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quant-ph9707002.txt |@word partial:2 consider:4 four:1 consists:1 certainly:2 depend:1 technique:1 tr:4 present:1 under:3 conjecture:1 very:1 implicitly:1 tends:1 corollary:3 every:3 matrices:1 høyer:1 dim:5 transmission:2 turns:1 noiseless:1 vector:1 eigenvalues:2 trs:6 noted:1 trw:6 trv:1 upper:3 neighborhood:1 rate:8 theory:4 3y:9 analogously:1 above:2 new:3 error:1 ranges:1 plenio:3 appropriate:1 sending:1 remark:1 vectors:1 allows:2 reason:1 ignoring:1 suggests:1 products:1 schumacher:1 formation:1 changes:1 plotted:1 via:2 family:1 apr:1 apply:1 establish:1 use:1 figure:1 usa:1 positive:4 contains:1 therefore:1 noisy:1 tell:1 more:6 preserving:1 operators:6 corrected:1 particular:13 known:3 producing:1 must:4 ρa:1 room:1 ρi:16 recall:1 work:1 concepts:1 following:2 def:2 proof:3 control:1 compare:1 weaker:1 stream:2 give:1 bennett:4 distillation:1 states:11 contradicts:1 numbers:1 allowed:2 unphysical:1 david:1 information:2 provide:1 get:1 fpi:1 write:2 how:1 pure:1 ensemble:1 fp:15 map:1 product:1 mapping:1 produce:1 multiplication:1 amenable:1 natural:1 third:1 sp:2 explicit:1 correspond:1 purification:5 so:3 fundamental:1 representation:2 bipartite:3 operations:8 indeed:2 over:1 vary:1 produced:1 enumerators:3 through:1 berthiaume:1 fidelity:15 still:1 tending:1 derive:1 thank:1 maps:1 chosen:1 fix:1 actually:1 production:1 systems:2 superoperators:13 decreased:1 image:1 correspondence:1 non:1 greater:5 combination:1 conversations:1 largest:1 fig:1 introduce:1 now:2 easily:1 february:1 always:1 2y:4 orthonormal:1 did:1 each:4 2n:5 traces:1 constraints:2 weight:4 reduce:1 extended:1 rippin:1 measure:2 quantum:8 operation:1 out:1 respects:1 shown:4 matrix:1 space:9 since:8 rev:4 research:1 eprint:1 print:6 log2:6 linear:6 associate:1 diagonal:4 quite:1 completely:2 complicated:1 definition:1 depolarizing:2 determining:1 could:2 nonnegative:5 first:2 separable:27 xn:2 mor:1 coding:1 number:2 channels:3 knight:1 impossible:1 separably:2 manuscript:1 given:2 similarly:1 construct:1 statement:1 john:1 gives:1 park:2 superoperator:15 than:6 coefficients:5 wootters:1 fuchs:1 second:2 preparation:1 were:2 result:1 false:2 correction:1 argument:2 say:1 epp:1 exchanging:1 apparently:1 tells:2 lim:2 latter:1 able:1 nonlocality:1 note:4 take:2 indexed:1 begin:1 unless:1 trace:2 any:12 measures:2 what:1 singlet:1 most:2 pair:1 extremely:1 class:1 clear:1 stronger:1 order:1 kv:2 quantifying:1 fact:4 quantity:2 precise:1 shor:3 purely:2 spaces:1 analogue:1 d2:7 agrees:1 d1:4 distributed:1 state:21 should:2 only:3 attained:1 local:11 achieve:1 mixture:1 correctly:1 quantph:1 means:1 cannot:1 words:2 procedures:1 ds:3 arxiv:1 fixed:1 analog:1 strengthened:1 set:6 exists:1 achieved:1 physically:2 tended:1 bounds:6 namely:1 w2:1 w1:1 close:1 satisfies:1 best:1 capacity:2 tensor:2 definite:2 tend:3 symmetric:1 written:3 closed:1 between:2 limit:1 terms:1 nature:1 qubits:2 wj:1 wi:2 however:1 wt:3 concentrated:1 both:1 realizable:1 reverse:1 equal:1 σz:2 σy:2 σx:2 divincenzo:3 qubit:3 relevant:1 bell:4 corresponds:2 dimensional:3 simply:2 polynomial:2 moreover:3 transformations:7 basis:2 locally:1 defined:1 much:1 interest:2 ph:7 pi:16 define:4 observe:1 maximally:3 protocols:1 case:6 invariants:1 value:2 will:4 while:2 suppose:2 applies:1 twoway:1 vb:1 unitary:3 laflamme:1 vj:1 thus:2 ave:1 id:14 macwilliams:1 author:1 clearly:3 improves:1 quant:7 arguments:1 distilled:1 finite:1 used:2 hand:3 v1:2 v2:2 entanglement:18 identity:1 well:4 roughly:1 analysis:1 obviously:1 without:1 components:1 dimension:2 know:1 obtain:3 questions:1 using:5 density:3 alternate:1 had:1 lett:2 theorem:3 input:2 transformation:5 identical:1 enumerator:1 replaced:1 possible:3 additivity:1 increases:1 entangled:5 distillable:5 immediately:2 shadow:1 unique:1 like:1 helpful:3 semi:2 follows:5 specific:1 arbitrary:2 output:3 old:1 qed:3 classical:8 sequence:2 some:3 deduce:1 peter:1 