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quant-ph9609018.txt |@word externally:1 epeau:1 consider:3 switched:1 magnetic:1 results:1 leads:1 privman:3 expressions:1 causes:2 inverse:1 depend:1 calculate:1 knill:1 factoring:1 presents:1 finally:1 nodes:1 presentation:1 applied:1 straightforward:1 choice:2 electron:3 putting:1 experimentally:1 matrices:3 høyer:1 condition:2 four:1 obvious:1 hamiltonian:23 transmission:1 dima:1 large:1 discrete:1 eigenvalues:1 optics:1 upper:1 force:1 computation:7 deutsch:2 grover:1 direct:1 hillery:3 elegant:1 second:1 design:1 further:2 dynamics:2 theory:1 will:5 what:1 errors:1 appear:1 sum:2 selected:2 version:1 new:3 margolus:2 full:1 simultaneously:1 component:1 teleportation:1 here:4 reported:1 iσy:1 simon:1 represented:1 consideration:2 change:1 accomplishes:1 involved:1 studied:2 allows:1 products:1 schumacher:2 fourier:1 studies:2 involves:3 buˇzek:2 via:1 useful:1 griffiths:1 family:1 turchette:1 verge:1 apply:1 unit:1 use:1 would:1 codewords:1 jozsa:2 calculation:3 duplicate:1 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quant-ph9609019.txt |@word casimirs:1 consider:3 similarity:6 trigonometric:4 leads:1 4e2:1 gr:3 whose:3 preserves:2 technique:2 finally:4 th:1 under:4 x02:1 norm:1 case:4 b185:1 d36:1 results:1 witten:2 ǫlmn:2 summarized:1 wipf:1 hamiltonian:4 solution:1 hyp:2 math:6 science:1 eigenvalues:5 csch2:3 sukhatme:1 sin2:4 japanese:1 cosh:13 implemented:1 canonical:9 what:1 invertible:1 morse:9 giving:1 section:2 expressed:1 new:2 method:4 ˆo:2 respectively:1 ginocchio:2 sinh:3 address:1 path:5 along:2 change:3 deduced:1 obtained:2 study:1 studied:1 allows:1 khare:1 fourier:6 relation:2 composed:1 2lm:1 4a2:2 polymer:1 sliced:1 propagators:5 use:3 would:1 remains:1 positive:1 contains:1 chooses:1 next:6 nucl:1 call:1 therefore:3 criteria:1 type:7 more:1 becomes:3 operators:10 particular:3 known:4 cases:1 iii:1 valued:1 klm:10 equation:11 work:3 oscillator:5 trig:2 infinitesimal:1 ulm:2 following:2 example:4 history:1 lφ:2 bordner:2 give:3 µa2:1 states:3 performed:1 hydrogen:1 respective:1 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quant-ph9609020.txt |@word represent:1 partial:2 consider:5 φn1:3 interference:2 particular:2 unique:1 results:2 perelman:1 four:1 consists:2 follow:2 expressions:1 contributions:3 ψcl:22 depend:7 those:1 under:1 analogous:1 circumstances:1 norm:1 applied:2 supported:1 evolves:1 account:1 focus:1 electron:1 novel:1 reforms:2 experimentally:3 nieto:1 difference:1 condition:1 θk1:7 vibrational:3 irreducible:1 t2:12 make:1 t1:12 large:1 small:4 degeneracy:1 smaller:1 periodicity:4 pulse:2 approximation:1 second:11 displays:1 further:1 dynamics:1 odd:4 subscripts:1 appear:6 sum:5 while:1 3t:3 localized:1 above:2 fractional:29 new:4 commensurate:3 consisting:3 satisfy:3 evolving:1 full:13 simultaneously:1 respectively:5 l1:23 component:8 here:5 atoms:1 l21:2 l22:2 q12:5 directions:1 bogdan:1 obtained:1 stark:6 study:1 larger:2 allows:1 hughes:1 p2:10 periodic:5 complicated:2 changes:1 involves:2 plotted:2 examining:1 via:1 useful:1 scales:6 inducing:1 noordam:4 visible:1 addressed:1 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quant-ph9609021.txt |@word represent:2 