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quant-ph9605024.txt |@word represent:2 emch:2 partial:1 consider:5 remarkable:1 rev:3 lack:1 leads:1 scalar:3 commute:1 involved:1 heller:2 passage:1 absorbing:1 finally:1 does:1 those:1 ti:1 division:1 supported:1 amplitudes:4 84a:1 very:2 wave:5 tantalizing:1 difference:2 encounter:1 four:1 metals:1 level:1 transmission:2 t2:1 t1:1 large:3 admissible:2 small:1 originally:1 smaller:1 consistent:1 sin2:1 unpolarized:1 approximation:1 zero:1 kaiser:2 further:1 crystallography:1 theory:20 even:1 section:3 thickness:1 wolff:2 above:4 new:3 method:1 slabs:3 coefficient:2 simultaneously:1 degree:1 respectively:1 never:1 here:2 atoms:1 mev:2 groups:1 represented:1 path:2 strong:1 appears:1 change:1 deduced:1 obtained:1 search:1 institute:1 shift:5 vectors:2 usually:2 makes:1 involves:4 ratios:1 explained:2 regeneration:3 highly:1 neutrons:2 unitary:1 logically:1 total:3 univ:1 research:1 unit:4 use:2 would:5 give:1 negative:2 discrepancies:1 few:1 nucl:1 ψn:1 therefore:3 taken:4 more:3 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quant-ph9605026.txt |@word unavoidable:1 consider:4 chain:1 induces:2 truncated:1 results:5 leads:1 concept:1 entropy:1 advice:1 computation:19 go:2 follow:2 whose:3 c0:2 terms:2 pointing:1 aug:1 alamos:7 description:3 deterministic:1 tr:1 factoring:1 charles:4 finally:1 hardness:1 th:4 skip:1 kwong:3 subtleties:1 activities:1 supported:1 string:2 advantage:2 orthogonal:3 very:8 tends:1 hard:1 embark:1 wishes:6 hewlett:1 trouble:1 exact:2 condition:1 rotating:1 school:1 obvious:1 did:1 induction:3 notes:3 tre:2 sketch:1 replaced:1 correct:1 leave:1 discrete:1 fourier:1 small:3 eigenvalues:1 granting:1 optics:1 round:13 smaller:1 grateful:1 deutsch:1 dealing:1 maximization:1 direct:1 literature:2 matrices:7 zero:4 cost:1 further:3 implemented:2 machines:2 theory:5 even:5 will:22 what:5 abc:3 sheng:1 richard:2 cast:1 giving:1 section:3 remain:1 current:3 lights:1 version:2 above:5 capital:2 shared:3 firms:1 john:1 equivalent:2 satisfy:1 evolving:1 full:2 bangalore:1 respectively:5 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quant-ph9605027.txt |@word concept:2 consider:9 remarkable:1 ciao:3 magnetic:7 particular:2 illustrated:2 scalar:2 commute:2 comments:2 consists:1 contributions:1 simon:1 depend:1 finally:1 stable:16 breach:1 te:1 p2:9 straightforward:1 orthogonal:1 far:1 frequencies:1 rise:2 geometrical:2 experimentally:3 difference:1 exact:1 condition:3 school:1 vibrational:2 hamiltonian:11 solution:5 contexts:3 vector:3 small:3 eigenvalues:1 optics:1 originally:1 tel:2 among:1 measurable:1 approximation:7 go:2 imply:1 pass:1 rigorous:1 further:3 chem:2 scientific:1 even:3 ramachandran:1 appear:1 sum:1 expressed:1 experiment:2 new:2 edited:2 evolving:2 full:1 degree:2 ansatz:1 path:5 along:2 appears:1 change:5 larger:1 allows:1 exiting:1 products:1 bhandari:1 published:1 complicated:1 birefringent:2 controled:1 jackiw:2 composed:1 see:3 projection:1 replace:1 total:1 unit:1 conventional:2 takes:3 would:5 massar:2 probabilities:1 contains:2 charge:4 hilbert:1 ψj:6 ψi:47 therefore:3 taken:2 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quant-ph9605028.txt |@word sci:2 results:13 leads:1 roy:1 scalar:2 complication:1 messy:1 expressions:3 leung:1 ac03:1 paris:1 subjected:1 equivalence:2 young:3 present:1 th:1 under:2 nodes:1 presentation:1 case:3 straightforward:2 wave:13 exact:2 condition:4 irreducible:1 solution:1 solved:2 demonstrated:2 science:2 originally:1 wronskian:3 compensated:1 sukhatme:2 approximation:1 second:1 plet:2 spectral:1 appear:1 sun:1 sum:1 expressed:3 find:1 henceforth:1 above:2 increasing:1 method:7 satisfy:1 full:1 ibid:1 eksp:2 reported:1 clns:1 berkeley:2 equations:1 logarithmic:1 obtained:6 division:1 nth:1 shift:4 california:1 conveniently:1 suitable:1 studies:1 