comments:1 does:1 assuming:1 noise:1 ba:1 bi:2 bj:1 although:1 bs:1 hilbert:6 simpler:1 about:1 central:1 would:3 anything:1 range:1 mixed:2 introduced:1 h2:11 communication:5 into:1 bound:13 hermitian:1 operator:1 strictly:3 there:4 vedral:3 low:1 way:3 was:2 lowest:1 form:4 smolin:3 but:6 true:2 partially:1 maximum:1 us:4 epps:3 below:1 those:1 problem:1 andr:1 similar:1 called:1 ub:2 proved:1 separability:1 up:1 ai:7 certain:1 ki:3 general:2 exist:1 identities:2 eric:1 physical:2 ni:5 nj:1 codes:2 no:1 rains:4 when:4 tight:2 other:6 conclude:1 ubs:1 uniformly:1 polynomials:6 studied:1 independently:1 implies:1 lanl:7 together:2 implied:1 far:1
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quant-ph9707003.txt |@word consider:6 squared:1 magnetic:4 dynamic:1 results:1 existing:1 four:1 scalar:1 generalize:1 grateful:1 consists:3 expressions:1 naukova:1 replacements:1 gab:4 γk:1 charge:50 conservation:2 p2:14 far:3 frequencies:1 conditions:2 induce:1 wave:5 electron:13 difference:1 matrices:12 condition:3 gov:1 accompanying:2 t2:14 solution:4 t1:18 large:1 discrete:11 vector:9 guiding:5 application:1 occurrence:1 consistent:1 sign:5 second:2 further:4 index:3 what:1 plays:1 ct1:1 ct2:1 diag:4 analogously:2 expressed:1 current:1 abs:1 conduct:1 new:2 acknowledgments:1 filled:1 movement:4 satisfy:1 exchange:1 respectively:1 equals:1 here:12 behaviour:1 equations:24 change:5 obtained:2 division:1 remarks:1 institute:1 spontaneous:1 study:2 vectors:3 periodic:1 products:2 usually:1 changes:1 useful:2 antineutrino:1 summation:2 neutrino:1 total:2 unit:4 use:1 takes:4 iae:1 found:1 positive:11 ψp:5 eφ:2 negative:16 m1:5 therefore:1 m3:5 m2:6 ψc:7 themselves:1 type:4 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quant-ph9707004.txt |@word supersymmetrical:1 allowed:1 consider:6 similarity:1 rev:4 magnetic:16 global:1 results:1 roy:1 scalar:8 commute:1 generalize:1 spiridonov:1 consists:2 expressions:1 gk:1 gj:2 gi:2 ihep:1 whose:1 depend:2 clarification:1 γk:1 finally:1 investigation:2 petersburg:4 th:1 under:1 discovering:1 analogous:1 include:1 γf:1 case:26 witten:1 g2:2 g3:1 2γi:1 straightforward:2 orthogonal:1 b188:1 wave:7 novel:1 polytechnic:1 nieto:1 matrices:13 semiaxis:2 condition:6 dim:9 presented:2 irreducible:3 presumably:1 list:1 solution:26 leave:1 discrete:2 2b4:2 gauge:1 deleting:1 equation:12 degeneracy:4 b44:1 periodicity:3 sukhatme:1 among:2 b22:6 b21:3 b20:1 fold:1 second:13 incidentally:2 further:3 dynamics:3 4x2:3 linear:4 spectral:2 aim:1 what:1 nonlinear:2 advantageous:1 section:5 expressed:1 nondegeneracy:1 univer:1 above:2 hull:1 new:3 increasing:1 method:5 satisfy:2 q1:10 agreement:2 pose:1 ibid:2 deduces:1 realizations:1 modify:1 residual:1 diagonal:6 behaviour:5 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quant-ph9707005.txt |@word partial:2 consider:1 remarkable:2 qian:1 global:2 results:5 leads:1 ge:1 whose:1 depend:1 essentials:1 iii:3 presents:2 quasi:1 monotonically:1 under:3 anharmonic:10 alternating:1 applied:1 very:1 continues:1 wave:10 additional:1 resonant:1 exact:5 four:1 rβ:14 morley:1 hamiltonian:1 ref:1 large:4 discrete:1 science:1 manifestly:1 eigenvalues:1 βx2:1 configurations:1 force:1 renormalized:1 det:5 consistent:1 zero:1 perspective:1 further:1 air:1 sub:1 selected:1 remain:1 version:1 above:2 scientists:1 kleinert:1 new:2 increasing:3 method:13 coefficient:3 justification:1 degree:2 respectively:2 desired:1 bj:2 xα:1 equations:2 appears:1 z2:1 calculate:1 digits:1 ψl:3 study:1 vectors:2 allows:2 resulting:1 published:2 resonance:1 suitable:3 studies:1 involves:3 via:1 regardless:1 clark:1 highly:2 expect:1 sugar:1 readily:5 plot:1 asymptotic:3 would:2 army:1 predictions:1 e0:4 comparing:1 bender:4 type:1 theoretical:3 minor:1 more:4 zeroes:2 sponds:1 successful:1 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quant-ph9707021.txt |@word magnetic:21 desirable:2 entropy:1 consists:3 kassel:1 localized:1 calculate:1 swap:1 under:7 