consider:3 remarkable:4 crucial:2 knotted:1 global:1 alternatives:1 results:1 yurtsever:1 existing:1 proposition:2 follow:1 conservative:2 causes:1 particles:2 certainly:2 assigning:1 deterministic:1 those:3 marks:2 sorkin:2 brown:1 very:4 rise:2 wave:1 probability:1 sons:1 exact:1 condition:1 exits:1 did:2 notes:1 michael:1 solution:6 try:1 solid:1 speculation:1 unifying:1 gerlach:1 consistent:10 second:1 further:1 linear:2 even:3 established:1 what:8 nonlinear:1 apparatus:6 incompatible:1 giving:2 imagined:1 annals:1 above:1 new:1 contrast:2 satisfy:1 evolving:1 full:1 prescribe:1 highly:1 following:2 objects:2 represented:1 path:1 equations:11 great:1 orthomodular:5 institute:1 study:1 changed:1 allows:2 stressed:1 spacetime:9 rafael:1 uniquely:2 emerge:1 via:1 useful:1 explained:1 outcomes:2 boolean:3 names:1 stern:1 apply:1 univ:1 planck:2 derivatives:1 use:3 superpositions:1 would:8 probabilities:2 positive:2 predictions:2 properties:3 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quant-ph9609022.txt |@word ibid:7 twistors:2 concept:2 sci:2 consider:6 pointing:1 illustrates:1 rev:13 magnetic:2 both:7 results:2 p20:1 leads:5 roy:1 commute:3 computation:1 centers:2 localized:2 scr:1 whose:4 depend:1 remarkable:1 equivalence:1 finally:1 efficiencies:3 device:2 protocols:1 caused:1 analogous:4 localizations:1 subtleties:1 p2:2 advantage:1 far:3 b188:1 translations:2 springer:3 wave:3 electron:1 selleri:1 decide:1 summarized:1 ma:2 matrices:2 deformations:1 preuss:1 four:2 presented:1 irreducible:2 notes:1 henri:1 applicable:1 tubes:1 occurs:3 contexts:1 vector:14 pati:1 eigenvalues:10 warszawa:1 lines:5 gerlach:2 natarajan:1 smaller:2 grateful:1 foundation:1 lecture:1 consistent:1 measurable:2 literature:1 lubanski:7 zero:3 dordrecht:2 odd:2 linear:2 even:12 what:3 giving:1 han:4 expressed:2 ˆb:2 experiment:9 above:2 new:3 acknowledgments:1 satisfy:2 edited:3 kalnay:1 led:1 degree:4 respectively:1 never:1 component:2 teleportation:1 here:6 atoms:1 ryszard:1 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quant-ph9609024.txt |@word represent:1 code:15 partial:1 consider:6 chain:1 limited:2 results:6 four:3 eds:1 tripartite:1 concept:1 entropy:78 l12:8 computation:4 follow:2 research:1 soc:1 anticipation:1 depend:1 calculate:5 transferred:1 eigenbasis:1 perfectly:1 subjected:2 deterministic:3 contained:1 factoring:1 environment:38 finally:3 program:1 preserved:2 under:1 stochastic:1 analogous:1 include:1 sent:13 inform:1 summarizes:1 applied:3 expressing:1 straightforward:2 orthogonal:4 very:4 dq:2 rise:1 account:2 print:3 novel:1 every:1 additional:1 traced:1 summarized:2 affect:1 emphasized:1 difference:1 matrices:2 convexity:6 paz:1 treating:1 leads:3 randomness:1 obvious:4 p4:1 level:2 transmission:33 issue:1 tre:2 excessive:3 correct:1 noiseless:1 unrelated:1 science:2 eigenvalues:2 nos:1 trr:1 barbara:3 alternatively:2 upper:5 strongly:1 smaller:3 consistent:4 direct:1 past:1 elegant:1 rate:12 dordrecht:1 equal:7 further:1 dynamics:2 even:1 established:2 subadditivity:13 errors:6 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quant-ph9610001.txt |@word logarithms:1 concept:1 alj:2 consider:4 magnetic:1 results:3 four:2 england:1 entropy:2 computation:2 sci:1 