survey:1 set:1 energy:2 hard:1 some:1 direct:1 detection:1 touch:1 second:1 computer:1 sec:1 cim:1 quantum:3 purest:1 borne:1 happens:1 separately:1 what:1 appear:1 space:3 nuovo:1 rev:2 otherwise:1 vol:1 state:5 experiment:2 above:3 simplest:1 new:2 net:1 gov:1 email:1 lapse:1 publishers:1 after:1 terms:1 theory:3 nature:1 initially:1 component:1 however:1 here:1 understanding:1 admits:1 wesley:1 completely:1 centenary:1 corp:1 york:2 violation:3 usual:1 put:1 imaginary:1 almost:1 would:4 cern:3 starts:1 compton:1 discussed:1 parts:1 times:1 introduction:1 products:1 context:2 genuinely:1 exotic:1 hyderabad:1 equally:1 snyder:1 natural:1 symmetry:1 point:1 puzzle:5 period:1 three:1 hermitian:1 references:1 been:3 directly:1 einstein:1 elementary:1 cp:2 consider:1 mass:1 speak:1 longman:1 given:1 sates:1 hd1:1 addition:1 positive:1 there:4 system:1 long:3 start:1 turlay:1 quanta:1 therefore:1 way:1 typical:1 harwood:1 ph:1 was:1 theoretical:3 preserved:1 separated:1 addison:1 life:1 lived:2 hawking:1 newtonian:1 kaon:5 johnson:1 explanation:1 exactly:1 principles:1 known:4 shortly:1 believe:1 true:1 than:1 present:1 case:2 relative:1 exception:1 pion:1 quantized:5 penrose:1 science:1 h12:1 work:1 see:1 us:1 tell:1 will:3 decays:4 values:1 field:1 problem:2 history:1 mechanics:2 symmetries:1 process:1 assymetry:1 abstract:1 israel:1 general:2 states:1 sidharth:3 beautiful:1 tiny:1 something:1 ind:1 seen:1 ijmpa:1 any:1 confirmed:1 place:1 infact:1 zero:1 no:2 provide:1 suggest:1 pp:1 h21:1 lett:1 same:1 h22:1 sciences:1 valid:1 quant:1 pure:1 test:1 mathematics:1 out:3 lectures:1 xxx:1 centre:2 may:1 time:17 upon:1 hand:2 chance:1 levels:1 delicate:1 rationale:2 cronin:1 cambridge:1 pais:1 invariance:3 electromagnetism:1 early:1 lee:1 short:1 nov:1 imply:1 considered:2 physics:3 lanl:1 well:4 analysis:1 cosmology:2 relativity:2 feynman:2 so:3 fact:3 mechanical:1 latest:1 words:1 order:1 fermilab:2 laws:1
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quant-ph9811078.txt |@word partial:3 consider:7 squared:6 results:3 leads:1 entropy:9 computation:1 consists:1 remarkably:2 issues:1 whose:2 maximally:2 accademia:1 paris:3 tr:2 nonlocal:1 does:3 squeezing:37 γn:5 th:1 breach:1 worth:1 amplitudes:1 straightforward:2 orthogonal:1 very:7 dell:1 mattle:1 mixing:1 difference:7 condition:1 splitter:7 tra:2 turns:1 trb:3 large:1 optics:3 vincenzo:1 inserting:1 disordered:2 dealing:1 sin2:6 sin3:2 cosh:2 rate:9 value:11 qualitatively:1 dynamics:1 ya2:1 expressions:1 ohmer:1 even:1 nonlinear:2 ˆu:1 section:4 ˆa:4 ˆb:2 new:1 increasing:7 acknowledgments:1 evolving:1 degree:24 respectively:1 modify:2 teleportation:1 here:2 diagonal:1 ranges:3 reported:1 plenio:1 cos3:2 cos2:7 excess:1 concluding:1 consideration:1 change:1 extreme:2 obtained:3 ref:1 shift:15 study:5 studied:2 exiting:3 renzi:1 resulting:2 action:1 suitable:1 klyshko:1 via:1 followed:2 win:3 namely:4 leonhardt:1 outcomes:1 hardy:1 support:1 total:5 unit:4 fed:4 asymptotic:2 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quant-ph9811079.txt |@word consider:1 chain:2 squared:3 magnetic:3 splitting:3 four:1 eds:1 broader:1 bergmann:8 cases:1 whose:1 amplification:1 overlapping:1 concerned:1 technique:7 young:4 passage:2 recurrence:1 finally:2 those:2 elliptic:1 stable:1 p2:1 amplitudes:6 consequently:1 straightforward:1 evolves:1 very:7 frequencies:4 implicitly:1 stroud:1 wave:1 sons:1 summarized:1 mixing:2 experimentally:1 difference:2 condition:9 splitter:2 presented:1 valentin:1 t2:2 t0:8 large:8 convenience:2 vector:1 small:3 eigenvalues:1 optics:3 setup:1 phillips:2 upper:15 smaller:1 10b:1 klaas:1 10a:1 estimates:4 pulse:61 sign:1 approximation:1 elegant:1 zero:5 enhancement:1 chen:1 dynamics:2 implemented:3 situated:1 theory:1 even:2 index:1 unpopulated:3 appear:2 advantageous:1 section:1 near:3 axial:1 above:5 fractional:14 new:2 method:4 satisfy:2 agreement:1 full:1 simultaneously:5 respectively:2 realizations:1 component:3 here:3 atoms:7 desired:5 cos3:1 cos2:3 others:1 directions:1 ratio:3 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quant-ph9811080.txt |@word represent:1 consider:1 ith:1 show:3 supported:1 speedup:1 computes:3 interpreted:1 combinations:1 paper:1 including:1 computation:8 edu:1 consists:2 useful:1 trivial:1 bit:5 ni:1 depend:1 just:3 subinterval:1 maps:1 theorem:1 should:1 lemma:5 rightmost:1 going:1 black:12 choose:1 factor:1 input:6 andris:1 dn:1 division:1 non:1 quantph:1 di:1 matches:1 dam:3 de:1 measurement:2 possible:2 number:2 interrogation:1 framework:1 p1:2 