conjecture:1 rise:2 connects:2 every:10 affect:5 solution:1 δh1:4 frozen:1 vector:11 degeneracy:10 10b:1 10c:1 consistent:3 10a:1 estimates:1 second:7 rigorous:1 estimated:2 b138:1 even:6 established:1 errors:7 above:4 new:13 never:1 equals:1 here:9 atoms:1 represented:8 path:4 interpret:2 obtained:1 property:6 study:2 changed:2 sjm:1 projection:1 classification:2 9a:1 9b:1 replace:1 castagnoli:2 sloane:1 total:1 unit:2 quasi:5 would:1 codewords:1 call:3 survive:1 type:24 λmj:1 separated:2 composite:1 odinger:1 correspondingly:1 hold:1 must:6 me:1 schrieffer:1 springer:1 mf:1 join:1 ml:1 work:7 theories:3 mr:1 my:2 mx:2 mz:2 give:9 bennett:1 involve:1 caution:1 want:1 end:3 provide:1 verify:1 feature:1 far:4 nontrivial:3 adjacent:6 answer:6 gate:1 ordinary:1 classify:2 description:5 cz2:7 kosygina:1 cz1:7 imaginable:1 diagram:1 gottesman:1 summarize:1 law:2 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quant-ph9707023.txt |@word replacing:1 code:14 partial:2 consider:14 chain:4 crucial:1 global:3 results:15 four:2 tripartite:3 concept:1 entropy:113 per:5 consists:2 follow:2 expressions:1 reasoning:11 devoted:2 whose:2 supposedly:1 amplification:20 depend:2 superpositions:1 transferred:1 effort:1 concerned:5 deterministic:4 tr:1 environment:23 finally:8 program:1 device:1 those:1 th:4 under:3 details:1 circumstances:1 worth:1 resources:1 summarizes:1 case:18 supported:1 expressing:2 straightforward:2 orthogonal:6 very:5 could:1 rise:3 codeword:2 emphasizes:1 focus:3 rl:2 every:1 additional:1 traced:1 summarized:1 mixing:1 affect:1 difference:5 exact:5 condition:16 partitions:3 entire:4 immediately:3 level:1 transmission:35 ref:12 tre:1 applicable:4 physics:2 noiseless:8 trx:1 undone:1 erasures:13 small:1 enhance:2 darpa:1 trr:1 equation:2 upper:41 averaged:6 concise:1 altering:1 consistent:3 maximization:1 direct:1 hillery:2 prevails:1 rate:41 today:2 displays:1 further:6 primes:1 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quant-ph9707024.txt |@word limited:2 concept:1 gs:1 consider:6 lagrangian:1 magnetic:15 dynamic:1 results:8 existing:6 leads:5 controversial:1 follow:1 expressions:3 increase:1 const:1 paris:2 irrelevant:1 deterministic:1 aggregations:1 superficially:1 finally:1 stable:2 kλ:1 analogous:2 presumed:1 prigogine:1 applied:2 presently:2 far:4 frequencies:1 p0i:4 wave:35 electron:15 every:4 additional:1 sud:1 experimentally:3 difference:1 exact:1 condition:2 four:1 level:4 turns:1 t2:5 solution:4 t1:1 solved:1 settle:1 section:2 small:2 eigenvalues:1 optics:1 equation:23 employing:1 consistent:3 sin2:3 approximation:2 imply:1 value:4 further:1 copenhagen:2 canonical:1 even:1 established:3 what:2 nonlinear:1 sph:4 rate:2 incompatible:1 sum:1 contracted:1 ρs:6 expressed:1 uniform:2 current:8 infinitesimal:1 values:3 paradoxical:1 schilpp:1 justification:2 simultaneously:1 exchange:3 respectively:1 error:1 component:4 equals:1 atoms:1 cos2:2 xν:1 directions:1 ratio:2 quite:1 equations:8 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quant-ph9707025.txt |@word represent:2 dewitt:6 managed:1 consider:8 marinov:3 believed:1 oscillator:2 varying:1 desirable:2 results:10 leads:2 scalar:2 commute:1 generalize:1 computation:1 consists:3 follow:2 denotes:2 localized:1 optical:1 compact:6 whose:1 simon:2 depend:2 but:6 graph:1 concerned:5 equivalence:1 tr:3 noncompact:2 passage:2 leboeuf:1 finally:5 manifolds:3 under:5 analogous:1 include:2 tc:1 ingredient:1 subtleties:1 applied:4 tanh:1 proved:1 straightforward:4 g0:9 very:2 frequencies:1 implicitly:1 rise:2 springer:3 gz:5 electron:1 every:1 additional:1 fall:3 hds:1 saraceno:1 exact:9 effectively:1 categories:1 dimensionality:1 mild:1 retaining:1 immediately:1 hamiltonian:17 irreducible:5 superconducting:1 developing:1 t2:1 iǫ:1 occurs:4 large:8 discrete:1 vector:5 δz:3 subscript:1 small:2 eigenvalues:1 referred:1 optics:2 equation:9 configurations:2 application:1 heckman:2 employing:1 zi:68 zj:1 zk:17 dealing:1 zf:48 