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quant-ph9802022.txt |@word represent:4 concept:1 partial:2 consider:3 chain:4 caused:13 desirable:1 leads:10 entropy:2 psycho:1 causes:4 devoted:1 dunod:1 paris:1 concerned:1 tr:3 braginsky:1 presents:2 finally:1 program:4 grabowski:1 applied:2 far:1 scattered:5 every:4 lecture:2 difference:2 condition:5 nonselective:14 school:1 presented:2 tra:4 turns:3 notes:2 t1:18 discrete:7 vector:1 succession:4 small:1 eigenvalues:6 concluded:2 consistent:3 imply:2 concludes:2 further:2 dynamics:1 even:3 what:2 stands:1 apparatus:58 section:17 selected:1 transforms:1 m31:1 experiment:7 above:9 new:5 falling:2 bn:1 satisfy:3 edited:1 led:1 notions:1 respectively:1 ρan:2 here:1 address:1 represented:4 path:1 along:2 quite:1 change:49 knowledge:6 obtained:8 accomplishes:1 clarify:1 leaves:2 vectors:1 prior:2 accomplished:1 ineffective:1 usually:1 mentions:1 changes:10 york:1 uniquely:2 formulated:2 projection:12 marginal:1 namely:3 vii:3 outcomes:2 aimed:1 apply:2 operational:1 unit:2 conventional:5 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quant-ph9802023.txt |@word rev:10 saves:1 amplifier:1 results:1 quadrature:3 row:1 whose:1 amplification:1 re:3 paris:1 eˆ:2 squeezing:1 th:3 include:1 ured:1 far:1 wave:4 figs:2 sidebands:1 experimentally:2 trouble:1 difference:1 fakult:1 smithey:2 modulator:1 schiller:6 proc:1 notes:1 large:4 small:3 optics:1 eiϑ:1 slower:1 direct:5 threshold:1 konstanz:2 port:1 canonical:9 spectral:1 errors:2 sub:1 sum:2 current:1 experiment:1 reconstruction:2 international:1 increasing:2 method:3 edited:2 full:1 simultaneously:2 ibid:1 component:3 desired:1 excess:1 table:1 obtained:5 remark:1 study:3 resulting:2 published:3 real:3 resonance:1 fourier:3 plotted:1 via:2 plenum:1 modulated:1 apply:1 total:1 unit:1 standing:1 feb:1 commun:1 contains:1 negative:1 ψk:15 therefore:1 type:1 theoretical:2 more:1 acceptable:1 berlin:1 sharply:1 particular:3 known:2 effort:1 blocking:1 sample:2 springer:2 locked:1 setup:1 work:1 oscillator:2 values:6 making:1 example:1 leonhardt:2 reflector:1 figure:5 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quant-ph9802024.txt |@word consider:11 chain:1 rev:19 global:4 results:2 leads:2 gc:10 computation:1 follow:1 gr:1 whose:1 amplification:9 violate:1 recurrence:1 neighbours:3 critical:7 squeezing:1 present:1 th:1 analogous:3 tc:4 indicating:1 wave:1 sons:1 cellular:1 experimentally:3 matrices:6 condition:1 four:1 conjugating:1 level:3 did:1 proposals:1 solution:1 optica:1 large:1 solved:1 vector:1 eigenvalues:5 equation:1 configurations:1 periodicity:1 deutsch:1 b22:1 b21:1 cosh:17 likely:1 will:4 what:3 trapping:1 rate:1 sum:1 near:1 expressed:2 availability:1 above:4 new:1 coefficient:2 edited:1 predicting:1 respectively:1 realizations:2 modify:1 here:4 atoms:2 behaviour:12 sinh:16 spinspin:1 interpret:1 obtained:1 woerdman:1 iπ:1 institute:1 shift:2 study:1 goldwasser:1 zener:1 suggests:1 periodic:1 therein:2 fourier:4 king:1 uniquely:1 formulated:1 useful:1 stenholm:2 extra:1 explained:1 leonhardt:1 private:1 coinciding:1 austria:1 turchette:1 names:1 total:1 alamitos:1 fed:1 feb:1 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quant-ph9802026.txt |@word consider:5 rev:11 magnetic:1 results:7 illustrated:1 edt:1 shimony:2 issues:1 discern:1 whose:2 theorist:1 violate:2 deterministic:5 under:1 include:1 division:1 conjecture:1 very:1 choice:1 orientations:2 bringing:1 four:7 ref:1 try:1 noted:1 concluded:1 says:2 findings:1 horn:2 past:1 zero:2 greenberger:3 linear:1 what:2 stands:1 incompatible:1 fine:3 sum:1 favour:1 expressed:2 experiment:1 above:11 new:4 ever:1 mea:1 ibid:1 respectively:3 component:2 here:4 understanding:1 behaviour:1 free:6 others:2 pati:1 consideration:1 along:11 obtained:1 root:2 leaves:1 vectors:4 simultaneous:1 resulting:2 involves:3 equivalence:1 put:2 stern:1 unit:4 predicted:2 feb:1 takes:2 would:3 positive:3 predictions:10 next:1 therefore:7 taken:3 type:1 theoretical:1 today:1 more:1 separated:1 bhabha:1 composite:3 holt:1 validity:1 clue:1 basically:1 must:1 account:1 eberhard:1 room:1 work:2 theories:13 reproduce:5 values:1 following:2 averages:1 example:5 heart:1 transition:1 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quant-ph9802027.txt |@word magnetic:5 consists:1 localized:4 whose:1 calculate:5 paris:1 under:1 worth:1 differently:1 every:1 affect:1 cause:1 solution:1 indices:1 force:2 ωaj:1 approximation:55 surrounding:2 second:3 7th:1 even:5 established:1 establishes:1 new:3 increasing:2 behavior:3 here:9 atoms:5 ionization:14 reported:1 ements:1 represented:4 logarithmic:2 obtained:10 rigorously:1 study:2 changed:1 completely:4 controversy:1 suitable:2 changes:2 golden:1 projection:4 explained:1 highly:2 visible:1 9q:1 total:8 linearly:2 would:1 negative:1 call:1 therefore:1 separated:2 solitons:1 odinger:3 berlin:1 must:4 ii:6 springer:2 work:1 sturmian:1 example:3 indicated:1 relativistic:1 organized:1 stressing:1 indicates:4 keep:3 end:3 turn:2 provide:1 verify:1 travel:1 recovers:1 how:2 answer:1 oscillatory:2 description:3 ladder:10 earlier:4 diagram:1 summarize:1 meaningful:1 constants:1 effective:5 acknowledged:1 keeps:1 order:12 diagonalizes:1 over:6 experimentally:1 fit:1 better:2 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quant-ph9802028.txt |@word sci:1 consider:3 activated:1 results:1 sergey:1 scalar:6 synapses:1 computation:7 edu:1 reasoning:1 factoring:1 petersburg:1 th:3 under:4 norm:6 logarithm:1 advantage:1 orthogonal:10 very:2 contemporary:1 level:1 discrete:2 vector:14 small:1 biological:1 upper:1 compensated:1 grateful:1 deutsch:3 threshold:1 second:1 street:1 further:1 machines:1 theory:2 bilinear:2 nonlinear:2 section:2 find:2 current:1 version:3 above:2 new:2 method:1 full:1 here:5 atoms:1 desired:2 protection:1 free:1 represented:1 consideration:4 standard:2 change:1 rosenblatt:1 wesley:1 vectors:13 amount:1 schumacher:1 symmetrical:1 useful:3 projection:5 extra:2 scaled:1 stern:4 unit:5 use:10 feb:1 would:4 positive:1 hilbert:3 ψj:1 few:3 ψi:6 memory:8 historically:1 qcm:1 more:4 flat:1 zh:1 neurophysiology:1 operators:3 minsky:1 mira:1 particular:2 known:1 projective:2 given:1 must:1 me:1 springer:1 ma:2 science:1 work:4 vlasov:5 example:6 figure:3 process:2 december:1 bennett:1 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quant-ph9802029.txt |@word since:3 partial:1 consider:12 chain:2 caused:5 dynamic:17 results:4 illustrated:1 offdiagonal:1 computation:23 foundations:1 consists:1 gn:3 totient:1 gk:1 gj:21 causes:1 coleman:2 particles:3 const:1 calculate:1 