every:2 half:1 bounding:1 variants:1 exact:1 2t:3 term:1 always:1 university:1 arxiv:1 2d:2 vector:1 queries:13 small:1 2m:1 2n:13 2o:4 mosca:1 xi1:3 parity:2 set:1 computed:1 sequence:1 do:1 there:6 variables:3 some:1 approximates:3 bounds:1 each:2 polynomial:6 namely:1 computer:3 result:5 28th:1 apply:1 quantum:12 approximated:3 differ:3 degree:6 index:2 network:2 space:1 ieee:2 sum:3 since:1 its:2 speed:1 fellowship:1 state:4 goes:1 between:2 fast:1 limit:1 induction:1 o1:4 coefficient:3 gives:2 terms:5 theory:1 extend:1 ambainis:2 uj:1 equals:2 interval:2 base:1 california:1 berkeley:4 xid:3 qubits:3 transformations:3 box:12 about:1 oj:3 getting:1 many:2 basis:3 allows:1 equal:2 o:6 p2:2 wolf:1 hence:6 qubit:1 ot:2 studies:1 foundations:2 first:2 arbitrarily:1 goldstone:1 xi:2 xn:14 computations:1 probability:3 gutmann:1 ca:1 address:1 bound:2 ut:4 39th:2 boolean:11 references:1 cleve:1 cs:1 constant:1 size:1 conference:2 given:2 applies:1 van:3 log:8 needed:1 introduction:1 inductive:2 arbitrary:1 u1:1 u0:3 least:2 next:1 their:2 returns:1 assumption:1 fraction:1 ph:4 determining:1 bits:3 beals:2 recovered:1 define:1 function:5 only:1 exactly:1 search:1 but:2 part:1 because:1 mail:1 known:1 implies:1 x1:14 than:1 coefficients:6 must:2 case:4 finitely:1 dth:1 compute:4 showed:1 science:3 require:3 up:2 value:3 final:1 assume:3 xi2:1 grover:2 values:1 error:7 accessed:1 more:1 uc:1 proof:3 sipser:1 unitary:2 proved:1 approximate:2 computing:2 almost:7 abstract:1 measure:1 them:2 states:3 say:1 acm:1 allowed:1 any:3 absolute:1 information:2 functions:13 compared:1 end:1 no:2 buhrman:2 pp:3 proceedings:3 graduate:1 note:1 tight:1 other:3 quant:4 split:1 subintervals:2 symposium:1 several:1 start:2 see:1 shall:1 assignment:2 price:1 use:1 different:3 polynomials:7 most:16 bounded:5 mechanical:1 variable:3 prove:1 lower:1 nov:1 algorithm:2 database:1 considered:1 into:1 required:1 intervals:2 efficient:1 complexity:2 cannot:2 algorithms:1 farhi:1 oracle:3 model:11
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quant-ph9811081.txt |@word since:5 consider:3 remarkable:1 switched:1 rev:10 magnetic:1 lack:1 results:4 sitz:1 four:2 eds:1 scalar:3 riesenfeld:1 expressions:3 disk:2 particles:1 inverse:5 const:4 λin:1 equivalence:1 finally:1 squeezing:12 th:1 under:10 worth:3 p2:3 supported:1 g0:2 very:1 2re:2 wave:24 normalizability:1 every:2 nieto:1 difference:1 exact:12 condition:2 preuss:1 annihilated:2 hamiltonian:17 knight:1 t2:6 solution:2 t1:6 large:2 discrete:7 differential:1 reγ:4 small:2 eigenvalues:1 warszawa:1 optics:2 noted:1 zm:4 zn:1 wronskian:1 sinh2:2 mi:1 literature:3 matrices:1 second:8 further:1 odd:3 substitute:1 canonical:3 even:3 index:5 nonlinear:1 suc:4 moments:8 section:5 associate:1 lαn:3 expressed:7 uniform:1 above:9 overcomplete:1 new:10 waveguide:1 method:2 fiducial:1 body:1 full:1 simultaneously:5 lee:1 relates:1 respectively:1 l1:9 here:2 l21:1 desired:1 l23:1 l22:1 xξ:1 sinh:1 making:1 concluding:2 depend:1 strong:2 equations:2 change:2 obtained:8 chumakov:1 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quant-ph9811082.txt |@word represent:1 code:37 partial:2 consider:6 canonical:5 alternatives:1 leads:2 roy:3 proposition:1 entropy:19 ts:1 computation:1 go:1 follow:1 gk:5 gj:1 compact:2 whose:9 certainly:1 referring:1 knill:2 concerned:1 equivalence:2 tr:41 acting:2 environment:14 preserved:1 under:3 suffered:1 norm:1 ingredient:1 string:3 takes:1 orthogonal:23 far:4 reversibility:6 rise:1 springer:1 choice:1 denoted:4 putting:1 additional:1 summarized:2 ρe:4 difference:1 exact:2 condition:22 paz:1 entire:2 immediately:2 accompanying:1 positions:1 list:1 ascertaining:1 large:1 vector:6 polling:3 dealt:1 indices:1 eigenvalues:5 trr:1 renormalizing:1 noted:1 proof:3 degeneracy:1 smaller:1 illustrating:1 dealing:1 direct:1 sign:1 equation:1 zero:9 equal:1 7th:3 further:3 dynamics:20 theory:6 even:1 index:2 what:4 errors:27 brackets:1 section:4 expressed:1 reasoning:1 henceforth:2 version:1 subspaces:8 new:5 boost:1 consisting:1 satisfy:4 dictates:1 explosion:1 slj:3 reverses:1 exchange:6 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quant-ph9811086.txt |@word childs:1 partial:1 consider:1 gupta:1 particular:1 results:4 follow:1 al10:1 al12:1 technique:2 those:1 under:2 tc:2 overlaps:1 very:2 handling:1 every:1 figs:5 exact:1 condition:1 al1:1 entire:1 level:2 damped:1 microlaser:8 small:1 lapse:1 upper:3 zn:3 sin2:1 sign:1 jump:2 rate:1 datta:1 displays:1 pass:1 further:5 dynamics:5 leakage:1 linear:2 even:1 what:1 sub:4 