measurable:1 hillery:1 zc:17 approximation:16 limǫ:2 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quant-ph9707026.txt |@word epeau:1 partial:1 consider:3 carolinae:1 results:9 four:1 commute:1 entropy:1 computation:1 primes:1 row:1 whose:2 depend:1 referring:1 irrelevant:1 tt:1 deterministic:1 tr:2 nonlocal:2 must:2 those:2 under:1 stochastic:1 include:1 norm:3 conjecture:1 supported:1 straightforward:2 orthogonal:3 very:1 primed:2 print:1 redefinition:1 experimentally:1 matrices:14 condition:12 dim:1 obvious:1 retaining:1 did:1 ascertaining:1 correct:1 large:1 discrete:1 subquantum:1 indices:17 eigenvalues:7 shows:2 originally:1 upper:1 work:2 deutsch:1 direct:3 perspectives:1 second:2 dordrecht:3 further:1 choices:1 canonical:1 even:3 what:3 3x:1 xor:4 unilateral:1 sum:2 henceforth:1 experiment:1 above:4 new:7 method:1 satisfy:8 edited:2 simultaneously:1 exchange:1 respectively:1 component:2 teleportation:1 here:2 address:1 represented:1 change:1 violate:1 obtained:3 search:4 spite:1 suitably:1 institute:1 my:1 larger:3 completely:2 leaving:1 suggests:1 products:2 permutation:1 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quant-ph9707027.txt |@word dewitt:1 magnetic:6 isotropically:2 eds:1 expressions:2 denotes:1 localized:2 whose:1 breach:1 divergent:1 g2:4 g1:5 g0:1 fall:13 condition:1 generalised:2 school:1 hamiltonian:1 solution:8 vector:6 small:1 optics:1 upper:1 pulse:1 rate:7 odd:1 even:1 expressed:1 d3:10 version:1 above:1 increasing:1 led:1 here:2 following:1 cylindrical:1 focused:1 equations:2 obtained:1 vectors:1 fourier:3 linearly:1 standing:1 derivatives:1 asymptotic:5 would:1 comparing:1 until:1 kˆ:1 train:1 eθ:1 particular:2 known:1 producing:1 must:1 high:1 rα:2 equation:1 remain:1 itself:1 believed:1 example:1 proof:1 give:1 calculation:1 states:11 2ls:1 rather:2 orthogonal:1 write:2 acta:2 may:5 law:7 explicit:2 their:1 provide:1 cannot:1 so:6 fundamental:1 representation:1 helv:2 wigner:1 indeed:2 course:1 paper:3 london:3 existence:1 its:2 coordinates:1 degrees:1 strand:1 defining:1 them:1 oxford:1 now:6 represents:2 finite:4 always:1 university:1 presented:1 orthonormal:1 ei:4 prompted:1 ej:1 energy:15 applicable:1 elementary:1 quantum:3 our:1 beyond:1 tenth:1 shown:5 space:5 furthermore:1 since:4 rev:5 research:1 particles:1 re:1 electronics:1 shows:1 inevitably:1 theory:2 localization:1 seventh:1 free:3 definition:1 ordering:3 gordon:1 hence:1 studentship:1 reflected:1 long:3 open:1 given:4 similarly:2 introduction:1 leading:2 relations:1 glauber:2 rates:2 calculations:1 eqn:1 unpublished:1 transverse:1 than:2 king:2 polarized:1 require:2 see:3 amplitude:1 powers:1 iωk:2 remained:1 imprimitivity:3 cohen:1 any:3 convenient:1 note:2 sciences:1 ideal:1 potential:5 detector:2 electric:11 normal:3 denominator:1 most:1 wc2r:1 observation:1 clear:1 principle:1 physics:1 show:2 supported:1 discovered:1 blandin:1 gauge:2 solutions:10 substituting:3 find:7 decade:1 state:11 only:2 explicitly:2 do:2 goes:1 notation:1 distance:2 aβ:1 normalizable:1 densities:6 fields:5 arxiv:1 wightman:1 remove:1 transversality:1 set:1 sensitivity:1 detection:5 depends:1 college:2 superseded:1 written:3 onephoton:1 recently:2 august:1 nature:1 however:1 configuration:1 region:1 equal:2 became:1 expression:1 arbitrarily:7 point:1 cb:1 asymptotically:4 simply:1 respect:1 ucl:4 ct:1 amrein:3 basis:1 z0:1 been:1 ph:1 meeting:1 helicities:1 direction:2 corresponding:3 photon:23 c2:3 spin:1 those:1 single:11 value:1 will:5 situation:1 thus:5 ij:2 normalisable:2 uqm:1 make:1 radiation:1 same:3 parts:1 quant:1 wavepacket:1 modification:1 constructed:2 uses:1 expand:1 suitable:1 off:13 acknowledgement:1 no:3 without:1 firstly:1 usual:2 newton:1 obtain:2 transforms:1 integer:2 polarization:1 rapid:1 density:9 photons:1 conclude:1 wavevector:1 source:1 mod:2 momentum:3 gave:1 real:5 possible:2 increases:1 helicity:2 vacuum:4 press:1 using:3 doughnut:1 formal:1 imposed:1 like:2 classical:12 some:1 choosing:1 