expressions:1 ptr:1 alp:2 alk:1 whose:2 inverse:2 tr:8 braginsky:1 environment:5 edward:1 present:1 th:1 under:1 analogous:1 include:1 sent:2 orthogonal:1 choice:4 summarized:1 experimentally:9 matrices:7 condition:1 nonselective:1 hamiltonian:1 turns:1 t4:1 t2:3 t3:1 correct:1 large:1 convenience:2 vector:2 relation:6 rk:1 barbara:1 equation:4 upper:1 ρj:12 occurrence:1 maximization:1 measurable:1 horn:1 elegant:1 second:1 evaluated:1 further:1 dynamics:8 implemented:1 theory:3 even:1 will:5 what:2 errors:4 appear:2 section:2 axes:1 brief:1 expressed:3 experiment:1 above:1 new:3 method:1 satisfy:2 led:1 aik:1 exchange:1 teleportation:1 here:2 desired:2 iσy:1 relaxation:1 alone:1 consideration:1 along:1 equations:3 change:6 box:14 derivable:1 great:2 naval:1 barnum:1 institute:2 study:1 vectors:1 amount:2 resulting:2 permutation:1 hospitality:1 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quant-ph9610011.txt |@word replacing:2 represent:2 code:51 partial:1 consider:6 limited:1 cial:1 results:9 existing:1 four:1 roy:1 abelian:1 generalize:1 overlap:1 computation:27 stochastically:3 consists:2 particularly:1 reasoning:1 localized:1 row:1 increase:1 c0:2 re:1 knill:9 subjected:1 technique:6 b265:1 environment:1 contract:1 focs:1 critical:1 journal:1 preserved:2 weakening:1 under:12 stochastic:13 include:2 worth:2 detect:1 case:8 supported:2 amplitudes:4 worse:1 advantage:2 yao:1 very:4 hughes:1 ective:2 cellular:1 word:3 bottleneck:1 special:2 entire:1 induced:2 level:14 issue:2 proposals:1 fewer:1 occurs:4 large:3 l2:3 spaces:1 dealt:1 small:6 referred:1 barbara:1 noted:1 smaller:1 force:1 specially:2 speci:2 l2h:1 transversally:6 ted:1 sign:11 approximation:5 across:1 second:9 design:1 follow:1 dynamics:1 implemented:8 odd:1 leakage:7 theory:3 even:8 established:3 what:1 errors:62 appear:3 rate:2 3r:1 section:7 log1:1 expressed:2 decoding:5 current:1 waiting:1 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quant-ph9610012.txt |@word logarithms:1 allowed:1 consider:6 results:2 leads:2 scalar:1 computation:22 foundations:3 whose:1 inverse:1 knill:6 deterministic:4 factoring:3 b265:1 program:24 helps:1 th:2 under:3 norm:1 supported:3 string:5 straightforward:1 far:1 choice:2 manipulated:1 every:1 exact:2 randomness:6 gov:4 exponential:8 solves:1 turns:1 notes:1 large:3 discrete:1 vector:1 laur:4 barbara:1 focs:1 speci:3 approximation:4 fold:1 imply:1 picked:1 growing:1 auspices:1 even:2 established:2 what:3 appear:2 complexities:4 section:2 near:1 supplied:1 uniform:3 access:2 version:5 above:1 new:1 unrestricted:2 increasing:1 method:4 notions:2 degree:1 component:2 here:1 understanding:1 desired:1 simon:1 cult:2 strong:1 observing:1 supplying:2 obtained:4 convert:1 institute:1 trial:1 accomplished:2 products:1 permutation:2 suitable:1 involves:1 genuinely:1 followed:1 santa:1 scales:1 outcomes:1 ips:3 apply:1 total:8 establish:1 unit:1 use:2 superpositions:1 would:2 probabilities:1 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quant-ph9610013.txt |@word 8d:1 secondly:1 code:1 consider:3 hint:1 varying:1 focus:1 leads:6 obstruction:1 computation:1 asymp:1 research:1 issues:1 inverse:1 collisions:1 alamos:5 tr:3 finally:1 those:1 th:1 under:1 cumulants:1 cm5:1 include:2 