giving:1 uniform:1 experiment:1 above:1 increasing:1 method:2 full:2 simultaneously:1 degree:1 respectively:3 here:2 atoms:18 met:1 cos2:1 address:1 represented:1 appears:3 obtained:2 incoming:1 wesley:1 study:2 completely:1 leaving:2 resulting:1 suitable:1 useful:1 grained:1 highly:1 rτ:1 addressed:1 streamed:1 should:1 conventional:2 indicated:1 tcav:3 commun:1 flights:1 nonnegligible:3 depicted:2 averaging:1 taken:3 themselves:1 type:2 until:1 more:1 fractions:2 india:1 operators:1 sharply:2 varying:1 given:5 iii:1 ρa:1 evolves:3 account:1 equation:1 theories:1 ρs:2 values:4 making:1 arrive:1 example:1 f1:5 f2:5 f3:2 figure:4 neglected:1 states:3 indicates:1 magnitudes:1 lamb:1 counterpart:2 needs:1 varied:1 travel:2 influences:1 parameter:4 sin:4 upto:1 description:1 may:2 earlier:1 derived:1 respective:1 reflect:1 fi:1 horizontal:1 constants:1 discusses:1 attempt:1 lines:2 su:1 order:1 reservoir:4 over:2 displayed:1 soon:1 thermal:1 paper:2 through:7 lasers:1 captions:1 satisfies:1 jaynes:6 its:4 before:2 thank:1 decay:2 energies:1 continued:1 scully:2 absence:1 fig:9 derivative:1 schmidt:1 versus:1 dissipations:1 yn:3 effects:1 nov:1 discuss:1 represents:1 gets:1 englert:1 2s:1 realistic:1 2g:6 mode:7 each:1 2n:12 higher:5 individually:1 generation:1 energy:1 literature:1 entering:1 happen:1 eq:1 factors:1 since:1 rev:11 increase:6 socalled:1 suggesting:1 induced:2 ref:14 shows:2 mτ:6 after:2 theory:9 interactions:3 pumping:3 davidovich:2 reason:1 rises:1 interaction:5 times:1 motion:1 length:1 hence:1 first:1 already:1 xn:3 number:6 restrict:1 clarity:1 city:1 differ:1 rempe:2 their:7 eqs:1 system:2 adopted:2 sargent:1 indicate:1 calculations:1 percentage:1 structures:1 shifted:1 mostly:1 explanation:1 hillary:1 optical:13 absorbs:1 peaked:3 second:1 annihilation:1 doubly:1 distinguished:1 enhancement:1 khoury:1 mind:1 curves:1 need:1 seen:1 demonstration:1 any:2 kolobov:2 depending:1 mechanism:1 sciences:1 gτ:2 take:1 forces:1 haake:1 towards:1 centre:1 an4:1 involving:1 cummings:6 successive:4 considered:3 average:4 steady:4 martini:1 yang:2 exp:5 velocity:1 salt:1 fact:3 sector:1 show:1 random:3 nτ:1 threshold:3 schenzle:1 find:7 aρ:1 based:1 just:1 parameters:2 situations:1 explain:2 pump:4 short:1 moments:1 only:3 kaler:1 factor:4 attained:3 dependent:2 words:1 during:8 experiments1:1 fields:3 arxiv:1 saturates:1 nayak:2 wavelenghts:1 fixed:6 setup:3 arrival:1 statistical:1 national:1 intensity:2 individual:1 enhanced:1 subject:1 interacting:2 ieee:1 away:1 state:4 various:1 between:2 reading:1 available:1 nature:5 initially:1 emitted:1 however:4 jr:1 jd:1 bose:1 problem:2 improve:1 cos:2 refinement:1 context:1 variance:2 passing:1 experimental:3 simple:2 poissonian:10 relaxation:1 normalisation:1 considering:1 cavities:1 capable:3 addition:3 due:5 been:1 damping:1 interest:1 basic:1 ph:1 pn:6 addison:1 generating:2 contribute:1 flight:3 photon:17 coherent:1 spin:1 present:7 case:3 p0:2 novel:1 laser:5 value:3 near:3 bergou:1 evaluating:1 situation:2 walther:2 almost:2 characteristics:6 thus:6 vm:1 vn:3 agarwal:2 different:2 author:2 make:1 radiation:3 same:1 quant:1 pauli:1 dimensionless:1 regime:4 events:4 difficult:1 independent:1 used:1 see:1 effect:1 purpose:1 recent:1 lower:1 disregards:1 well:3 analysis:1 solve:1 calcutta:1 model:1 recasting:1 proposed:2 being:2 intervals:2 atomic:12 alternative:1 enters:1 photons:2 character:1 lake:1 other:1 lett:4 input:1 extensive:1 opt:3 saturation:2 increased:2 depends:1 possible:2 judgement:1 increases:3 vacuum:2 using:1 necessary:1 like:1 follows:1 flux:1 because:1 experiments:1 streaming:1 proper:1 happens:1 lead:1 javanainen:1 cavity:42 microwave:1 does:2 provides:1 proc:1 ba:1 selecting:1 analysed:1 broken:5 orszag:1 dictated:1 properties:1 about:4 would:3 discussed:1 dependence:1 o:2 briegel:1 range:1 introduced:1 slightly:3 block:1 own:2 presence:1 into:5 obtaining:1 included:2 references:1 operator:1 proportional:2 statistics:5 strictly:1 there:1 noticed:1 way:2 analyze:1 assumes:1 coarse:1 function:4 analyse:1 but:1 atom:25 line:6 dissipative:2 zhu:1 micromaser:2 resonator:2 us:1 pumped:1 distribution:4 professor:1 purcell:1 regimes:1 constant:5 curve:1 abstract:1 describe:2 influence:4 duration:1 single:3 reservoirs:2 lifetime:4 moves:1 irrespective:1 resonating:1 functions:1 compared:1 dotted:4 whereas:1 detail:3 field:25 valid:1 nonclassical:5 generated:1 important:1 peak:1 dissipation:4 feld:4 meystre:2 structure:4 upwards:1 coupling:4 assume:1 physics:1 interval:1 pseudo:1 mass:1 time:10 n0:4 4g:2 n2:1 having:2 once:1