concerned:1 technique:2 ρs:2 factoring:3 γt:3 environment:76 finally:2 those:4 th:6 under:2 td:6 circumstances:2 norm:5 case:25 belonging:7 tanh:3 g2:3 asume:1 outside:1 very:6 pascazio:1 springer:1 wave:5 electron:1 ed1:1 drexel:1 chuang:1 affect:3 emphasized:1 difference:1 condition:2 paz:1 leads:2 subsets:3 presented:2 diverging:1 cause:2 developing:1 guo:1 applicable:1 large:6 discrete:2 spaces:1 excellence:1 math:1 avoiding:4 small:1 study:1 degeneracy:2 application:1 smaller:1 force:1 tem:1 deutsch:1 sin2:14 direct:3 ρl:2 surrounding:3 second:7 appears:1 dynamics:3 accompanying:2 gm:1 canonical:1 even:2 errors:1 plays:2 appear:1 sun:12 section:15 remain:1 expressed:3 uniform:1 ˆb:1 ˆd:1 above:10 lond:1 ˆi:1 ˆk:1 method:2 contrast:1 satisfy:3 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quant-ph9802030.txt |@word represent:2 consider:3 particular:3 results:11 existing:1 illustrated:2 eds:3 quadrature:2 bohm:1 consists:1 particularly:1 compact:1 whose:2 inverse:1 const:1 reformulate:1 fokker:2 equivalence:1 tr:1 acting:3 tn:1 finally:4 those:1 th:3 stochastic:2 analogous:2 must:3 worth:2 kν:3 p2:1 iǫ:5 hibbs:1 straightforward:1 very:1 wave:17 µq:1 interpreting:1 husimi:2 condition:7 ǫf:1 smithey:1 exponential:1 presented:1 turns:2 t2:2 solution:11 t1:1 leave:2 solved:1 vector:1 science:3 hyz:1 der:1 oscillation:1 measurable:1 literature:1 cosh:1 approximation:1 theo:2 further:2 dynamics:1 cfr:1 theory:2 even:1 established:1 what:4 nonlinear:1 plays:2 appear:2 giving:1 section:7 xρ:1 analogously:2 expressed:1 establishes:1 overcomplete:1 new:17 method:2 respectively:1 eif:3 here:3 understanding:1 behaviour:3 beck:1 free:2 sinh:2 eikx:2 represented:2 path:4 along:1 quite:1 equations:8 nonstationary:1 z2:1 extreme:1 obtained:11 scienze:1 hamiltonian:3 compute:2 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quant-ph9802031.txt |@word dewitt:9 consider:4 pairing:1 global:3 ds:3 gg:4 eds:3 go:1 gn:2 expressions:8 contributions:3 scs:2 gh:5 certainly:1 inverse:2 ver:1 collisions:1 tr:2 tn:2 list:1 dereli:1 lecomte:1 th:1 alg:2 rham:1 analogous:1 case:9 g4:4 g2:20 straightforward:3 g0:1 very:3 regularise:1 translations:1 witten:2 putting:1 iup:1 condition:1 generalised:1 dim:1 dampen:1 hamiltonian:3 tra:1 turns:1 tre:1 solution:4 trg:1 t1:2 large:2 discrete:3 indices:1 eigenvalues:2 glued:1 effective:1 slower:1 oscillator:5 imply:1 tep:1 copenhagen:1 odd:1 zq:2 quite:1 linear:1 even:2 index:2 stands:1 brackets:1 giving:4 sum:6 poles:2 above:4 ˆh:1 new:3 full:1 dahl:2 ibid:1 definitely:1 fields:1 here:4 behaviour:1 objects:1 path:9 along:1 ggn:1 interpret:1 ordinary:1 obtained:2 great:1 algebra:5 institute:1 allows:4 kontsevich:1 products:2 poisson:4 p4:1 action:1 suitable:1 spacetime:2 involves:2 plotted:3 via:2 chim:1 family:3 merely:1 dimakis:1 first:2 orderings:1 readily:2 derivatives:2 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quant-ph9802032.txt |@word consider:3 results:1 four:2 eds:1 consists:1 nonlocal:4 decide:4 experimentally:2 difference:3 condition:2 arrange:1 splitter:3 did:1 smaller:1 second:1 traveling:4 further:4 will:1 what:1 2cos:12 version:1 above:1 new:2 here:1 represented:1 path:7 strong:1 observing:1 box:1 institute:1 study:1 stressed:1 suitable:1 studies:1 useful:1 modifying:1 herzog:1 orderings:5 causal:11 scarani:1 conventional:2 feb:1 figure:1 working:1 probabilities:6 predictions:3 call:1 therefore:1 taken:2 type:1 more:1 separated:1 foundations:1 must:1 mc:12 permits:1 setup:3 values:2 following:4 stimulating:1 impacts:8 stated:1 calculation:1 relativistic:2 indicates:2 exclude:1 distinguishable:2 deserves:1 arrangement:1 delay:1 necessary:1 influences:1 ordinary:1 ensemble:1 description:1 superluminal:1 may:4 after:1 different:2 produce:3 antoine:1 fits:1 revealed:1 short:3 joint:3 light:2 acknowledged:1 so:1 allow:3 order:1 interpretation:1 experiments:9 through:2 argued:1 existence:1 still:2 before:6 thank:1 fit:1 ll:24 subensemble:1 better:1 detected:3 fig:2 downconversion:1 interdisciplinary:1 wolfgang:1 half:6 now:2 discuss:1 february:1 university:1 each:3 2l:2 side:11 characterized:1 referred:1 successively:2 zurich:1 series:8 interferometer:3 sketched:1 quantum:20 laboratory:2 out:2 god:1 since:1 rev:1 acting:1 electronics:1 supports:1 fiber:1 theory:1 conflicts:3 pairs:8 backwards:1 determining:1 could:1 length:4 hence:1 first:2 already:1 philosophical:1 done:1 long:3 behaves:1 gives:1 geneva:1 explanation:2 tapster:1 undoubtedly:2 than:2 imply:1 rarity:1 contrary:2 lines:1 seem:1 clearly:1 lie:1 nonlocality:5 unless:1 impacting:1 eight:1 plenty:1 successive:2 pair:3 measured:1 dordrecht:1 implications:2 principle:6 mechanical:5 left:3 show:1 text:1 anyway:1 relation:2 keywords:1 d2:4 d1:4 impact:7 causality:5 only:4 experiment:4 pretty:1 local:1 dl:2 quantph:1 means:1 bear:1 beam:6 regarding:1 emc:1 settings:1 suarez:6 arxiv:1 yield:1 paper:4 switzerland:1 qm:26 view:1 set:1 frame:2 testing:2 detection:1 see:2 lausanne:1 us:4 discussions:1 arm:3 philosophy:1 eman:1 owens:1 label:1 favor:1 pump:1 between:4 nature:1 emitted:1 however:1 gratefully:1 cos:20 many:1 according:10 against:2 sensitive:1 exceeds:1 experimental:1 otherwise:1 splitters:3 ch:2 point:1 coincidence:2 concluding:1 non:2 table:2 speak:1 undecidability:1 described:1 equations:3 much:1 interest:1 ph:3 corresponding:3 quantities:1 sufficient:1 coherence:2 photon:10 those:3 case:3 laser:1 brendel:1 value:1 aim:1 while:1 characterizing:1 would:3 them:1 ramifications:1 confirmed:1 same:1 any:2 quant:3 events:2 used:2 paths:2 hand:7 moving:1 entanglement:1 recent:1 driessen:1 center:1 largely:1 well:1 valerio:1 patterns:1 without:1 model:11 usual:1 proposed:10 less:1 being:2 distribute:1 rest:3 alternative:1 enters:2 kluwer:1 photons:1 bell:1 seems:1 source:1 lett:1 real:3 insensitive:1 rules:1 subensembles:2 possible:8 integer:1 outcomes:3 appearing:1 like:3 follows:1 detections:3 yields:2 either:2 become:1 works:2 mathematical:1 right:4 phenomena:1 indistinguishability:1 counts:1 lead:1 measurements:1 does:1 step:1 epfl:1 carried:1 getting:1 discussed:1 o:1 mutually:2 realism:1 consequently:1 road:1 mechanics:12 appropriate:1 references:1 detectors:1 support:1 question:1 fast:1 way:1 assumes:2 questionable:1 offer:1 some:1 but:3 arranged:1 whether:1 devices:2 gisin:2 detailed:1 certain:1 abstract:1 single:4 tittel:2 interferences:1 physical:1 again:3 whereas:2 application:1 other:1 test:1 conclusion:1 briefly:1 superposition:11 models:4 allowing:1 zbinden:1 assume:1 odds:1 time:6