via:1 useful:2 9a:1 requiring:1 9b:1 summation:1 apply:3 use:1 asymptotic:1 would:1 chi:1 negative:2 few:1 going:2 chu:3 a29:1 sternheimer:2 theoretical:1 diagrams:1 more:4 zh:3 becomes:2 particular:1 known:1 cardinality:1 logarithm:2 states:6 effectively:1 recall:1 equation:1 work:3 reproduce:1 growing:1 example:2 proof:1 f0:6 f1:6 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quant-ph9605029.txt |@word consider:2 rev:5 brownian:19 results:3 kc0:4 mazur:1 calculate:4 ac02:1 technique:2 environment:3 th:3 under:2 subtleties:1 case:7 straightforward:1 ρj0:4 wave:17 every:1 experimentally:1 exact:1 hamiltonian:7 solution:3 damped:1 large:2 small:1 ρj:4 zj:2 direct:1 approximation:3 zero:2 further:1 chem:2 auspices:1 even:2 rate:2 sun:2 section:1 agrees:1 experiment:2 above:1 3c:1 3b:1 method:1 3d:1 2kt:2 full:1 sinh:2 address:1 path:1 logarithmic:1 obtained:1 studied:5 completely:1 narrow:1 studies:1 followed:1 convolution:1 replace:1 visible:1 addressed:1 decrease:1 apply:2 linearly:1 plot:3 use:4 takes:1 would:1 next:1 process:1 therefore:3 until:1 more:2 introducing:1 sessions:1 becomes:6 visibility:2 known:4 evolves:2 equation:2 work:2 oscillator:10 mj:5 values:1 following:4 example:2 stimulating:1 figure:7 give:1 calculation:4 neglected:2 minimum:3 performed:1 sense:1 provide:1 clarke:1 write:1 how:4 pure:1 ordinary:1 explains:1 sin:5 simplicity:1 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quant-ph9605030.txt |@word secondly:1 comparatively:1 desirable:1 idealised:1 entropy:9 consists:3 localized:1 whose:4 eligible:5 contained:1 aut:1 under:5 divergent:1 every:2 experimentally:1 suffices:1 vector:3 markov:1 consistent:1 direct:1 approximation:8 second:4 rigorous:1 even:4 established:1 christ:1 incompatible:1 specification:7 pragmatism:1 reconstruction:1 new:2 increasing:1 consisting:1 simultaneously:1 notions:2 never:1 here:22 asymmetry:1 represented:1 path:4 interpret:1 obtained:2 rigorously:1 naturel:1 leaves:1 controversy:2 natures:1 fourier:14 spacetime:44 criticism:3 appropriately:1 yamada:1 classification:1 explained:3 highly:1 univ:1 linearly:2 would:2 bundles:3 axioms:4 call:7 therefore:3 type:3 separated:1 naive:2 curvature:1 must:8 join:2 theories:14 concepts:4 example:16 renormalization:10 relativistic:5 organized:1 want:5 absolute:10 end:1 provide:3 far:2 nontrivial:1 description:1 after:4 inessential:2 law:4 meaningful:1 constants:1 effective:2 complexity:1 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quant-ph9605031.txt |@word code:26 saturating:1 caused:1 rob:1 results:1 four:10 roy:1 commute:2 computation:15 cameron:1 contributions:1 repetition:1 aug:1 combinatorial:1 knill:1 subjected:1 show:2 containing:1 environment:4 finally:2 under:2 suffered:1 insights:1 presentation:11 applied:3 amplitudes:1 presently:1 returning:2 very:3 choice:1 every:2 entries:1 affect:1 emphasized:1 matrices:4 entire:1 presented:3 knight:2 list:2 solution:1 correct:4 large:2 undone:2 succession:1 small:1 eigenvalues:3 shows:1 prevent:1 zn:1 zi:10 past:2 rate:1 initialized:1 estimated:1 targets:1 eigenspaces:6 even:4 established:2 errors:16 xor:6 witnessed:1 kantor:1 above:4 designing:1 new:2 schumacher:2 margolus:1 justification:1 simultaneously:3 degree:1 teleportation:1 composed:2 reported:3 plenio:2 others:1 represented:2 z0:1 appears:1 change:4 z3:2 obtained:4 derivable:1 suitably:1 shift:1 popescu:1 completely:5 eigenspace:1 products:3 permutation:2 tolerantly:4 hamming:1 suitable:1 makes:1 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quant-ph9605034.txt |@word logarithms:1 measurements:1 partial:1 consider:4 excellent:1 results:1 four:1 scalar:1 proposition:5 generalize:2 montr:4 computation:6 c2:2 go:1 follow:1 denotes:2 gj:1 whose:1 technique:2 factoring:2 recurrence:2 finally:5 monotonically:1 tk:1 th:5 under:1 norm:1 u2:2 random:2 amplitudes:1 