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quant-ph9811087.txt |@word show:1 violation:4 eres:1 pointed:1 half:1 scattered:1 results:3 ne:2 presence:4 paper:3 including:1 schulz:1 organisatie:1 research:3 scattering:11 nonintegral:1 note:1 family:1 density:3 point:1 enough:1 scientific:1 hall:4 ρxy:1 charge:1 potential:1 corresponds:2 lett:5 under:2 main:1 local:1 magnetic:2 momentum:2 applied:2 spinless:1 string:1 dependent:1 between:1 sonin:1 possible:1 wave:1 δl0:5 simply:1 effects:1 they:1 new:2 integer:1 discuss:4 dp:1 alexander:1 easily:1 modifications:1 netherlands:2 imposed:1 like:1 particle:1 made:1 ref:1 arxiv:1 rotationally:4 kruislaan:1 δl:1 europhys:2 yields:1 either:1 el:4 through:1 der:1 mean:1 coefficient:1 en:1 modulo:1 namely:1 vortices:2 fundamenteel:1 energy:4 some:3 ends:1 self:2 see:4 radius:1 result:1 amsterdam:1 quantum:1 invariant:5 2me:1 neglecting:1 nonstandard:5 transport:1 out:2 nonzero:1 separately:1 what:1 total:1 interacting:1 flux:7 contributions:1 section:9 apply:1 rev:4 vortex:3 comments:1 tend:1 particles:1 state:3 does:1 various:1 boundary:5 fom:1 instituut:1 cosmic:1 conditions:6 contrast:1 nv:1 commute:1 foundation:1 outgoing:1 bound:4 theory:2 ıˇcek:3 equivalent:1 mechanisms:1 however:1 here:1 standard:1 incident:1 concentrate:1 substitution:1 virial:1 respect:2 appears:1 bz:1 differential:7 hc2:1 both:2 cos:6 anyons:1 my:1 electrons:1 discussed:1 voor:3 etc:1 shift:3 periodic:1 extensions:2 receives:1 consequence:1 resonance:2 contribution:1 flip:1 support:1 wetenschappelijk:1 exotic:1 ouvry:1 features:1 symmetry:5 nonrelativistic:1 number:1 channels:3 appropriate:1 dilute:1 references:3 aharonovbohm:1 comtet:1 moreover:2 should:1 electronic:1 angular:2 aharonov:5 conventional:3 long:1 additional:1 second:1 indicate:1 remains:1 positive:1 adjoint:2 give:1 only:2 been:3 their:2 sin2:1 much:1 fermions:2 way:1 onderzoek:2 ph:2 was:1 ann:1 more:1 function:1 field:2 direction:2 corresponding:1 discussion:1 asymmetric:3 quantities:1 regard:2 stichting:1 jul:1 pierced:2 neutral:1 part:2 known:1 hc:1 cases:1 manifests:1 spin:1 than:1 coupling:1 case:8 rotational:6 organization:1 pacs:3 gravitational:1 work:1 depends:3 us:2 matter:1 while:1 limit:3 were:3 anomalous:1 magnetotransport:1 example:2 history:1 program:1 resistivity:1 sousa:1 do:1 certain:1 abstract:1 surprisingly:1 nederlandse:1 general:3 states:2 financial:1 itself:1 o:1 dθ:3 mod:1 vanish:1 occur:1 currents:2 physical:1 different:1 compared:1 angle:1 materie:1 no:1 generic:1 latter:2 breaking:1 moroz:3 cross:9 arctan:1 write:1 sound:1 other:1 quant:1 becomes:1 units:1 resulting:1 parameter:1 sin:8 channel:1 rise:1 multiple:1 electric:1 singular:1 persistent:2 effect:6 moment:1 plane:2 significant:1 waves:1 phase:3 verified:1 invariance:1 class:1 recent:1 ago:1 dϕ:2 longer:1 scenario:2 nevertheless:1 up:1 calculated:2 dσ:5 bohm:5 sj:1 de:1 mass:1 fundamental:1 time:2 position:1 backward:1 tube:5 fact:1
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quant-ph9811088.txt |@word partial:2 ceases:1 particular:1 leads:1 expressions:1 saved:1 reˇ:2 spector:1 const:1 attracted:1 mutatis:1 equivalence:1 quasi:3 th:1 under:2 mutandis:1 nodes:1 summarizes:1 straightforward:1 g0:2 very:2 misunderstanding:2 choice:1 normalizability:3 anonymous:3 fall:1 exact:4 condition:11 obvious:1 presented:1 did:1 notes:1 solution:3 manifestly:2 inspection:1 originally:1 prevent:1 dutra:10 integrability:1 canonical:1 even:4 what:1 nonlinear:1 appear:1 contributed:1 current:1 evoked:1 new:4 method:1 satisfy:3 degree:1 component:2 here:2 behaviour:1 simon:1 represented:1 equations:4 appears:2 change:1 roychoudhury:1 leaves:1 thoroughly:1 resulting:1 usually:1 makes:1 der:1 varshni:2 formulated:1 useful:1 extra:1 hermite:4 merely:2 private:1 highly:1 decrease:1 counts:1 use:1 feb:1 asymptotic:3 would:3 remains:1 positive:1 contains:1 finally:1 next:1 few:5 type:1 more:6 becomes:1 operators:1 odinger:5 validity:1 tested:1 berlin:1 excellent:1 known:2 iv:1 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quant-ph9811089.txt |@word represent:3 sci:1 consider:2 illustrates:1 caused:1 davies:2 global:1 results:6 illustrated:3 known:1 scalar:2 mile:1 defining:1 grateful:1 consists:3 follow:3 amplified:1 localized:2 optical:2 whose:3 maximally:1 depend:4 4ns:1 clarke:1 description:2 deterministic:2 editors:5 nonlocal:11 presents:2 violation:1 monotonically:1 present:3 under:1 stochastic:7 include:3 nouvelle:1 synchronized:1 outside:1 very:4 none:1 choice:1 isham:1 