electromagnetic:2 shall:2 demonstrated:1 power:10 powerlaw:1 imaginary:4 properties:1 kd3:4 pike:4 about:1 freedom:1 numerator:1 o:1 consequently:1 localised:2 maxwell:3 into:3 photodetection:4 sharpness:1 bound:1 down:1 references:1 operator:3 proportional:3 support:2 there:4 question:1 transform:2 fast:4 ziolkowski:5 way:1 was:3 function:1 piron:2 jul:1 construction:2 delta:1 junior:1 directed:1 made:1 whether:1 us:2 ωk:17 limit:2 demonstrate:2 jauch:2 associated:1 abstract:1 general:2 engineering:1 exist:3 formulation:1 sarkar:4 physical:1 polarisation:1 when:1 field:5 other:1 department:1 coulomb:2 required:3 tightest:1 time:4 having:1
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quant-ph9707028.txt |@word sci:1 consider:1 helstrom:1 isotropically:3 leads:1 computation:1 consists:1 compact:1 increase:1 dimensionality:1 depend:2 tr:15 finally:2 under:1 suite:1 resources:1 applied:2 global:1 far:1 bratislava:1 hewlett:1 matrices:1 condition:7 entire:1 trl:1 level:2 irreducible:2 solution:1 standards:1 discrete:1 vector:1 small:1 eigenvalues:3 optics:1 noted:1 upper:5 averaged:1 concise:1 direct:5 fold:3 second:2 cost:1 design:1 concludes:1 implemented:1 substitute:2 theory:5 even:1 what:1 ˆs:1 sum:3 urss:1 version:1 above:3 new:7 consisting:1 satisfy:7 full:1 simultaneously:2 chose:1 prescribe:1 here:4 diagonal:12 growing:1 objects:2 ansatz:1 extrema:2 equations:5 2bz:1 suitably:1 institute:1 vectors:2 resulting:1 action:3 fourier:1 via:2 classification:1 2δm:1 eiφs:1 outcomes:1 addressed:1 apply:4 use:2 projector:2 would:1 massar:5 remains:1 positive:7 negative:1 scenarios:1 therefore:3 eiωm:1 associated:2 stage:1 type:2 reflects:1 more:5 composite:1 tions:1 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quant-ph9707029.txt |@word acts:1 consider:1 show:2 being:1 magnetic:3 wagner:1 results:5 rotating:2 underlying:1 relation:2 using:1 analogue:1 its:1 whose:1 calculate:2 corroborated:1 subjected:1 iφ:1 finally:1 does:2 carruthers:1 ehrenfest:1 theorem:1 derivative:1 circle:2 mod:2 lz:6 over:2 momentum:2 gives:1 2mr:1 do:1 them:1 affected:1 eigenvalue:1 very:1 regard:1 pegg:9 expectation:3 number:2 2mc:1 affect:1 rotation:3 now:2 gen:1 becomes:2 suppose:1 loss:2 europhys:1 particle:6 hamiltonian:3 follows:1 university:1 arxiv:1 remove:1 large:3 discrete:3 commute:1 yields:1 2l:7 through:1 2h:1 reasonably:1 therein:1 talked:1 physically:1 hindered:1 barnett:9 some:1 displacement:1 semiclassical:1 eb:1 rate:2 used:1 radius:2 examples:2 quantum:5 terms:1 eq:2 schenzle:1 abe:2 lead:1 space:2 ˆz:2 ensures:1 rev:5 eigenstates:1 state:3 difficulties:1 above:2 new:4 concluding:1 email:1 math:1 mullen:2 accord:1 recently:2 theory:1 2m:1 bl:1 weak:1 component:1 however:1 understanding:1 bp:5 references:2 eiφ:7 put:1 standard:1 hilbert:2 change:3 suggested:1 definition:3 property:1 r2:1 shift:1 study:1 studied:1 equal:2 motion:1 amount:1 periodic:1 nothing:1 walther:1 introduced:1 zˆ:1 criticism:1 relevant:1 panjab:1 presence:1 simple:1 h0:3 within:3 sign:1 harmonic:5 system:2 dimensional:2 pair:1 hermitian:1 done:1 comprehension:1 brecha:1 operator:21 apply:1 ring:3 should:1 infinite:1 angular:13 use:2 charge:1 chd:1 would:1 strictly:1 question:1 predictions:1 relations:1 next:1 genuine:1 restricts:1 therefore:1 expected:3 ph:1 was:4 final:1 speaking:1 define:2 raman:1 chandigarh:1 direction:2 only:2 θn:5 θm:1 successful:1 thus:2 acceptable:1 continuous:2 jul:1 mn:1 nieto:1 hl:1 decreased:1 vaccaro:1 given:5 dt:2 serves:1 those:2 applied:1 applying:1 deformed:3 equation:3 work:1 oscillator:5 us:1 2πn:1 will:1 frequency:1 values:3 following:1 more:1 deformation:1 obtains:1 mechanics:1 opt:1 unitary:3 give:1 defined:4 abstract:1 india:1 general:1 states:4 proper:1 dual:3 our:1 unphysical:1 limit:5 formalism:9 seek:1 clearly:1 physical:5 result:3 θ2l:1 respective:1 angle:6 ie:1 write:1 get:3 when:1 lett:1 same:3 note:2 field:3 hω:1 quant:1 take:1 significance:1 department:1 so:1 finite:1 parameter:1 operators:4 2mr2:1 heisenberg:3 simplicity:1 extended:1 opposite:3 may:2 nic:1 remarked:1 inherently:1 displace:1 moving:1 but:1 letter:1 phase:11 representations:1 meaningful:1 natural:1 center:1 calculated:1 well:4 correspond:2 looked:1 elucidating:1 without:1 mass:2 time:3 velocity:11 physics:1 fact:1 charged:2