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quant-ph9802033.txt |@word code:1 consider:7 caused:1 desirable:1 results:1 switches:1 quadrature:1 generalize:1 computation:2 bergmann:1 involved:1 causes:1 whose:3 calculate:1 knill:1 concerned:2 show:1 tr:3 send:1 passage:4 environment:4 those:5 under:2 γe:2 case:19 supported:1 infinite:1 g2:15 g1:14 outside:1 very:5 rise:1 choice:2 condition:2 leads:1 school:1 pbs:1 level:3 issue:1 proposals:1 t0:2 t1:2 large:4 small:5 optics:3 upper:1 smaller:1 aρa:2 houches:1 direct:1 pulse:1 jump:2 rate:4 summer:1 pass:1 qualitatively:1 dynamics:10 ρn:6 leakage:2 quite:1 linear:5 even:5 what:1 errors:1 decoding:1 experiment:2 above:3 supplies:1 method:2 coefficient:1 edited:1 degree:1 respectively:1 never:1 modify:1 here:3 atoms:3 protection:6 separation:1 strong:1 because:4 transformation:4 obtained:4 root:5 study:1 losses:2 allows:2 completely:1 leaving:1 significantly:1 procedure:1 usually:1 hamming:1 suitable:1 makes:1 involves:1 king:1 appropriately:2 via:3 regardless:2 polarizers:1 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quant-ph9802034.txt |@word represent:2 measurements:2 consider:4 rev:10 varying:2 results:5 four:1 quadrature:17 expressions:1 causes:1 evicted:1 millisecond:1 whose:1 feeding:1 tr:2 braginsky:2 environment:2 finally:1 squeezing:1 those:2 γm:28 under:1 stochastic:4 p2:1 kρ:1 random:1 g2:4 orthogonal:3 very:5 2re:3 rise:1 springer:1 wave:3 resonant:2 experimentally:2 hamiltonian:3 turns:1 trb:1 proposals:1 solution:1 damped:4 large:1 pˆ2:1 small:8 optics:1 round:1 bd:1 strongly:1 smaller:1 force:2 oscillation:2 direct:1 tef:3 approximation:1 rate:2 dissipation:1 ρa2:1 further:3 dynamics:4 theory:2 even:3 chicago:2 giving:1 ned:1 xρ:1 near:1 expressed:1 current:3 above:5 new:1 satisfy:2 devoted:1 ρaa:1 gravitation:1 ibid:3 respectively:1 proper:1 modify:1 behaviour:1 desired:1 γx:1 capacitor:1 2kb:1 relaxation:1 equations:2 appears:1 obtained:5 transmittivity:1 remark:1 ctr:1 shift:3 allows:2 loop:5 usually:3 resonance:2 suitable:1 york:1 via:1 followed:1 explained:1 plenum:1 replace:1 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quant-ph9802035.txt |@word logarithms:1 code:1 consider:8 illustrates:1 particular:2 results:1 leads:5 executing:1 computation:4 consists:3 follow:1 whose:2 preserves:1 inverse:1 disposal:3 concerned:1 technique:3 ts:41 factoring:1 created:1 presents:3 those:1 th:1 under:1 analogous:1 applied:3 amplitudes:4 string:4 advantage:1 orthogonal:1 very:1 minded:2 stays:2 difference:1 matrices:2 categories:1 presented:2 transmission:2 proc:3 solution:16 t0:1 item:1 vector:6 small:2 smaller:1 deutsch:1 sign:3 approximation:1 redone:1 second:1 design:4 evaluated:1 subtle:1 further:3 dynamics:1 what:1 xor:1 sub:1 section:16 selected:1 near:1 expressed:1 experiment:1 above:5 3c:1 obvious:2 full:1 simultaneously:1 respectively:1 component:2 equals:1 here:2 desired:3 explore:1 selective:2 inversion:5 represented:2 consideration:1 along:1 equations:1 obtained:1 vazirani:2 search:40 items:1 vectors:3 gle:1 leaving:1 prior:2 accomplished:2 resulting:2 action:1 fourier:1 makes:2 helps:1 offs:1 via:1 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quant-ph9802036.txt |@word gv:5 consider:3 similarity:1 rev:8 both:2 primed:3 leads:1 φ1x:3 montr:2 computation:1 go:1 dimensionality:2 terms:4 concerned:3 tr:16 presents:1 finally:1 th:1 sent:3 supported:1 orthogonal:51 very:5 emphasizes:3 induce:1 choice:3 chooses:1 telling:3 matrices:12 entire:2 induced:1 presented:1 did:1 tre:1 eve:24 solved:1 prevent:1 smaller:1 0x1:3 sin2:4 second:10 arms:1 even:3 plays:1 sum:1 access:3 version:2 above:2 new:6 respectively:1 concepts:2 here:2 understanding:1 following:2 protection:2 them:6 cos2:5 separation:2 strategies:2 alone:1 change:2 search:1 receive:1 study:1 vectors:1 resulting:1 schumacher:1 bob:9 changes:3 composed:3 useful:1 secure:1 explained:1 unitary:2 achievable:1 apply:1 use:9 feb:2 would:1 prove:1 jozsa:1 faint:1 1x:1 hilbert:2 therefore:5 encode:1 means:1 goldenberg:5 type:2 tell:1 more:6 knows:1 composite:4 initial:2 corrected:1 normalized:1 particular:1 known:3 cases:2 must:3 keeping:1 extension:1 der:1 work:7 ρp:24 fock:2 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quant-ph9802037.txt |@word consider:2 rev:2 magnetic:2 global:1 focus:1 leads:1 computation:35 consists:5 expressions:1 decisions:1 gi:1 whose:2 depend:1 alamos:2 deterministic:12 tr:25 b265:1 environment:2 finally:1 compensate:1 swap:1 th:3 include:1 resources:7 case:2 amplitudes:1 string:10 zhang:1 very:2 results:4 experimentally:1 difference:1 hamiltonian:4 suffices:1 proposals:1 applicable:1 vector:2 indices:1 eigenvalues:2 grover:1 estimates:1 literature:1 sign:2 fold:1 second:4 value:1 further:2 implemented:4 linear:3 even:3 index:1 what:3 errors:2 adds:1 appear:1 sum:6 4r:1 expressed:1 access:5 experiment:1 above:3 ρu:1 consisting:4 coefficient:3 edited:2 iσa:3 applies:1 component:1 here:4 understanding:1 desired:3 b2k:2 represented:1 quite:1 observing:1 appears:2 obtained:6 study:1 tial:1 suggests:1 accomplished:1 products:1 postprocessing:3 permit:1 usually:1 resonance:3 implement:2 fourier:2 makes:1 involves:1 composed:1 technique:1 useful:2 plenum:1 private:1 highly:4 pp:1 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quant-ph9802038.txt |@word represent:4 concept:3 jason:2 consider:22 remarkable:1 limited:1 groundwork:1 hint:1 rob:2 lack:1 desirable:1 results:9 four:2 eds:3 scalar:5 commute:8 generalize:1 comments:2 reinhold:1 go:7 partial:1 research:1 ivi:1 reasoning:1 issues:8 relationships:9 whose:3 certainly:4 physica:1 depend:1 wish:1 disposal:1 concerned:1 reviews:1 tr:6 company:1 finally:7 preserved:1 excluded:1 under:9 aqj:1 claim:9 insights:1 presentation:1 worth:1 norm:2 wiley:1 p2:33 straightforward:1 orthogonal:19 far:3 could:2 later:1 differently:2 focus:2 non:32 corollary:9 p1:41 every:25 interpreting:1 implausible:1 join:8 associated:3 difference:3 condition:12 summarize:1 preserve:1 gov:1 obvious:2 bring:2 did:3 suffices:2 list:1 large:1 discrete:18 vector:19 recall:7 manifestly:1 eigenvalues:3 noted:1 homomorphism:16 unsatisfied:1 strongly:8 smaller:1 says:5 andrew:1 dealing:1 sidestep:1 measurable:1 equation:2 consists:1 second:3 perspective:2 infimum:3 gn:5 further:2 specker:3 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quant-ph9802041.txt |@word represent:2 unavoidable:1 words:1 just:2 being:2 pointed:1 results:6 integration:1 stability:1 paper:1 questions:2 existence:6 satisfies:1 still:2 pointer:4 its:1 density:1 irrelevant:1 technique:1 character:2 exclusively:1 separability:3 environment:7 pathological:1 lett:1 mail:1 scripta:2 