every:4 experimentally:2 difference:3 condition:6 leads:9 school:1 routledge:1 lucien:1 level:1 interpretations:1 unsuspected:1 solution:5 t0:2 large:6 solid:1 convenience:1 metaphysics:1 small:6 study:1 optics:3 equation:5 solutions:1 outstanding:1 smaller:1 says:1 foliating:1 consistent:12 strunz:1 qmw:1 past:1 zero:4 noise:1 dordrecht:2 further:3 dynamics:41 linear:2 even:3 what:1 plays:2 stands:1 apparatus:5 incompatible:2 giving:1 sun:2 section:16 localization:2 brief:1 uniform:2 current:2 version:1 goes:2 values:2 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quant-ph9812011.txt |@word represent:1 concept:4 consider:12 limited:1 eph:1 separates:1 results:3 existing:1 four:8 commute:3 plays:1 follow:2 expressions:7 localized:14 poorly:1 whose:4 depend:4 tx:7 ty:7 assumptions:2 equivalence:1 tr:6 ts:8 interactions:5 finally:10 hampered:1 indicate:2 present:5 th:2 under:1 desiderata:1 td:9 must:15 dramatically:1 applied:1 conjecture:1 amplitudes:2 provides:1 outside:1 very:4 frequencies:1 rise:1 myself:1 mph:1 wave:20 electron:3 eberhard:1 every:3 chooses:1 zeitschrift:2 difference:1 matrices:8 condition:1 preuss:1 obvious:2 solves:1 hamiltonian:5 did:2 irreducible:1 developing:1 solution:10 try:4 discrete:2 vector:5 minimal:1 small:3 eigenvalues:2 shows:2 originally:1 como:1 application:1 force:1 periodicity:1 maneuver:1 dealing:1 za:7 zb:5 cosh:2 approximation:1 second:10 cost:1 lines:1 enhancement:1 further:1 copenhagen:1 quite:1 canonical:1 even:4 xψ:1 adds:1 appear:1 incompatible:2 giving:1 section:15 probably:1 favour:1 expressed:10 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quant-ph9812012.txt |@word consider:3 pointing:1 rev:3 equalities:2 results:2 four:5 reasoning:1 dimensionality:1 depend:2 violate:1 subjected:1 technique:1 nπ:5 finally:1 spain:1 worth:2 straightforward:1 very:1 rise:1 choice:2 every:2 condition:4 level:1 turns:2 t4:3 t2:3 t3:3 t1:3 vector:10 indices:2 eigenvalues:6 equation:1 degeneracy:5 zn:77 zi:20 10b:1 dealing:1 10a:2 direct:3 10d:2 sign:2 elegant:1 zero:2 evaluated:1 greenberger:4 what:1 stands:1 giving:5 version:1 above:3 obvious:2 satisfy:1 edited:1 simultaneously:2 respectively:1 diagonalises:1 here:2 met:2 directions:3 µmax:1 along:7 respect:1 z1:89 z2:96 z3:19 alto:1 involved:2 vectors:4 contradiction:5 amount:1 published:1 suitable:4 involves:1 uniquely:2 examining:1 regardless:1 outcomes:1 hardy:6 sgn:21 summation:2 total:1 linearly:2 readily:1 use:2 takes:2 would:3 prove:2 remains:1 negative:2 noting:2 ψn:1 therefore:1 means:1 type:3 entails:1 today:1 more:1 becomes:1 operators:2 apparent:3 particular:3 iii:1 must:11 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quant-ph9812013.txt |@word partial:1 consider:1 illustrates:1 results:2 existing:2 four:4 entropy:3 research:1 whose:1 finally:1 under:3 2γl:1 applied:1 belonging:1 kent:1 continues:1 experimentally:1 illustrated:1 swapping:22 exits:1 accompanying:1 knight:4 large:1 indefinitely:1 divides:1 optics:1 smaller:4 degrading:1 sin4:2 sin2:2 second:1 pass:1 further:3 implemented:1 even:2 what:1 redistributed:1 section:1 shares:4 henceforth:1 experiment:2 above:6 fractional:3 shared:18 3a:2 increasing:1 method:12 contrast:1 coefficient:1 degree:3 exchange:1 never:1 teleportation:4 here:7 cos4:2 cos2:6 path:2 along:1 change:2 obtained:2 convert:2 involved:1 larger:1 allows:1 completely:1 procedure:12 schumacher:2 implement:1 suitable:1 makes:1 golden:1 via:6 followed:2 projection:6 appelbaum:1 extra:1 apr:1 outcomes:5 brought:2 hardy:1 unabsorbed:1 decrease:1 unit:1 use:5 additive:2 proceed:4 would:4 massar:1 remains:3 positive:2 next:1 classically:1 depicted:1 call:1 therefore:2 centre:1 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quant-ph9812014.txt |@word monte:2 evidence:1 consider:13 washed:2 varying:1 replot:1 focus:2 four:1 qmc:7 shone:1 lewenstein:4 incommensurable:1 alt:1 faster:1 contributions:1 whose:4 dimensionality:2 depend:1 technique:1 canonical:1 franck:6 presents:1 accordingly:1 quasi:6 those:5 under:1 tf:11 analogous:2 dramatically:1 eliminate:1 applied:4 belonging:1 random:1 amplitudes:1 string:6 evolves:1 very:5 frequencies:11 huang:1 modes:19 springer:1 induce:1 results:7 p1:2 sidebands:7 summarized:1 resonant:2 experimentally:2 difference:5 exact:2 semiaxis:2 condition:9 cool:7 treating:1 europhys:2 incoherent:1 vibrational:25 level:3 yin:1 accidentally:1 large:5 solid:13 addressable:1 small:6 markov:2 refer:2 der:1 degeneracy:3 phillips:1 application:1 smaller:5 slower:1 oscillation:2 hamann:1 dealing:1 approximation:15 