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quant-ph9707030.txt |@word represent:1 remarkable:2 rev:18 results:1 illustrated:2 tξ1:1 edu:1 consists:1 expressions:1 whose:3 alamos:1 young:1 berstein:1 supported:1 orthogonal:1 barium:1 wave:1 condition:3 entire:1 brendel:1 guo:2 large:2 coincidences:1 optics:1 setup:2 deutsch:1 second:3 canonical:1 nonlinear:1 stands:1 experiment:3 steinberg:1 ever:1 method:1 contrast:1 satisfy:1 degree:1 respectively:4 teleportation:1 china:3 address:1 directions:1 ratio:1 strong:1 observing:3 appears:1 obtained:1 rigorously:2 schumacher:1 usually:1 involves:1 counts:1 total:3 use:2 k0x:1 coupled:2 hong:1 aperture:5 introducing:1 visibility:3 berlin:1 normalized:1 varying:3 nkx:1 springer:1 quantized:1 science:3 equation:3 remain:1 following:4 spontaneous:1 example:2 f3:1 transmissivity:1 process:2 bennett:3 states:3 slit:15 numbers:1 counting:3 occur:1 axis:4 rosen:2 feature:1 delay:1 varies:1 verlag:1 sin:4 brassard:2 may:1 after:5 confirmed:1 applications:1 plane:6 ky2:1 horizontal:1 natural:1 beam:33 light:11 so:2 correlation:20 order:11 developed:1 years:1 produced:2 thermal:7 experiments:1 through:3 still:1 derive:3 sergienko:3 interesting:1 detected:2 lu:1 fig:4 underpin:1 correspondence:1 non:1 splitter:10 propose:1 they:1 represents:1 university:1 l2:3 l3:4 each:2 macchiavello:1 2k:3 t2:1 energy:2 measure:4 quantum:14 eq:5 rt:1 acknowledgment:1 since:3 interference:19 eprint:1 dxdy:1 denoted:4 occurs:1 shows:1 foundation:1 fiber:7 theory:1 gardiner:1 put:1 jozsa:2 generate:1 determining:1 days:1 chiao:1 hence:1 spdc:3 undergo:2 first:10 features:3 striking:2 variables:1 number:2 xd:1 huttner:1 another:2 electronic:1 angular:4 passes:2 los:1 eqs:4 πn:1 approximately:1 their:1 1k:1 scheme:8 gives:2 transverse:1 tapster:1 optical:2 than:1 center:1 distance:2 wootters:2 determines:2 double:4 rate:1 project:1 determined:1 crepeau:1 bertani:1 electrodynamics:1 alley:2 ming:1 idler:19 need:1 ben:1 conversion:1 note:2 k0:3 detector:2 play:1 normal:6 measures:1 most:2 beta:1 connected:1 letter:1 inserted:6 appear:1 observation:2 detectors:1 part:1 exp:5 ky:7 kx:9 physics:1 fact:2 probe:1 relation:1 substituting:1 kx2:1 o:2 based:3 popescu:2 parameters:2 only:1 explicitly:1 factor:3 reck:1 cryptography:1 get:2 beams:7 famous:1 dv:1 ωc2:2 areas:1 podolsky:2 fields:1 arxiv:1 yield:1 paper:1 common:1 fixed:5 scanning:4 national:1 correlations:2 observed:2 intensity:2 result:1 probable:1 pattern:9 state:9 various:1 between:9 boundary:3 gedanken:1 screen:1 hefei:1 equals:1 incident:4 twophoton:1 uncertainty:2 fulfilled:1 propagation:1 passing:1 whole:1 experimental:2 splitters:1 cn:1 simple:3 coincidence:2 simply:1 bbo:1 equations:1 absence:1 been:2 much:1 combined:1 ph:2 direction:2 corresponding:2 photon:5 borate:1 zeilinger:1 those:1 applied:1 multi:1 pacs:1 heidelberg:1 will:1 superposed:1 played:1 thus:2 surprisingly:1 reads:2 duan:2 technology:1 different:2 quant:1 split:2 independent:2 used:1 driver:1 phe:1 klyshko:1 focal:4 recent:2 modes:17 well:1 patterns:2 lenses:1 components:1 coordinate:1 parametric:1 ekert:2 guang:1 proposed:2 among:2 being:1 when:2 sanpera:1 obtain:1 distant:1 λf:1 polarization:2 mohler:1 had:1 source:3 lett:14 input:9 transformation:1 opt:1 easily:2 early:1 vacuum:3 press:1 mod:2 follows:2 signal:19 yields:1 output:3 essential:1 classical:1 people:1 reveals:1 convex:1 strekalov:1 mode:14 measuring:1 noise:1 l1:3 notable:1 bs:1 bz:1 fringe:1 generated:3 recognized:1 kwiat:1 ou:2 mean:1 maxwell:1 into:9 nsc:1 due:1 down:1 variable:1 references:1 determine:2 einstein:2 proportional:1 width:1 mandel:2 was:2 function:9 considerably:2 form:1 fraunhofer:4 smolin:1 jul:1 encoder:1 line:1 role:2 true:1 2πc:1 characteristic:6 crystal:1 fermi:1 2πx:1 distribution:2 called:2 mechanics:2 shih:4 rightly:1 defined:2 abstract:1 measurement:1 proven:1 denote:2 peres:1 single:4 scanned:2 formalism:3 archive:1 physical:1 functions:2 compared:1 no:2 whereas:1 tip:5 field:5 other:2 republic:1 department:1 tic:1 symbol:2 kirchhoff:2 lens:4 meaning:1 dissipation:2 structure:2 ghost:9 correlated:3 faster:1 pointlike:1 diffraction:38 together:1 ustc:1 starting:1 original:4