main:5 defining:1 forbidden:1 details:2 makes:1 his:1 above:5 deeper:3 orthodox:1 rules:3 universality:6 zurek:7 measurement:1 possible:1 preferred:2 cf:1 methods:1 implicit:1 october:1 should:2 they:1 new:1 part:1 now:1 yu:1 discuss:1 condition:1 formal:3 normalizable:1 represents:3 evolution:1 effectiveness:1 necessary:11 appart:1 hamiltonian:1 follows:2 arxiv:1 tre:1 occurs:1 realistic:1 underlying:1 follow:1 each:1 calls:1 out:2 side:2 making:1 requirement:1 set:3 occurrence:6 exists:1 existing:1 dealing:1 some:4 fr:1 plausible:1 wider:2 see:1 investigated:1 yugoslavia:1 obtains:1 proportional:1 quantum:3 further:1 establishing:1 satisfied:2 concern:2 spectral:1 appear:2 superselection:3 sub:1 lead:1 space:2 tasks:2 bility:1 since:2 rev:1 while:1 expressed:1 research:2 particles:1 below:1 state:4 does:3 decomposition:1 subspaces:1 prog:1 progress:3 justified:1 induced:2 conditions:17 method:2 refer:3 missed:1 diagonalizability:1 recently:2 theory:11 slight:1 derived:1 arbitrary:1 here:2 standard:1 address:1 distinguish:1 path:1 refers:3 equations:1 hilbert:2 obtained:2 definition:5 essentially:2 interaction:3 r1:7 r2:3 transition:1 technical:1 tracing:1 zmm:7 o:1 example:1 fulfilled:1 mutually:1 involve:2 statement:3 plus:1 rule:10 context:5 adopting:1 introduced:1 onto:1 projectors:2 first:1 initial:3 statements:1 cm:2 point:2 simple:1 seems:2 number:2 due:1 en:1 references:1 adopted:1 another:1 modeling:1 operator:1 methodological:1 apparent:1 precisely:2 open:3 tem:1 necessarily:1 feb:1 classical:1 puts:2 basis:10 bears:1 there:2 question:3 system:9 been:4 next:4 defined:1 appears:1 master:1 interest:1 criteria:1 expected:1 ph:1 recent:2 was:1 opens:1 more:1 box:1 refered:3 corresponding:1 calculations:1 form:1 both:1 composite:4 brings:1 concerning:3 exactly:2 but:5 investigation:2 operational:3 appendix:1 investigating:3 particular:1 cases:5 presented:1 iii:2 considerable:1 present:1 states:2 hamiltonians:1 defines:1 consequences:2 consist:1 pacs:1 science:1 distinguishes:1 reads:1 us:1 strategies:1 ρs:1 limit:2 today:1 amplitude:1 exceptions:3 field:3 problem:3 called:1 result:2 hypothetical:2 bearing:1 ac:1 unitary:1 proved:1 d26:1 int:11 likewise:2 abstract:1 modern:1 mind:1 needs:1 ii:3 proper:1 uis:1 assumptions:4 exist:1 numbers:1 chim:1 formalism:1 occur:2 physical:6 fundamental:1 different:2 conclude:1 ref:2 lim:4 orthogonal:1 problems:1 any:1 note:1 very:1 emphasis:1 other:3 quant:1 idealization:1 department:1 physica:2 subject:1 nonexistence:1 sufficient:1 deviation:1 independent:1 briefly:3 used:1 nondemolition:2 shall:1 models:2 correlation:1 upon:2 effect:12 effectively:1 meaning:5 faculty:1 summarize:2 model:1 matrix:1 relies:1 prove:1 task:2 kg:1 effective:4 whenever:2 adapted:1 later:2 lines:1 theor:1 analysis:2 element:1 γmn:1 directly:1 points:4 so:1 expression:1 apart:1 time:2 addition:1 decoherence:5 ρˆs:6 physics:2 original:3 fact:1
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quant-ph9802042.txt |@word concept:3 consider:6 pointing:1 magnetic:1 results:17 leads:4 eds:2 comments:1 controversial:1 mcmullin:1 go:1 follow:2 issues:1 certainly:1 clarification:1 tv:1 spin:5 deterministic:2 nonlocal:7 intensive:1 those:3 under:2 mwi:2 applied:2 supported:1 advantage:1 very:2 rise:1 choice:3 fall:1 difference:1 exact:1 condition:2 school:1 did:3 notes:1 t2:7 applicable:3 ascertaining:1 t1:7 leave:1 team:1 tel:2 pragmatic:1 deutsch:2 trend:1 miller:2 consistent:3 prediction:1 past:15 bergmann:2 second:2 concludes:1 rigorous:3 scientific:1 even:4 what:7 plays:2 appear:2 incompatible:2 specification:2 selected:3 abl:3 current:2 experiment:4 above:2 new:4 learned:1 consisting:2 contrast:4 paradoxical:1 1997c:1 1997b:3 1997a:7 explosion:3 1997d:1 here:2 asymmetry:3 free:4 lev:1 situation:2 consideration:2 november:1 standard:3 change:1 obtained:2 rigorously:1 allows:2 experience:1 controversy:4 prior:1 suggestion:1 difficulty:1 usually:2 opinion:2 narrow:1 changes:4 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quant-ph9802043.txt |@word limited:5 riccardo:1 magnetic:1 andre:1 entropy:1 consists:6 relationships:1 whose:12 rise:1 every:4 affect:2 encounter:1 induction:1 solution:40 vector:8 enhance:1 deutsch:4 10b:2 consistent:3 10a:3 direct:6 approximation:2 second:10 implemented:1 machines:5 even:10 errors:3 remi:1 selected:5 consequent:1 designing:3 new:12 increasing:1 simultaneously:3 behavior:20 csps:4 here:10 reported:1 obtained:2 study:3 drr:2 couplings:1 calculators:1 suitable:3 changes:5 highly:8 brought:1 conflicts:72 counts:2 total:3 univ:1 plot:5 would:13 jozsa:1 motivate:1 negative:4 definiteness:1 spike:1 25th:1 until:1 successful:2 reversible:4 separates:1 must:5 ma:4 work:1 theories:2 grover:1 example:21 indicated:1 give:17 preserving:1 involve:1 indicates:1 want:1 scheduling:1 david:7 provide:1 recovers:1 machine:4 how:10 symposium:3 brassard:1 description:2 turing:2 after:15 minimizes:1 excited:1 types:2 las:1 attempt:3 third:3 summing:1 complexity:1 algorithms:13 menlo:1 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quant-ph9802047.txt |@word secondly:1 consider:6 rev:13 child:1 results:3 entropy:1 gn:4 cases:1 localized:2 preserves:1 dimensionality:1 respectively:3 equivalence:2 environment:1 does:1 stable:8 stochastic:1 analogous:2 tb:1 ψc2:2 brown:1 very:1 zibin:2 lyapunov:39 reinterpret:1 mixing:5 experimentally:3 difference:1 exact:1 exponential:2 hamiltonian:3 did:1 discrete:3 convenience:1 vector:1 small:1 ups:1 upper:2 direct:1 imply:1 pass:1 dynamics:1 cat:1 garcía:2 even:2 wyatt:1 voros:3 euclidean:2 giving:1 sum:2 expressed:2 infinitesimal:1 above:1 new:2 increasing:2 contrast:1 pioneering:1 kicked:2 degree:1 mω:1 behaviour:1 giles:1 cos2:1 path:4 strong:1 obtained:11 technical:1 study:9 vectors:4 adopt:1 amount:1 fourier:1 changes:3 numerical:1 boundedness:2 schack:3 useful:1 hogg:1 classification:8 unit:1 recurrence:2 use:4 feb:1 figure:12 working:1 ψr:16 ψs:47 ψq:1 properties:1 classically:4 therefore:2 taken:3 ψc:2 type:1 theoretical:1 more:1 relax:1 successful:1 operators:1 under:2 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quant-ph9802049.txt |@word represent:4 monte:2 measurements:1 partial:6 consider:14 remarkable:1 secondly:2 results:12 existing:1 proposition:3 generalize:1 computation:24 edu:1 query:15 research:1 children:1 whose:1 simon:6 depend:1 deterministic:11 cheney:2 factoring:2 finally:2 monotonically:1 those:2 under:1 alberta:1 analogous:2 multilinear:10 indicating:1 ingredient:1 applied:3 amplitudes:7 string:2 advantage:2 very:1 p0:1 corollary:4 vegas:1 every:13 smolensky:1 