rate:19 noise:1 value:1 perfect:1 chen:1 further:4 dynamics:5 carlo:2 substitute:1 theory:3 even:3 index:3 nonlinear:1 plays:1 trapping:9 pax:1 giving:1 sum:2 selected:1 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quant-ph9812015.txt |@word ambiguities:1 set:1 consider:1 xˆ:6 supported:1 find:1 obtain:1 ds:4 x2:1 relation:3 y0:6 still:1 trivial:1 its:1 δx0:1 write:1 depend:1 knowledge:1 commutators:5 seems:1 actually:1 explicitly:1 tj:6 ti:5 derivative:1 lagrangians:2 momentum:1 correspondence:2 do:2 non:14 notation:1 zagreb:1 introduce:2 bjorken:1 every:1 know:1 they:1 using:1 boˇskovi:1 now:1 discuss:4 special:1 february:1 equality:4 δx:1 hamiltonian:3 approach:2 δt:2 arxiv:1 solution:2 roy:1 large:1 discrete:1 croatia:2 fields:1 δf:2 london:1 fixed:1 δb:2 side:1 δa:2 right:1 classical:5 some:1 proc:1 see:2 quantum:8 dynamics:1 analog:1 canonical:2 putting:1 provided:1 commutation:3 brackets:17 schr:2 coincide:2 label:1 rudjer:1 does:3 between:3 new:1 irb:1 conditions:1 satisfy:1 theory:5 degree:2 however:3 tacit:1 standard:2 manifestly:1 identifications:1 york:1 although:1 article:2 drell:1 equations:4 πg:4 obtained:2 definition:2 cos:8 instant:1 ministry:1 institute:1 freedom:3 transition:1 discussed:2 dependence:2 o:1 motion:4 p2:1 faust:1 poisson:20 interesting:1 other:1 first:1 among:1 soc:1 initial:1 ours:1 point:1 simple:2 communication:1 variables:2 xg:13 private:1 because:2 references:1 directly:1 illustrate:1 given:1 described:1 reference:1 similarly:1 ordering:1 there:2 mcgrawhill:1 system:1 relations:1 their:2 linear:5 pg:12 way:2 relativistic:2 degrees:1 ph:1 was:1 theoretical:1 define:1 corresponding:3 relationship:3 hr:2 operators:4 under:1 odinger:2 δti:1 part:1 textbook:1 particular:3 known:1 specialists:1 x0:6 general:3 coefficients:1 case:4 eit:1 d3:2 science:1 work:2 us:4 replaced:1 dec:1 example:3 peierls:1 mechanics:4 ae:1 division:1 defined:1 explicit:2 abstract:1 conventional:2 thus:1 generalization:6 equal:22 indicates:1 pˆ:11 contract:1 need:1 technology:1 any:1 constructed:3 functions:2 form:2 no:2 lim:4 nikoli:1 generally:2 note:2 field:5 antisymmetry:1 bracket:3 quant:1 generalized:1 φg:4 ordinary:3 analogs:1 sin:8 heisenberg:2 picture:3 marolf:1 shall:1 different:1 hand:2 class:1 give:1 acknowledgement:1 republic:1 calculated:1 space:1 well:3 shortly:1 more:1 construction:4 completely:1 time:24 representation:1 laws:1 physics:2 covariant:1
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quant-ph9812016.txt |@word operations:1 construct:1 set:1 consider:3 pointing:1 show:1 buzek:1 supported:7 merit:1 interpreted:1 leads:1 ηd:12 transforms:1 during:1 constituent:1 mentioned:2 followed:1 fidelity:16 volta:1 d2:2 find:1 down:1 τj:1 massar:1 derive:3 depend:1 calculate:1 candidate:1 density:6 concerned:1 tr:2 acting:1 theoret:1 better:3 only:2 version:1 generators:1 systems:6 pavia:2 factor:4 input:6 transformation:2 erp:1 identical:6 reconstructing:1 workshops:1 di:2 far:1 familiar:1 popescu:1 decomposed:1 processes:1 introduce:1 process:4 cannot:3 entangled:1 identically:1 arriving:1 using:2 now:1 spanned:1 helpful:1 restrict:1 february:1 equality:3 like:1 particle:2 level:1 follows:2 reduces:1 arxiv:1 immediately:1 european:1 establishing:1 bailey:1 network:1 vector:3 shrunk:1 output:8 universit:1 conclusion:1 out:1 reduced:3 upper:1 2δij:1 could:3 villa:1 reference:1 map:2 a52:1 thank:1 related:1 affiliation:1 namely:3 cloning:11 measurement:7 quantum:17 invariant:1 λi:2 generates:1 preparation:1 shown:2 est:15 matrix:2 lead:1 space:1 shrinking:5 furthermore:2 rev:6 reach:1 bruß:1 research:1 symmetric:9 state:24 does:1 decomposition:1 above:6 between:3 αi:6 formula:1 hold:1 method:2 mahler:1 available:1 notice:2 performing:3 creating:2 extend:1 associate:1 qubits:1 problems:1 each:1 fisica:1 here:1 paper:1 clarify:1 same:2 group:1 estimate:1 refers:1 lett:3 stage:2 received:1 outcome:1 would:1 always:1 macchiavello:1 chiara:1 τi:5 according:2 contradiction:2 bassi:1 connection:3 due:3 context:1 permutation:1 concatenation:1 inst:1 estimation:18 bloch:3 first:1 composed:1 considerations:1 via:1 hd:1 physik:1 probability:1 conclude:1 into:1 number:1 copies:5 dimensional:10 multiply:1 appropriate:1 ddimensional:1 least:1 directly:1 described:1 operator:5 apply:1 total:4 establish:1 unit:1 constructing:1 given:7 necessarily:1 viale:1 transformations:1 prepare:1 prove:2 covariant:2 positive:2 dipartimento:1 support:1 question:1 system:4 been:4 center:1 povm:2 ψi:8 call:1 therefore:4 way:2 second:2 length:1 ph:1 was:2 