straightforward:3 very:3 rise:1 choice:1 worst:2 decide:2 entries:1 bringing:1 høyer:1 obvious:2 solution:18 occurs:2 large:6 solved:3 2r2:5 recall:3 small:9 ups:2 programme:1 upper:3 zn:2 smaller:2 grateful:1 deutsch:2 sin2:12 mβ:1 4u:1 approximation:2 consists:1 second:2 cost:1 query:6 further:1 estimated:1 quite:1 goes:1 even:4 what:3 richard:1 giving:1 section:3 celebrated:1 uniform:1 henceforth:1 3n:4 above:3 new:3 christiansen:1 method:1 full:1 flip:1 never:2 lem:1 gilles:3 bi:1 behaviour:2 desired:2 cos2:1 ℓ2m:1 observing:1 appears:2 obtained:3 search:1 ahead:3 shift:2 inspired:1 reminiscent:2 allows:5 odense:3 leaving:1 resulting:2 fourier:5 makes:1 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quant-ph9605035.txt |@word logarithms:1 epeau:1 consider:3 results:1 proposition:1 montr:2 computation:9 forget:1 whose:1 concerned:1 nonlocal:3 environment:2 finally:2 those:1 whatsoever:1 under:1 apparatus:1 supported:1 confidential:2 very:5 rl:1 matrices:1 disturb:1 went:1 transmission:3 louis:1 xyz:1 prototypes:1 random:3 discrete:1 circuitry:1 recall:3 small:2 optics:2 ville:1 deutsch:1 feasibility:2 likely:1 cost:1 implemented:1 machines:1 linear:1 even:4 what:1 xor:2 business:1 richard:3 version:1 above:1 new:2 public:1 exercise:1 leeuwen:1 simultaneously:1 reliably:1 teleportation:28 gilles:7 represented:2 strong:1 obtained:3 luther:1 shift:1 leaves:1 allows:4 leaving:1 prior:1 amount:1 usually:1 bob:13 makes:3 genuinely:1 via:1 regardless:1 explained:1 outcomes:1 unitary:3 factoring:1 apply:1 circumvent:1 jan:1 use:1 takes:2 working:1 pedagogical:1 next:1 comparing:1 therefore:2 memory:4 mysterious:1 today:1 more:3 outputs:2 particular:2 known:2 foundations:2 easiest:1 must:1 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quant-ph9605037.txt |@word represent:3 concept:2 semantic:1 consider:6 incorporate:2 davies:1 results:6 synonymously:2 leads:1 baby:1 einf:1 proposition:15 generalize:2 houches:2 foundations:7 follow:1 expressions:1 zinn:1 reasoning:10 inferences:1 restrictions:1 preserves:4 depend:2 essentials:1 equivalence:4 tr:7 contained:3 former:3 environment:1 critical:2 tk:4 grabowski:2 under:2 tf:2 norm:1 case:3 belonging:3 kent:4 orthogonal:2 reader:1 focus:1 isomorphism:4 every:27 summarized:1 emphasized:1 matrices:1 condition:9 school:3 induced:5 level:1 altering:1 suffices:1 notes:3 classical:1 t2:7 solution:1 t0:9 t1:13 hartle:12 admissible:18 vector:1 guiding:1 science:1 entropy:1 refer:3 unsharp:1 der:1 programme:2 htn:2 consistent:37 htk:2 measurable:1 literature:1 imply:3 infimum:1 equal:5 further:9 copenhagen:1 uhrung:1 linear:3 spectral:1 aim:1 what:3 ct0:15 appear:2 apparatus:1 fine:1 section:5 graduiertenkolleg:1 expressed:6 consistently:1 sequential:1 above:13 values:2 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quant-ph9605038.txt |@word partial:12 consider:2 remarkable:2 rev:9 results:3 scalar:2 entropy:8 computation:1 compact:2 pb2:2 subjected:1 tr:9 nonlocal:1 finally:3 does:2 those:1 under:1 at2:1 norm:1 case:5 conjecture:3 departament:1 t12:2 very:2 mν:2 putting:1 matrices:4 condition:23 dim:1 presented:1 tra:1 trb:1 t2:13 deals:1 convenience:1 vector:1 trp:1 trv:1 effective:1 says:2 deutsch:1 second:4 further:1 λcp:5 established:2 stands:1 pawel:1 above:6 new:2 satisfy:1 notions:1 respectively:4 teleportation:1 here:8 ryszard:1 others:1 represented:2 strong:1 respect:1 appears:2 obtained:2 michal:1 technical:1 allows:2 contradiction:1 p2:3 schumacher:1 t21:2 t22:2 formulated:1 useful:2 fµ:2 family:1 first:5 apply:1 operational:2 univ:1 theory:2 use:4 projector:2 would:1 prove:4 positive:51 negative:1 definition:2 classically:2 noting:1 call:1 m3:2 m2:3 e2:4 theoretical:2 more:3 hahn:2 operators:12 holt:1 odinger:2 appendix:3 virtue:2 particular:4 known:1 cases:5 kraus:1 isomorphism:1 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