zeitschrift:1 ending:1 exact:20 adaptive:1 quantumly:1 obvious:2 turns:1 notes:3 solution:1 fewer:3 discrete:1 convenience:1 vector:2 minimal:2 harry:1 small:1 noted:3 upper:9 zn:1 focs:4 lance:1 version:9 zj:3 deutsch:2 consistent:11 among:1 likely:1 cost:3 run:1 implemented:1 carlo:2 linear:2 even:3 index:3 what:1 xor:6 appear:1 richard:1 t2n:1 complexities:3 section:6 near:1 expressed:2 networks:4 access:1 uj:1 suspect:1 fortschritte:1 above:3 certificates:2 new:4 method:3 contrast:2 satisfy:1 degree:44 tapp:4 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quant-ph9802050.txt |@word consider:2 remarkable:1 results:4 four:1 edu:1 follow:1 expressions:1 finally:2 present:1 th:1 under:1 must:2 worth:4 p2:8 wave:2 difference:1 exact:2 hamiltonian:3 positions:2 solution:6 t0:4 solved:1 small:2 prevent:1 smaller:1 force:1 periodicity:1 sukhatme:2 zero:5 street:1 further:3 even:2 what:1 chicago:2 sum:2 above:1 net:1 avinash:1 3g:1 body:25 outgoing:5 respectively:1 discrete:2 here:4 ranges:1 them:2 irrespective:3 equations:1 change:2 bhubaneswar:1 obtained:3 remark:1 generalizing:1 incoming:4 institute:1 shift:2 larger:2 permutation:1 complicated:1 via:5 family:3 suddenly:1 9g:5 use:1 feb:1 asymptotic:2 would:1 recalling:1 contains:1 next:1 noting:2 type:1 reflects:1 more:2 initial:4 everywhere:2 particular:2 cases:4 discontinuously:1 room:1 collision:1 work:2 oscillator:1 values:3 mr:1 following:6 proof:1 weaker:1 figure:1 give:1 process:2 introduces:1 india:1 effectively:1 sense:2 exclude:1 tan:2 distinguishable:2 axis:1 rather:1 discussion:1 six:1 how:2 nontrivial:1 answer:1 parameter:3 sin:13 simplicity:2 singular:1 replacing:1 after:2 derived:1 different:3 constants:2 stress:1 sectors:2 interpolates:1 so:3 xj:1 holds:2 indeed:1 years:1 course:1 paper:4 through:1 still:2 before:2 37a:1 interesting:1 37c:1 coordinates:7 systems:1 jacobi:1 decades:1 non:3 good:1 b2:2 repulsive:1 they:4 now:9 discuss:4 easily:4 gets:1 university:1 applied:1 2b:3 2m:5 characterized:1 independent:3 related:4 isospectral:8 obtains:1 quantum:4 our:1 operation:1 eq:22 special:2 shown:2 matrix:1 space:1 furthermore:1 particles:13 may:1 ref:3 occurs:2 math:4 shows:1 given:21 completely:1 khare:2 besides:2 rutherford:1 interaction:6 marchioro:6 motion:1 place:1 hence:4 interact:1 first:1 origin:1 major:1 xi:5 symmetry:2 variables:1 another:1 angular:3 differ:1 similarly:1 ordering:1 leading:1 eqs:8 system:3 relations:3 their:2 final:2 gives:1 collapse:2 relationship:4 exactly:1 17c:2 x2:21 x3:14 x1:24 than:1 distance:1 showed:2 cyclic:1 limiting:1 matter:1 were:1 unchanged:1 argument:2 already:1 manner:1 seen:2 any:2 angle:2 calogero:14 note:4 potential:18 take:2 coincide:1 continuous:1 shall:1 beta:1 phase:3 class:6 eigenfunctions:1 later:1 stronger:1 points:1 mechanical:2 physics:2 fact:1 sector:2 iopb:1 show:5 purely:2 relation:1 find:1 only:2 integrable:1 goes:2 notation:1 p2φ:1 dt:2 dr:1 nicely:1 arxiv:1 satisfy:3 requirement:1 ses:1 frame:3 relative:2 see:2 result:4 best:1 wonder:1 closer:1 interacting:4 state:2 between:6 invariant:1 approach:1 terms:6 nature:1 however:1 p2r:1 configuration:1 come:1 both:5 cos:10 equal:2 context:2 expression:1 simple:7 corresponds:1 translationally:1 throughout:1 pr:1 marg:1 raise:1 three:19 been:1 ai:5 much:1 ph:1 pi:10 define:1 arises:1 corresponding:3 restrictions:1 spectrum:2 denote:2 those:1 case:5 p3:8 p1:8 might:1 value:4 will:3 while:3 replaced:8 situation:1 property:1 procedure:1 refs:2 thus:2 surprisingly:1 vanish:1 containing:1 same:2 clearly:1 quant:1 arguments:1 finite:1 φl:3 difficult:2 fairly:1 used:1 closest:1 iop:1 purpose:1 potentials:19 jour:4 center:5 well:1 position:1 dimension:3 usual:1 just:1 being:3 intervals:1 immediately:3 momenta:10 scattering:14 heuristic:1 except:1 discontinuous:2 add:2 solvable:1 transformation:1 gave:2 identical:2 eigenfunction:1 period:1 five:1 using:3 apart:1 dimensional:2 like:1 particle:2 follows:3 permuting:1 disconnects:1 continue:1 steps:4 arbitrary:1 soft:1 twelve:1 classical:10 smoothly:2 pφ:1 sight:1 specified:2 provided:1 2e:1 harmonic:2 yields:1 run:1 jumps:1 takes:1 discussed:4 range:1 2x3:5 h2:1 backscattering:4 appropriate:1 references:1 operator:1 additional:3 strictly:8 there:5 question:1 was:2 complete:1 form:1 but:3 elimination:1 true:1 made:1 places:1 whether:1 us:4 dφ:1 problem:11 similar:2 uic:1 taylor:1 constant:4 reconcile:1 defined:3 abstract:1 general:1 again:1 functions:2 no:3 whereas:2 when:9 illinois:2 other:2 department:1 polar:4 problems:2 includes:1 deriving:1 qπ:3 variable:1 ago:1 coupling:5 assume:3 4m:1 mass:7 having:1
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quant-ph9802051.txt |@word consider:2 switched:1 activated:2 invent:1 leads:3 scalar:1 commute:1 consists:1 follow:1 expressions:1 row:1 looking:1 calculate:1 tr:6 nonlocal:1 tb1:2 finally:3 under:4 tr1:1 applied:1 advantage:1 orthogonal:1 very:3 differently:1 lyapunov:1 decide:1 trouble:1 little:1 condition:1 nska:1 entire:9 level:1 did:1 notes:2 solution:4 correct:2 try:2 small:5 smaller:1 sin2:5 second:5 dynamics:12 amplified:1 even:1 trick:1 what:4 nonlinear:28 sub:1 sum:1 selected:1 uniform:1 version:1 above:3 values:1 calculations:1 respectively:1 never:1 equals:4 here:3 atoms:1 contemplate:1 cos2:4 active:1 safer:1 equations:2 change:3 obtained:4 involved:3 leaves:1 vectors:3 allows:1 contradiction:1 amount:1 periodic:1 products:1 implement:1 makes:1 options:1 involves:1 formulated:1 projection:2 mobility:9 apply:2 use:4 feb:1 projector:1 would:4 prove:1 positive:1 contains:1 ψt:8 explicitly:4 therefore:12 taken:1 type:5 reflects:1 more:4 separated:2 abrams:5 becomes:1 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quant-ph9802052.txt |@word concept:1 allowed:1 maximum:3 results:1 entropy:8 follow:1 row:1 compact:1 depend:1 calculate:4 tr:2 environment:1 finally:3 monotonically:1 under:7 stochastic:1 characterised:3 p2:2 fax:1 conjectured:1 choice:2 worst:1 δjk:1 matrices:1 condition:1 generalised:1 dim:1 randomness:3 tra:2 dsb:2 notes:2 michael:1 vector:4 eigenvalues:7 trs:1 noted:2 concluded:1 yjk:1 consistent:1 direct:1 approximation:1 second:4 value:4 further:4 generator:1 4x1:1 what:1 ubner:1 appear:1 apparatus:1 section:8 uniform:5 version:1 above:4 new:2 consisting:1 seeks:1 full:1 degree:1 respectively:3 here:2 desired:2 address:1 alone:1 slater:1 strong:1 knowledge:9 obtained:2 shift:1 popescu:1 studied:1 allows:2 published:1 prior:2 schumacher:1 dre:1 york:2 schack:2 useful:4 marginal:3 plenum:1 generality:1 unit:3 eψ:3 would:5 commun:1 positive:1 contains:1 properties:2 process:2 