1l:5 qcm:8 more:1 corresponding:1 both:1 clarity:1 outputs:4 operators:1 under:1 subspace:8 larger:1 benasque:1 fest:1 generalizing:1 link:2 particular:1 arranging:1 cloner:5 line:2 role:1 than:5 present:1 must:1 case:2 explicitly:1 infm:1 valued:1 coefficients:1 ρd:2 a58:2 concatenated:1 shrink:1 equation:4 work:1 depends:1 us:2 ur:1 will:2 below:1 limit:2 germany:1 were:1 following:3 dec:1 similar:1 taking:2 procedure:6 result:2 zanardi:2 opt:16 written:2 werner:1 figure:1 defined:3 expanding:1 universal:11 thus:5 argument:2 general:2 states:7 discussions:1 performed:1 want:1 sense:1 create:1 any:2 viewed:1 information:1 subsystems:1 italy:2 together:1 perform:2 lim:1 ekert:3 torino:1 isi:2 start:1 note:4 how:1 quant:1 generalized:4 pure:11 universality:1 finding:1 optimal:21 those:1 finite:2 ensemble:2 higher:2 inputs:11 inequality:4 extended:1 oneself:1 see:1 opposite:1 proving:1 after:2 derived:4 tmr:1 noticing:1 linearity:2 fd:14 purpose:1 letter:1 possible:2 moreover:1 completed:1 consisting:1 dimensions:1 value:1 hannover:2 remember:2 algorithm:2 pµ:2 assume:1 acknowledge:1 average:3 factors:1 well:1 su:1 think:1 concatenate:1 part:1 prepared:1 fundamental:1 subsequent:2 severo:1 optimality:1 physics:2 order:2
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quant-ph9812017.txt |@word secondly:3 limited:2 lagrangian:1 dynamic:6 entropy:1 consists:5 localized:2 whose:5 calculate:1 presents:1 under:8 ergo:1 desirable:1 every:1 experimentally:1 basics:1 supports:1 solution:3 vector:16 markov:1 straight:1 force:5 specially:1 decoherent:1 consistent:10 japanese:1 pulse:3 approximation:1 surrounding:1 second:4 even:7 established:1 selected:7 supplied:1 above:4 new:15 coefficient:6 deemed:1 never:1 here:3 atoms:5 represented:16 path:57 obtained:10 rigorously:1 study:3 changed:1 completely:8 projection:2 highly:1 brought:1 total:5 propagators:4 unit:2 would:4 negative:3 definiteness:1 call:1 therefore:3 survive:2 cαα:3 type:7 until:1 separated:1 nauka:4 composite:4 brings:1 odinger:27 berlin:3 excellent:4 continual:1 hold:3 circumstances:1 springer:4 word:1 work:1 theories:1 macroscopically:3 mq:1 root:2 example:17 give:12 relativistic:6 indicates:4 absolute:1 end:4 feature:1 how:12 nontrivial:1 answer:6 ordinary:1 description:41 reconciled:2 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quant-ph9812021.txt |@word secondly:1 measurements:2 consider:2 remarkable:1 similarity:1 broaden:1 amplifier:10 results:2 quadrature:8 gd:1 gc:1 edu:1 amplified:3 manipulations:3 looking:1 amplification:4 technique:2 under:1 sent:2 fax:1 very:4 frequencies:2 figs:2 mixing:1 difference:1 entire:1 transmission:2 12th:1 proposals:2 attempts:1 large:2 discrete:2 noted:1 work:1 versatility:1 direct:3 demonstrations:2 further:1 port:2 trick:1 appear:1 sum:1 current:3 reconstruction:2 new:1 respectively:1 teleportation:16 here:2 desired:1 represented:1 november:1 strong:2 great:1 incoming:1 sender:3 shift:2 study:1 simultaneous:2 narrow:1 equivalence:1 see:2 replace:1 hardy:1 tools:1 use:1 would:2 remains:1 process:3 depicted:2 australian:1 noisy:1 today:1 more:2 flat:1 sharing:1 formally:1 vacuums:1 becomes:1 detects:1 insights:1 high:2 science:2 taguchi:1 when:2 oscillator:2 london:1 following:2 dec:1 example:1 boschi:1 employs:1 give:1 calculation:1 bennett:2 states:1 effectively:1 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quant-ph9812022.txt |@word represent:2 forger:1 allowed:1 consider:1 remarkable:1 caused:1 results:8 leads:1 commute:2 entropy:1 anticorrelated:1 consists:2 particles:7 certainly:1 amplification:6 barnett:2 pointing:1 transferred:1 subjected:1 technique:3 advances:2 send:2 supported:1 finally:3 device:1 those:1 under:3 sent:3 case:2 probe:3 mainstream:1 straightforward:1 orthogonal:2 far:1 circa:1 continues:1 secretly:2 springer:1 implausible:1 exact:1 electronics:2 disturb:1 subsets:1 presented:8 transmission:6 mor:1 guo:1 eve:20 large:1 discrete:1 convenience:1 subway:1 small:1 optics:6 noted:2 locate:1 measurable:1 demonstrations:1 elegant:1 likely:1 design:1 further:3 implemented:5 fibres:1 theory:2 refereed:1 reconciliation:3 what:4 errors:1 rate:2 incompatible:1 sun:1 section:6 selected:1 brief:1 networks:1 henceforth:1 experiment:1 above:2 shared:3 method:2 implementable:1 publications:1 satisfy:2 simultaneously:4 whose:1 respectively:6 error:10 component:1 following:4 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quant-ph9812023.txt |@word limited:2 extrapolated:1 partial:1 consider:7 helstrom:1 varying:1 desirable:1 results:32 