dramatically:1 mottola:5 division:2 random:1 advantage:1 very:5 results:15 lyapunov:16 difficult:1 sensitivity:1 totically:1 associated:1 difference:1 exact:27 condition:3 treating:2 four:1 quantitatively:1 hamiltonian:28 did:2 cause:1 notes:1 t2:2 solution:9 b285:1 large:56 solved:1 differential:1 indices:1 speculation:1 stay:1 optics:1 noted:1 possibility:1 inserting:1 ten:2 consistent:5 direct:1 dimensional:3 approximation:56 integrators:1 second:9 tildes:1 salman:1 qualitatively:2 dynamics:40 implemented:2 canonical:3 even:5 what:3 nonlinear:5 power:1 brackets:4 blum:1 section:6 near:1 ingraham:1 current:1 version:1 above:11 new:3 increasing:1 ever:1 method:1 contrast:1 edited:1 full:5 nonlinearly:1 degree:2 relates:1 component:1 here:4 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quant-ph9610017.txt |@word consider:1 alternatives:1 results:2 founded:1 commute:3 anticorrelated:1 go:1 content:1 aud:1 spain:1 under:1 ontological:1 circumstances:1 very:2 gun:1 coincidences:1 noted:1 consistent:2 sin2:1 unpolarized:1 sign:2 further:1 specker:2 attributable:1 odd:1 click:1 even:5 what:1 appear:1 giving:1 expressed:1 above:1 obvious:1 coefficient:1 edited:1 full:1 never:1 here:3 reported:1 cos2:1 strong:1 equations:1 change:1 obtained:1 suitably:1 vectors:1 contradiction:1 ignoring:1 der:1 invalidate:1 projection:1 coecke:1 namely:1 plenum:1 logical:1 contradictions:1 total:1 circumvent:1 planck:1 probabilities:1 predictions:1 duplicate:2 therefore:1 taken:1 more:4 becomes:1 operators:3 duplicating:1 known:1 cases:1 hold:1 must:2 tokyo:1 alia:1 equation:3 work:1 theories:3 values:1 dispute:1 example:1 something:1 give:1 purposes:1 states:4 assumptions:1 performed:1 degenerate:1 weimar:2 axis:2 get:1 pure:1 symposium:1 sin:1 may:1 23c:1 waves:1 fits:1 law:1 data:1 correlate:3 light:2 cat:1 correspond:1 so:5 fundamental:1 correlation:3 horne:1 dx:2 essence:1 interpreted:1 professors:1 course:1 experiments:3 through:1 differs:1 its:1 perfect:3 thank:1 la:2 actually:1 derivative:1 hidden:6 defining:1 virtually:1 non:1 orthodox:1 they:1 transparent:1 structural:1 easily:1 dirac:1 preclude:1 each:1 found:1 side:1 oviedo:1 another:1 doing:3 series:1 measurement:1 quantum:9 beyond:1 eq:4 event:1 shown:1 factors:1 restricted:1 rev:1 particles:3 cause:1 correct:1 attending:1 york:1 attendant:1 beginning:1 qm:18 generalizations:1 xj:1 intuition:1 xn:2 features:1 variables:1 rank:1 intuitively:1 xx:1 directly:1 impossible:1 given:1 grangier:1 cambridge:2 their:2 dichotomic:12 observations:1 restrictive:1 testing:1 copenhagen:1 explanation:1 speakable:1 optical:3 july:1 representing:2 than:3 polarized:2 conforms:1 require:1 intensity:2 annihilation:2 matter:1 supposed:1 were:1 allee:1 false:1 epr:1 generalization:1 say:1 conjugate:1 need:2 seen:3 any:2 conversion:1 chem:1 mermin:1 academic:1 essentially:1 self:1 able:1 polarization:8 internal:1 correlating:1 play:1 multiple:1 precluded:1 most:1 involving:2 germany:1 nothing:1 measured:1 inconsistency:1 fossi:1 observation:2 dordrecht:1 clear:6 implications:1 traditional:1 investing:1 proceedings:3 points:2 artificially:1 mechanical:1 physics:4 shimony:1 fact:2 random:1 anyway:1 colors:1 spaces:1 plumb:1 should:2 analytic:2 only:4 indeed:1 