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quant-ph9707031.txt |@word homomorphism:3 dynamic:1 ullman:1 four:1 consists:11 aua:1 whose:12 under:12 forbidden:2 every:12 updates:2 affect:1 encounter:1 mw2:2 mw1:2 solution:3 correct:1 vector:16 markov:3 deutsch:1 consistent:2 direct:8 approximation:1 second:3 puchta:2 machines:5 even:3 errors:1 iterating:1 blum:1 tσ2:1 tσ1:1 above:6 designing:1 new:19 ever:1 consisting:1 compilers:1 coefficient:1 philippe:1 never:3 here:2 subword:3 active:3 path:11 interpret:1 study:1 mǫ:1 fourier:1 changes:4 appropriately:2 projection:5 rosenberg:1 highly:1 counts:1 total:3 circumvent:1 unit:10 dna:2 would:6 negative:2 m1:3 therefore:5 m2:1 tell:3 fractions:1 relax:1 composite:1 brings:1 expose:1 nkl:1 odinger:1 berlin:3 must:3 springer:2 ma:9 mn:3 mi:5 mw:13 ms:1 concepts:1 intervening:2 example:4 unmarked:2 give:8 fibonacci:1 times:5 uaf:1 end:7 provide:1 machine:11 how:4 answer:1 symposium:1 ordinary:1 replacing:1 turing:5 after:6 wrong:1 reidys:1 constants:2 summing:4 think:2 complexity:2 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quant-ph9707032.txt |@word concept:1 consider:6 results:1 eds:1 comments:1 expressions:3 issues:2 simon:1 finally:1 monotonically:1 under:9 anharmonic:10 norm:1 case:11 chennai:1 very:2 wave:3 associated:1 difference:1 exact:2 condition:2 entire:1 hamiltonian:14 suffices:1 proposals:2 large:6 strayer:1 small:1 eigenvalues:2 noted:2 zn:1 approximately:1 ze:1 approximation:1 zz:1 pass:1 dynamics:5 canonical:17 errors:1 dr2:2 above:3 new:6 increasing:1 method:1 coefficient:1 degree:1 respectively:1 never:1 diagonalises:1 here:1 understanding:1 ionization:1 rotator:1 groups:2 address:1 multivaluedness:1 diagonalised:1 equations:1 implicit:1 obtained:5 institute:1 involved:1 suggests:1 periodic:8 action:4 studies:1 involves:1 identification:3 requiring:3 vis:2 limn:1 apply:4 univ:1 rω:1 readily:1 use:2 dpdq:2 would:10 properties:7 therefore:9 criteria:2 means:2 more:1 started:1 brings:1 operators:3 odinger:3 berlin:1 rigid:1 labelled:3 particular:6 known:1 iii:1 evolves:2 a29:1 equation:1 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quant-ph9707041.txt |@word secondly:1 partial:1 consider:4 lack:3 results:7 leads:2 lewenstein:2 shimony:1 go:2 equivalences:1 whose:1 certainly:1 violate:1 presents:1 estructura:1 under:1 tb:5 p2:22 belonging:1 global:1 departament:1 straightforward:1 ρta:1 very:3 springer:1 print:2 corollary:4 every:1 ρts:2 matrices:6 condition:3 catalonia:1 dim:7 obvious:1 incoherent:3 transposing:1 small:3 eigenvalues:2 shows:1 cosa:1 direct:1 second:2 further:2 implemented:1 canonical:5 established:1 what:2 3x:3 stands:1 sum:3 expressed:2 sur:1 above:3 new:4 subtracting:1 consisting:1 simultaneously:1 ρai:1 here:3 understanding:2 les:2 others:1 appears:1 obtained:3 vectors:3 allows:1 action:4 pascual:1 via:1 useful:1 family:1 rρ:1 support:2 prove:2 recalling:2 positive:3 contains:1 finally:5 france:1 classically:3 therefore:3 memory:1 type:4 until:1 reflects:1 more:1 ambiguity:2 composite:14 becomes:1 holt:1 normalized:1 known:7 cases:3 hold:2 ρa:3 account:1 ρb:3 subcases:1 recall:1 des:1 ρq:5 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quant-ph9707042.txt |@word limited:2 consider:1 remarkable:1 illustrates:1 caused:1 varying:1 results:3 existing:1 knbo3:3 eds:1 avalanche:1 comments:1 controversial:1 perturbations:2 issues:1 increase:1 number:2 violate:1 