bases:2 therefore:2 robertson:1 australian:1 theoretical:2 more:4 bennett:1 composite:6 becomes:2 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quant-ph9802055.txt |@word secondly:1 consider:3 ceases:2 illustrates:1 caused:1 particular:1 dynamic:5 results:6 gx:3 illustrated:1 follow:1 expressions:1 causes:1 scr:2 calculate:1 finally:1 does:1 those:2 under:1 include:1 divergent:1 summarizes:1 p2:19 far:1 rise:1 figs:2 formula:1 affect:1 difference:2 exact:2 gurion:1 level:5 2κn:1 t2:2 solution:2 plotting:1 large:3 small:1 configurations:4 upper:3 literature:1 approximation:1 rate:26 exter:1 81a:1 further:3 mill:1 even:2 what:1 nonlinear:1 plays:3 near:1 above:2 increasing:2 jumps:1 contrast:2 respectively:2 atoms:3 behaviour:2 relaxation:4 sheva:1 strong:1 equations:10 appears:1 change:1 box:1 woerdman:1 involved:1 study:1 larger:1 approaches:1 changes:4 plotted:3 ix:5 smax:3 inequality:1 decrease:3 total:1 plot:1 takes:1 distinct:1 positive:1 lasing:28 jpn:1 comparing:1 bottleneck:1 therefore:4 type:8 today:1 more:1 lowering:1 israel:1 becomes:3 apparent:1 emission:10 validity:1 separates:2 known:1 iii:6 account:1 fuction:1 science:1 equation:1 work:1 modified:2 mu:2 values:6 following:5 spontaneous:12 example:2 figure:2 process:1 high:2 indicates:1 sense:2 cooperativity:1 provide:1 breaking:2 feature:2 very:3 instead:1 parameter:35 mar:1 description:1 derived:2 types:2 so:2 decreasing:1 operate:1 order:1 restriction:5 interpretation:1 gradual:1 over:1 mainly:1 years:1 saturates:3 lasers:7 omitting:1 existence:1 its:5 derive:1 decay:3 jin:1 interesting:1 solving:1 decreases:2 writing:1 destroyed:1 systems:1 main:1 nienhuis:1 maximal:3 non:3 investigated:1 break:1 now:3 transparent:1 term:1 several:1 always:1 university:2 p2max:7 2g:1 mode:6 reasonable:2 turns:2 found:2 2n:1 referred:1 schemes:11 another:3 gennady:1 related:1 decays:1 our:2 hart:2 eq:9 out:1 shown:8 matrix:1 restricted:4 since:2 immigrant:1 increase:1 print:1 wich:1 occurs:2 lugiato:1 linear:3 state:14 pumping:13 possibility:1 standard:2 reason:2 hand:1 definition:1 derivation:1 ministry:1 transition:5 turn:3 hence:1 destruction:1 first:4 origin:1 major:1 xi:5 relate:1 number:31 approximate:1 done:1 directly:1 xv:3 differ:1 their:2 xii:6 eqs:2 sargent:1 1a:3 needed:1 1b:3 master:1 too:1 xiv:2 realization:1 rates:3 scheme:21 observations:1 mostly:1 exactly:1 part:1 authors:1 operates:1 than:5 begins:2 kind:1 ben:1 zero:1 determined:2 gives:1 sees:1 rewrite:1 fluctuation:1 curves:5 manner:2 seen:2 clearly:1 note:3 ideal:2 analogy:1 most:1 device:1 considered:1 calculated:1 steady:3 nsat:3 points:1 physics:2 fact:2 drastically:1 phenomenon:1 show:1 supported:1 relation:1 threshold:18 ground:3 parameters:5 pump:46 pretty:1 factor:16 emitting:1 rice:1 pointed:1 do:1 slows:1 means:1 rept:1 altogether:2 determines:1 collisional:1 carmichael:1 transversal:3 approach:1 arxiv:1 summary:1 paper:2 fixed:1 occupy:1 approaching:1 set:3 exists:2 kink:1 namely:1 recently:1 israeli:1 ways:2 tend:1 enough:3 various:2 closed:2 between:5 conditions:1 terms:1 emitted:3 however:5 configuration:3 both:6 essentially:2 limits:1 many:1 quiet:1 sensitive:1 became:1 γij:1 excites:5 experimental:1 afterwards:1 point:9 corresponds:4 semiclassical:1 scully:1 kocharovskaya:1 second:2 due:2 been:3 beer:1 interest:1 ph:2 fig:18 obtained:4 coherence:2 photon:24 observe:1 present:1 case:10 negev:1 p1:8 laser:12 pokrovsky:1 solid:1 value:14 spontaneously:2 arimitsu:1 dephasing:1 replaced:1 viii:5 behavior:5 property:1 yi:1 played:2 vi:5 thus:2 iv:5 ii:7 reads:1 il:1 disappear:3 different:7 grant:1 make:1 same:5 any:1 quant:3 gibbs:1 physical:3 grows:1 used:5 see:3 upon:6 possible:1 mandel:1 levels:2 introduce:1 recent:2 lower:5 off:4 makes:1 well:3 without:3 less:4 being:1 kinks:6 atomic:1 yamamoto:1 polarization:2 renewed:1 density:1 absorption:1 photons:11 lett:1 excited:1 saturation:15 vii:5 depends:2 inversion:8 increases:3 using:1 like:3 kennedy:2 follows:1 either:1 become:2 therein:1 because:2 qed:3 some:5 growth:1 b2:1 happens:1 savage:2 describing:1 cavity:3 depletion:1 critical:10 minimal:4 refer:1 equivalent:1 expansion:1 stem:1 broken:1 properties:1 comparison:1 about:2 khitrova:1 surprizing:1 discussed:2 dependence:8 o:3 range:1 bgu:1 bloch:4 soc:1 rev:7 presence:1 orders:1 maxwell:4 into:6 within:1 three:3 down:5 phase:3 references:2 van:1 additional:2 there:3 depicted:1 fast:1 start:2 low:1 fraction:1 crucially:2 valley:1 was:2 function:5 medium:1 complete:1 form:2 but:1 magnitude:2 atom:4 line:3 directed:3 condition:3 prevents:1 up:1 books:1 limit:4 similar:2 regimes:2 ac:1 constant:1 defined:2 describe:2 linearity:1 xiii:2 physica:1 lifetime:1 fizika:1 regime:5 functions:3 dotted:1 no:3 dashed:1 whereas:1 when:8 slusher:1 field:1 other:3 role:5 brings:2 department:1 picture:2 provided:1 excite:1 meaning:2 important:1 shibata:1 βmin:4 implies:2 coupling:1 practically:1 curve:3 together:1 portion:1 time:3 4g:1 meystre:1 4c:1 4a:2
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quant-ph9802056.txt |@word positions:2 consider:4 interference:2 magnetic:2 results:2 four:5 per:4 computation:1 clairvoyant:1 go:4 gn:1 expressions:1 faster:1 reasoning:1 causes:1 compact:1 particles:3 certainly:1 tn:3 finally:1 chapt:1 helps:1 connecting:1 case:2 amplitudes:2 presently:4 g1:1 very:3 rise:1 wave:6 experimentally:1 difference:1 condition:1 philosopher:2 leads:2 incoherent:1 cable:10 transmission:17 turns:1 t2:1 solution:1 t1:3 large:4 solved:1 vector:2 recall:1 rev:3 relation:1 optics:3 lines:2 configurations:2 concluded:1 application:1 employing:1 slower:1 measurable:1 worm:2 past:4 zero:5 noise:1 traveling:1 further:1 defines:1 employ:1 what:6 plays:1 rd3:1 chicago:2 trivial:1 sum:1 interactions:1 fingers:1 current:1 experiment:1 above:3 new:2 rd:1 method:1 counters:2 satisfy:1 edited:1 notions:1 exchange:1 respectively:3 here:13 understanding:1 possibility:1 directions:6 along:1 equations:2 z1:2 z2:2 sending:1 institute:1 involved:3 allows:2 loop:1 action:3 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quant-ph9802057.txt |@word ambiguities:1 wigner:5 consider:1 show:1 rev:3 rotated:1 kanai:4 friction:5 purely:1 quadrature:1 relation:1 partial:1 satisfies:1 its:1 ground:1 caldirola:4 q2:2 based:1 parameters:1 density:1 ln:1 written:1 γt:1 quadratures:1 explicitly:1 fig:2 under:1 stochastic:2 4γt:2 main:1 sin:2 excited:1 momentum:1 real:1 dk:1 combination:1 means:2 quasidistribution:1 wave:4 framework:2 philos:1 safonov:2 2γt:7 using:3 rotation:1 e2γt:10 discuss:1 dp:1 dq:1 loss:2 evolution:4 like:3 hamiltonian:2 follows:1 