oct:1 interstate:1 do:5 notation:1 means:1 de:2 db:3 expectation:1 da:3 famous:1 cannot:1 words:2 new:1 arxiv:1 yield:2 kochen:2 conform:1 requirement:1 reference:1 physically:2 correlations:10 ends:1 stipulation:1 detection:1 see:1 individual:1 result:6 nonlocality:2 israeli:1 inequalities:3 away:1 state:2 unable:1 identification:1 publishers:1 accord:1 terms:2 extend:1 nature:1 confusion:1 analogues:1 however:3 hypothesis:1 key:1 interpretations:1 realizable:1 many:1 ill:1 according:1 etc:1 context:1 logic:1 photons:4 cj:1 relevant:1 bell:13 harmonic:4 anti:2 sequences:2 cancel:1 respect:1 considering:2 sensible:1 pp:2 basis:1 addition:2 three:3 been:1 extraction:1 pa:1 replicate:1 certain:1 ph:1 arises:1 cos:5 zeilinger:1 demand:1 spin:3 present:1 case:2 rigorously:1 empirical:1 will:2 replaced:1 thus:1 them:2 ii:1 itself:1 different:4 make:2 formulations:1 same:2 wherein:1 quant:1 arguments:1 used:1 moment:1 tracking:1 contest:1 well:1 analysis:3 obviously:1 barut:1 contact:1 na:1 model:1 parametric:1 just:2 less:1 underlying:1 aspect:1 differentiation:1 alternative:1 multiples:2 note:2 preprint:1 kluwer:1 hab:1 exclusively:1 mathematically:1 source:1 theorem:4 mod:1 tests:2 aspects:1 depends:1 bands:1 showing:1 sums:1 press:2 integer:1 unique:1 occurring:1 particle:2 follows:1 specific:1 imposes:1 yields:1 integrals:1 exploiting:1 simply:1 inter:1 university:1 right:1 classical:7 exposed:1 creation:2 phenomena:1 exposes:1 moreover:2 describing:1 lead:2 establish:1 cosines:1 does:1 expressing:1 proc:1 minimal:1 bj:1 broken:1 symp:1 although:1 post:1 hilbert:1 malus:1 theorems:6 dependence:1 o:1 compatible:1 rendered:1 within:1 isomorphic:1 down:1 because:3 references:1 roads:1 statistics:1 van:1 question:1 was:1 function:2 elsewhere:2 form:1 relaxed:1 pe:1 but:3 delta:1 made:1 converted:1 those:2 verification:1 mechanics:5 constant:1 int:2 likewise:1 aj:1 am:1 general:1 multiparticle:1 associates:1 dλ:1 again:1 functions:13 nm:1 no:2 absurdity:1 when:1 rubber:1 other:2 mathematics:1 conclusion:2 problems:2 ultimately:1 variable:6 structure:1 correlated:1 required:2 rule:1 principle:2 unspeakable:1
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quant-ph9610018.txt |@word represent:1 concept:7 consider:1 caused:1 results:1 leads:2 eds:3 scalar:2 commute:4 entropy:13 go:2 localized:7 particles:1 inverse:1 depend:2 paris:2 program:1 under:7 maryland:2 include:1 friendly:1 norm:1 applied:1 very:5 implicitly:1 translations:2 wave:5 sons:1 every:2 difference:13 matrices:1 condition:2 did:1 applicable:3 deals:1 convenience:1 vector:1 optics:3 prevent:1 employing:1 ten:1 insignificant:2 consistent:1 cosh:2 approximation:1 second:13 kaiser:2 further:1 defines:1 even:1 what:1 plays:1 section:1 contracted:1 brief:1 above:4 new:4 boost:8 satisfy:4 respectively:3 never:1 here:4 understanding:1 objects:1 sinh:2 consideration:1 standard:2 change:2 allows:4 fourier:2 makes:2 windowing:3 york:1 examining:1 formulated:3 useful:2 requiring:1 replace:1 translational:2 use:2 takes:3 would:1 covariant:10 positive:1 stated:1 negative:1 next:1 call:2 therefore:2 scope:1 type:1 theoretical:2 more:2 introducing:1 becomes:12 odinger:1 carrying:1 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