disposal:1 technique:1 nonlocal:5 environment:3 program:2 excluded:1 exit:1 include:1 cm3:1 sent:2 southwest:1 case:1 supported:1 amplitudes:1 advantage:1 outside:1 very:1 could:3 desired:1 wave:1 spool:1 every:1 difference:5 continued:1 common:1 leads:1 europhys:2 level:1 transmission:1 evaluation:1 pacs:1 proposals:1 eve:2 large:3 coincidences:4 epstein:1 small:2 shows:1 optics:1 dis:1 smaller:2 ten:1 pulse:1 past:1 second:6 cost:1 further:1 dynamics:1 chem:1 port:1 aim:2 rate:1 giving:1 mw:1 find:1 current:1 experiment:18 above:1 net:1 increasing:1 contrast:2 counters:1 quenched:1 full:1 simultaneously:1 ibid:5 newyork:1 respectively:2 teleportation:1 interferogram:2 reported:1 magnetism:1 focused:2 free:1 kilometers:1 path:1 along:1 strong:7 change:2 calculate:2 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quant-ph9707043.txt |@word partial:2 consider:4 rev:10 global:1 results:3 leads:3 entropy:1 lewenstein:1 contributions:1 compact:1 whose:1 inverse:2 const:1 violate:2 tr:11 finally:3 program:1 under:2 ergo:2 indicating:2 p2:9 belonging:1 ρtb:3 ρta:1 very:2 choice:1 p1:8 every:4 difference:4 matrices:9 condition:11 dim:2 presented:3 knight:1 solution:1 large:2 vector:1 minimal:1 eigenvalues:1 upper:1 smaller:1 computation:1 approximation:6 second:2 rigorous:1 further:1 linear:1 spectral:1 index:1 what:1 hide:1 appear:1 sum:5 expressed:2 sur:1 above:4 values:1 increasing:1 method:4 respectively:1 teleportation:1 plenio:1 address:1 represented:1 equations:1 calculate:1 difficulty:1 vectors:11 reason:2 trial:1 products:1 stressed:1 usually:1 bob:1 makes:1 formulated:1 regardless:1 projection:4 family:2 convexity:1 apply:1 total:1 circumvent:1 linearly:1 plot:1 use:1 projector:6 would:1 prove:2 distinct:1 positive:1 negative:3 france:1 few:2 ψi:4 therefore:5 type:2 more:2 composite:10 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quant-ph9707047.txt |@word represent:6 epeau:1 consider:2 results:2 leads:1 scalar:2 computation:6 intricate:1 duplicated:1 theorist:1 superpositions:1 irrelevant:1 factoring:1 environment:8 behave:1 stabilizing:1 analogous:1 include:2 sent:1 digit:1 supported:1 orthogonal:4 wave:2 coprime:1 affect:1 difference:2 exact:1 entire:2 obvious:2 incoherent:1 altering:1 large:1 discrete:5 restoring:1 science:1 small:1 equation:1 smaller:1 periodicity:1 repetitive:1 direct:5 zb:1 sign:1 feasibility:1 second:6 evaluated:1 zt:1 implemented:1 zr:1 zs:1 even:3 index:4 errors:8 appear:2 apparatus:1 section:1 while:2 decoding:6 reminiscent:1 above:1 new:4 method:2 paradoxical:1 satisfy:2 respectively:2 concepts:1 teleportation:5 here:1 alone:1 standard:2 z0:10 appears:1 obtained:1 institute:2 vectors:7 ignoring:1 amount:1 periodic:1 products:3 knill:1 usually:3 therein:1 fourier:5 uniquely:1 secure:1 merely:1 explained:2 logical:10 highly:2 brought:1 extraneous:1 apply:1 establish:1 xz0:10 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quant-ph9707050.txt |@word concept:1 consider:10 chain:4 caused:1 branches:1 leads:4 eds:1 mnn:1 3a3:1 localized:2 whose:2 inverse:1 depend:1 calculate:2 technique:1 essentialy:1 finally:1 program:1 petersburg:5 under:4 nodes:2 ingredient:1 case:2 fax:2 r12:4 advantage:1 orthogonal:2 translations:1 springer:2 wave:3 electron:9 every:1 entries:1 difference:1 exact:2 condition:1 treating:1 hamiltonian:20 turns:1 notes:2 solution:3 discrete:17 vector:2 eigenvalues:6 subindex:1 hospitality:1 coinsides:1 auxilary:2 upper:8 tel:2 zi:1 periodicity:1 lecture:2 direct:1 jump:3 second:2 haan:1 cosq:1 dynamics:3 linear:2 bilinear:1 established:1 what:3 developed:1 stands:2 brackets:2 section:4 near:1 expressed:1 levitan:1 poles:10 above:12 international:2 construction:2 consisting:1 contrast:3 lee:6 respectively:4 even:1 here:11 diagonal:7 friedrichs:9 compose:1 separation:4 represented:2 consideration:2 along:1 strong:1 z1:2 z2:2 obtained:1 convert:1 sobolev:1 institute:1 study:8 studied:3 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