arxiv:1 solution:1 damped:6 nwn:2 dodonov:1 invariants:3 output:1 dolgoprudny:1 mathematical:1 satisfy:1 res:2 classical:9 energy:4 idea:1 related:1 operator:3 see:2 frequency:1 result:1 b2:8 w0:2 quantum:21 dynamics:1 alternative:2 out:2 appear:1 shown:3 tombesi:2 matrix:1 space:1 operators:2 nuovo:1 since:1 µq:2 analogously:1 expressed:2 find:1 state:15 wn:5 conditions:1 w1:1 coefficient:1 terms:3 linear:1 respectively:1 proc:1 here:2 moyal:2 measurable:1 following:1 cambrige:1 found:2 described:1 imaginary:1 distribution:15 takes:2 obtained:3 observable:1 cos:2 rederived:1 institute:1 region:1 discussed:1 o:1 motion:2 a2:8 act:1 action:1 introduced:1 expression:1 first:1 soc:1 contains:1 probability:11 extra:1 hermite:1 integral:1 period:1 negative:1 variable:3 wα:2 frames:1 complex:1 pr:1 iω:1 given:1 feb:1 reference:2 introduction:1 positive:1 initial:1 system:7 appears:1 ordinate:1 describes:1 ψn:1 taken:1 ph:1 scheme:1 was:5 theoretical:1 lett:1 function:12 suggested:1 progr:1 complete:1 form:7 moscow:2 odinger:2 gaussian:1 coherent:4 correspondingly:1 hn:1 normalized:2 derivative:1 known:1 periodicity:1 present:1 p2:2 laser:2 equation:14 work:2 oscillator:12 ωt:2 us:1 ρn:1 aim:1 assume:3 fock:6 values:1 squeezed:1 about:1 problem:1 property:1 obtain:2 russia:1 mechanics:6 correspondence:1 constant:1 νp:1 vogel:2 rewrite:1 vol:10 abstract:1 conjugate:1 turned:2 spectrum:1 states:4 ik:1 formulation:6 tomography:2 ib:4 technology:1 check:1 physical:1 information:1 functions:1 angle:1 cim:1 no:1 generic:1 distributions:1 discussion:1 acts:2 x2:2 dependent:2 hn2:1 quant:1 theor:1 ensemble:1 formulas:1 phi:1 used:1 description:3 calculating:1 asterisk:1 polynomials:1 meaning:1 levels:1 uses:1 phase:1 risken:2 measured:1 man:7 schr:2 abscissa:1 considered:2 depending:1 ko:7 russ:2 mancini:2 optical:1 homodyne:1 exp:16 time:3 position:2 physics:2 notion:1 dot:1
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quant-ph9802058.txt |@word secondly:1 code:1 consider:13 maximum:3 caused:2 magnetic:19 lack:1 desirable:1 results:8 ds:1 leads:2 eds:1 computation:4 obtaining:2 inefficient:4 gm:9 contributions:1 reasoning:1 gi:1 soc:2 whose:2 inverse:2 depend:1 calculate:3 graph:1 concerned:1 technique:4 contained:1 james:1 γi:2 device:1 γn:1 th:1 under:1 phil:1 government:1 γf:6 necessary:2 applied:1 g5:3 eigenstate:1 g3:1 worse:2 advantage:2 orthogonal:1 very:8 frequencies:10 tends:1 conditions:1 javanainen:1 readout:3 electron:4 figs:1 sidebands:12 resonant:6 affect:1 difference:3 exact:2 pumping:8 condition:6 cool:1 treating:1 school:1 propagating:1 magic:1 exponential:1 vibrational:12 bring:1 schawlow:1 bessel:1 steeply:1 solution:6 standards:2 large:16 solved:1 coincidences:1 min:2 small:9 refer:1 optics:1 equation:9 leibfried:2 still:2 prevent:1 approximately:6 lewenstein:1 oscillation:1 ij1:1 consistent:1 d3:6 pulse:10 aip:1 approximation:2 second:7 cost:1 design:1 gn:2 manipulating:1 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quant-ph9802060.txt |@word limited:2 partial:1 consider:2 secondly:1 rev:9 excellent:2 existing:1 four:1 commute:1 microwave:1 computation:1 consists:2 sci:1 antinode:1 adjustment:1 compact:1 c0:10 systematic:1 iii:1 contained:2 finally:1 according:1 tj:8 those:2 th:1 under:2 sent:1 belonging:1 supported:1 amplitudes:1 presently:1 advantage:1 orthogonal:3 far:1 frequencies:2 rise:1 atoms:1 wave:5 mixing:1 experimentally:1 emphasized:1 difference:2 condition:1 leads:2 evaded:1 level:3 solution:1 t0:1 t1:2 large:3 discrete:1 detected:1 science:1 markov:1 barbara:1 equation:2 upper:4 smaller:3 direct:1 pulse:12 approximation:4 zero:1 timescales:1 further:1 dynamics:3 leakage:1 subclass:1 spectral:4 index:2 what:1 errors:6 rate:4 near:1 networks:1 above:1 bergou:1 guns:1 satisfy:1 quenched:1 outgoing:3 led:1 ibid:3 respectively:5 teleportation:1 here:3 κc:11 them:1 departamento:1 mes:3 active:1 equations:1 obtained:1 great:1 technical:1 leaves:1 allows:2 host:1 commonly:1 resulting:1 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quant-ph9802061.txt |@word code:59 saturating:1 consider:1 maximum:1 interference:1 gz:2 gx:2 leads:2 gf:4 broader:1 gi:1 row:1 aug:1 knill:1 finally:1 those:2 th:1 include:1 subtleties:1 case:1 g2:1 advantage:1 orthogonal:1 very:1 choice:1 worst:1 matrices:3 condition:7 swapping:1 roy:1 proc:1 list:1 correct:1 large:3 vector:6 small:2 deleting:1 upper:7 smaller:2 mceliece:2 zero:4 equal:1 further:3 odd:1 linear:1 even:7 established:1 errors:2 rate:3 giving:1 sum:1 shares:1 decoding:1 bdt:1 3n:1 above:4 new:7 method:3 filled:1 3d:7 satisfy:3 tabulation:1 never:1 here:1 ranges:1 met:1 packing:1 nonbinary:1 change:1 obtained:11 involved:2 larger:3 commonly:1 amount:1 resulting:3 published:3 deg:1 involves:1 via:2 useful:1 sloane:3 welch:2 undergone:1 additive:2 asymptotic:1 codewords:1 remains:2 contains:6 h1t:1 generate:4 few:1 m1:2 therefore:9 memory:1 more:3 duals:1 successful:1 known:5 must:3 involve:1 permits:2 obvious:2 stabilizer:4 ms:6 concepts:2 following:3 trans:3 root:1 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quant-ph9802063.txt |@word limited:3 interference:15 dynamic:1 rˆ:5 entropy:6 consists:3 localized:3 whose:2 under:2 characterised:1 summarizes:1 conjecture:6 comm:1 summarized:1 experimentally:5 school:1 cause:3 solution:2 vector:8 succession:1 markov:3 ups:1 degeneracy:1 force:1 miller:5 consistent:4 estimates:3 direct:3 pulse:1 approximation:1 surrounding:5 second:2 sustaining:1 currie:1 estimated:10 even:4 established:1 selected:1 above:41 new:5 increasing:1 consisting:1 1997b:4 1997a:7 presynaptic:5 here:12 atoms:21 localisation:1 met:5 mev:2 represented:4 path:1 referring:1 obtained:2 study:1 guide:1 procedure:1 stressed:1 complicated:2 adopting:1 suitable:1 changes:2 hydrophobic:2 diameter:1 projection:3 explained:3 redefinitions:1 total:2 univ:2 unit:2 waveguides:1 negative:3 delocalised:2 inevitable:1 riv:1 therefore:5 m3:1 distortions:2 type:2 separated:1 solitons:6 expose:1 odinger:6 berlin:1 hole:1 hold:1 must:2 springer:1 ma:1 room:5 mc:1 mm:1 work:22 mk:1 theories:1 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quant-ph9802069.txt |@word represent:1 consider:4 limited:1 leads:1 recami:1 violate:2 letokhov:1 presently:1 very:1 wave:11 difference:2 transmission:10 large:1 relation:2 optics:1 disclaimer:2 upper:5 past:2 imply:1 boyce:2 linear:1 even:1 index:2 what:5 sum:2 thickness:1 lifshitz:3 slabs:1 outgoing:2 respectively:1 component:1 objects:1 along:1 incoming:4 involved:1 scatter:1 amount:1 definitively:1 fourier:5 genuinely:1 merely:1 vin:4 total:1 propagators:1 