quadrature:1 expressions:3 discretized:1 scr:1 berry:1 depend:1 paris:9 producing:1 technique:5 tr:1 mials:1 squeezing:3 those:2 under:5 stochastic:3 include:1 divergent:1 p2:2 worse:2 advantage:2 zhang:1 far:9 2re:1 springer:3 choice:1 figs:1 entries:1 experimentally:6 difference:6 exact:4 entire:2 4n0:1 hamiltonian:1 did:1 turns:1 notes:1 solution:7 correct:2 large:13 solved:1 vector:1 h11:1 small:5 eigenvalues:1 optics:2 noted:1 upper:3 smaller:2 lecture:1 cosh:1 approximation:6 second:7 further:1 estimated:3 ohmer:1 linear:1 even:3 errors:1 power:7 2cos:1 giving:1 diag:1 sum:1 11b:1 xφ:1 while:1 expressed:2 agrees:2 consistently:1 experiment:1 above:10 roundoff:2 new:2 method:4 contrast:2 satisfy:1 edited:2 full:2 respectively:2 promising:1 here:6 sinh:1 excess:2 consideration:1 along:1 equations:2 imperfections:1 19b:1 obtained:10 great:1 increments:1 shift:2 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quant-ph9812024.txt |@word consider:2 similarity:3 lack:1 eds:1 edu:1 certainly:2 referring:1 alamos:4 malley:1 finally:1 under:1 maryland:1 case:2 finkelstein:3 attribution:1 distorting:1 very:2 wishes:1 every:1 treating:1 presented:1 notes:1 list:2 applicable:1 t1:1 vector:7 noted:2 says:1 what:3 appear:1 selected:1 abl:5 reply:1 here:1 free:2 lev:2 others:1 obtained:2 larger:1 suggests:1 action:1 antecedents:2 history:1 studies:1 appropriately:1 useful:1 requiring:1 merely:1 private:1 outcomes:4 apply:1 causal:1 would:6 negative:1 call:1 strike:1 dogma:1 foundations:1 hold:2 ontological:1 md:1 none:1 values:7 dec:1 my:8 example:2 something:1 claim:3 weaker:1 indicated:1 december:1 bennett:2 states:1 sphere:2 performed:2 sense:2 evidently:1 end:1 hoc:1 rather:3 how:3 significance:1 philosophy:2 italics:1 light:1 element:1 so:1 order:1 talk:1 interpretation:2 course:1 paper:5 differs:1 thank:1 temporal:1 jim:1 differently:1 hidden:2 might:5 arguments:2 correspondence:2 non:3 material:3 they:2 worlds:7 term:3 fully:1 university:2 each:2 bona:1 t2:3 measurement:6 quantum:6 beyond:1 special:1 space:1 defend:1 rev:1 supports:1 correct:1 theory:3 rely:1 possibility:4 amato:2 could:2 first:2 xi:2 probability:1 variables:2 philosophical:1 aharonov:4 xii:1 system:12 statement:5 exactly:1 albert:4 regards:1 believe:1 than:3 distance:1 kind:2 were:1 outcome:3 pre:1 false:2 cohen:1 modern:1 mind:1 argument:1 kastner:3 say:2 defending:1 counterfactuals:7 clearly:1 symmetrized:4 genuine:1 mermin:3 latter:1 note:1 instance:1 unless:1 park:1 most:2 nothing:1 acknowledgements:1 measured:1 considered:1 physics:2 notion:1 fact:2 conditionals:3 saying:1 lewis:2 charles:1 merit:1 find:1 q1:1 q3:1 q2:1 based:1 title:1 assertion:1 should:1 only:6 explicitly:1 adequate:1 dispute:1 do:1 his:5 criticized:1 cannot:3 conjunction:2 arxiv:1 borrow:1 experiments:1 ascertain:3 qi:1 fixed:2 valid:1 qn:1 set:1 conjuncts:2 see:3 individual:1 college:1 discussions:1 forthcoming:1 violates:1 closer:1 apparently:1 review:2 definite:1 state:7 between:3 justified:1 reading:4 conditions:2 publishers:1 recently:1 weak:4 however:3 harvard:1 article:2 observable:2 essentially:1 uncertainty:1 σz:2 σy:2 σx:2 context:1 argue:1 arbitrarily:1 co:1 point:1 maintained:1 assertions:1 moreover:2 throughout:1 publishing:1 been:1 much:2 pf:1 ph:7 pi:1 pn:1 empty:1 direction:1 corresponding:1 relevance:1 understand:1 spin:2 p2:1 p3:1 p1:1 applies:1 them:2 comparative:1 author:1 suggest:1 make:4 jerry:1 same:5 any:2 member:1 quant:7 emphasize:1 fide:1 jeffrey:1 indianapolis:1 closest:4 uses:1 entanglement:1 nevertheless:1 analysis:1 vaidman:12 bohm:1 academic:1 sets:1 claims:4 obtain:1 intervals:1 identify:1 potentiality:1 using:1 facts:1 yet:1 preprint:4 kluwer:1 seems:1 unambiguously:1 lett:1 usage:1 match:1 designate:1 possible:6 background:2 press:1 world:5 advanced:1 necessary:1 like:2 particle:4 because:1 classical:1 some:3 elements:7 curious:2 happens:1 measurements:1 counterfactual:16 umd:1 does:2 passion:1 vacuously:1 post:1 refers:1 properties:3 about:3 actual:3 usa:1 anything:1 discussed:2 modal:1 cambridge:1 letters:1 within:1 appropriate:2 references:1 wam:1 support:1 there:1 dispersion:2 los:4 way:2 was:3 form:1 regard:1 but:8 properly:1 bub:1 trying:1 true:2 he:8 made:1 applying:1 intuitive:1 up:1 mechanics:1 ad:1 abstract:1 am:3 general:1 single:1 hackett:1 commuting:1 physical:1 no:2 fixing:2 reality:6 other:4 department:1 permitting:2 accidental:1 convincing:1 antecedent:9 syntactical:1 required:3 rule:5 time:6 observables:5 having:1
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