would:3 prove:1 remains:1 negative:2 going:1 criteria:3 taken:1 type:1 theoretical:1 more:3 vout:3 populations:2 eiθ:1 odinger:1 acausality:3 hold:1 hints:1 ma:1 electrodynamic:5 equation:1 work:2 theories:1 temperatures:1 following:2 example:1 proof:2 numbers:1 employs:2 sense:2 evidently:1 axis:1 information:1 needs:1 basov:1 discussion:1 holds:2 delay:4 how:1 dg:2 sin:1 continous:1 mar:1 superluminal:5 may:3 tact:1 plane:5 response:6 spielmann:1 light:4 explicit:1 correspond:1 asserts:1 media:3 definitions:3 order:1 typical:1 produces:1 indeed:3 over:1 move:3 expects:1 held:1 experiments:3 through:12 group:2 relativity:1 exhibits:1 microscopic:2 pergamon:1 might:2 non:2 views:1 material:12 landau:3 transmissions:1 half:5 oxford:3 now:1 discuss:3 dielectric:2 easily:1 several:1 profound:1 university:1 inequality:2 transmitted:1 found:1 entirely:1 side:1 scattering:2 domain:4 doing:1 ed:1 energy:2 displacement:1 inverted:2 frequency:9 quantum:12 our:3 eq:10 event:1 special:1 out:1 space:3 since:2 rev:4 i0:11 tdelay:2 theory:8 barrier:4 little:1 possibility:1 quite:1 completely:1 finite:1 care:1 times:5 place:1 chiao:3 speeds:1 already:1 mistakenly:1 reflected:1 approximate:1 done:1 passes:2 given:2 introduction:2 eqs:3 system:2 behaved:1 fraction:1 continuous:1 schr:1 than:2 accordance:1 intensity:1 iωz:1 future:1 amplitude:6 were:1 garrison:1 absorb:1 electrodynamics:4 berestetskii:1 say:1 unlikely:1 demonstration:1 any:1 output:2 lim:1 mechanism:1 note:1 take:1 electric:1 shall:1 incidence:1 molecule:1 propagate:1 especially:1 sometimes:1 acausal:2 feynman:4 mechanical:1 velocity:1 physics:2 notion:3 akhiezer:1 violation:1 purely:2 gauge:1 solutions:1 ground:1 causality:10 analytic:6 only:5 explicitly:1 employed:1 ocs:1 local:2 do:1 dk:1 viewpoint:2 df:3 lected:2 report:1 widom:1 4πp:1 arxiv:1 view:1 kryukov:1 violated:2 blurred:1 observed:1 depends:4 result:1 violates:1 subject:1 pictures:1 state:2 between:2 boundary:2 nature:1 however:2 jetp:1 both:1 cos:1 many:2 conclusions:1 according:1 propagation:2 context:1 refraction:2 passing:2 finds:1 mechanics:1 ch:1 conclude:1 appeared:1 northeastern:1 corresponds:1 2nd:1 semiclassical:1 dependent:1 respect:1 considers:1 pp:1 described:1 transformations:1 basis:2 locally:1 been:4 much:2 boston:1 ph:1 causal:6 photon:7 krausz:1 evidence:2 iσ:1 present:1 case:2 pacs:1 reliable:1 value:2 excited:2 will:2 steinberg:1 mitchell:1 manner:1 thus:2 sting:1 ii:1 im:5 cone:3 different:4 perform:1 slab:10 wherein:1 complex:4 quant:1 fill:1 literature:3 see:1 titchmarsh:2 retarded:4 interscience:1 effect:1 uses:1 purpose:1 vref:2 off:1 reflection:1 modeled:1 materials:2 studying:1 firstly:1 model:6 soviet:1 imζ:1 rest:1 bandwidth:2 speed:1 yet:1 previous:1 polarization:2 cut:1 secondly:1 hint:1 vω:2 point:2 mathematically:1 signals:3 transformed:1 lett:3 theorem:1 input:2 violations:1 transit:1 momentum:1 read:1 possible:3 vacuum:3 press:2 follows:2 signal:7 velocities:3 integrals:1 become:1 essential:1 mathematical:6 methods:1 classical:16 2iη:1 some:2 understood:2 examples:1 duration:1 transport:1 ωp2:3 lead:1 electromagnetic:15 avoid:1 normal:1 cv:1 does:1 ωim:8 noise:1 clarendon:1 olkhovsky:1 bs:1 central:2 theorems:1 kwiat:1 obeys:5 op:2 conserving:1 presence:1 maxwell:2 into:1 within:2 appropriate:1 references:1 einstein:4 theoretically:1 often:3 elastic:1 strictly:4 there:5 transform:2 long:1 dispersion:2 strict:1 describes:1 way:1 forward:1 propagator:3 function:4 form:1 but:4 atom:3 true:4 made:1 evident:2 whether:2 us:2 cit:2 similar:2 emit:1 detailed:1 proved:1 abstract:1 general:1 dθ:1 moves:1 physical:1 functions:1 no:1 when:2 virtual:1 field:3 department:1 models:2 building:1 faster:1 dω:5 required:2 rule:2 time:11 backward:1
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quant-ph9802070.txt |@word zonal:2 impression:1 shor:1 code:11 they:2 show:1 indeed:1 over:3 random:3 satisfied:3 appearing:1 course:1 enumerators:4 existence:2 satisfies:1 trivial:1 k3:4 preserves:1 hold:1 monotonicity:4 solution:2 technique:2 tr:12 should:4 matrix:1 only:4 explicitly:2 present:2 lp:12 theorem:7 mail:1 easier:1 ought:1 nj:1 real:1 enumerator:7 notation:1 means:1 coding:1 expectation:1 feasible:2 number:1 operaˆ:1 corollary:1 additional:1 words:1 bounding:2 immediately:1 shadow:2 matrices:4 entire:1 february:1 subcodes:3 products:1 turns:1 arxiv:1 applicable:1 specific:1 theory:2 inequality:2 follow:1 either:1 follows:4 rev:1 att:1 2n:3 fixed:1 noted:1 constraints:5 homogeneous:2 tensor:2 set:2 laflamme:1 weight:10 some:2 lett:1 group:1 operator:2 see:2 result:3 deduce:1 apply:1 quantum:32 aˆh:1 eq:1 ep:2 exists:2 out:1 hilbert:1 ˆq:3 3y:13 satisfying:4 dimensions:1 factors:1 ieee:1 since:3 definite:1 while:1 research:3 symmetric:1 reformulate:1 com:1 above:1 s12:5 print:2 readily:1 suffices:1 consisting:1 math:1 satisfy:2 terms:2 reformulation:2 linear:10 degree:1 qubits:2 respectively:2 equivalent:3 arbitrary:1 however:2 standard:1 bu:1 reason:1 wt:7 bq:4 key:1 address:1 depend:1 picking:1 equations:3 appears:2 irreducible:1 simpler:1 remark:2 constraint:2 phrases:1 lanl:2 aˆ:3 programming:10 o:4 nonnegative:1 suggests:2 subcode:4 misleading:1 resulting:1 2k:1 makes:2 first:1 note:1 xn:4 projection:2 nonbinary:1 encoding:2 powerful:2 bound:17 smaller:1 references:1 directly:1 polynomial:4 impossible:1 glance:1 actually:1 size:2 considering:1 use:1 pq:4 feb:1 classical:2 usa:1 similarly:5 introduction:1 positive:2 support:1 there:4 eπ:2 relations:2 aˆq:3 πp:3 appear:1 interest:1 πu:1 ph:3 ann:1 define:3 alphabet:1 preserved:1 th:1 clearly:1 given:1 sequel:1 park:2 but:1 larger:1 particular:3 known:2 nonidentity:1 general:2 true:1 sˆ:1 coefficients:1 must:1 distance:4 aq:4 room:1 unlike:1 invariants:1 holds:1 recall:1 equation:1 harder:1 namely:1 will:3 below:1 itself:1 obvious:3 cˆ:1 following:3 au:1 trans:1 obtain:2 average:4 proof:4 point:1 claim:2 unitary:2 false:1 give:1 defined:2 abstract:1 formulation:1 denote:1 states:2 eu:5 ik:1 minimum:4 exist:2 purity:1 dual:1 sense:1 disjoint:1 ave:1 inf:1 epq:1 identities:1 eric:3 again:1 functions:2 codes:8 macwilliams:1 lemma:4 james:1 rains:7 s2:4 orthogonal:1 able:1 σy:1 same:1 any:2 write:1 k2:10 σx:2 quant:3 analog:1 pure:2 becomes:1 instead:2 proved:1 satisfiable:1 independent:1 after:1 monotonic:8 polynomials:7 tor:1 most:2 a2:2 characters:1 carries:1 constants:1 inequalities:4 prescribed:2 lower:1 implies:1 imply:1 onto:1 clear:1 space:1 well:2 together:1 original:1 4n:4 so:5 expression:1 decreasing:2 dimension:4 fact:1
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