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quant-ph9706020.txt |@word represent:1 consider:7 ali:1 results:2 existing:2 computation:1 edu:1 consists:1 errors:1 contributions:1 whose:1 depend:1 calculate:2 alamos:4 subjected:1 tr:1 environment:11 under:4 include:1 far:1 choice:1 exact:3 condition:4 al1:2 hamiltonian:7 knight:1 guo:3 applicable:2 d2:1 trs:1 trr:1 direct:1 approximation:1 second:3 nonlinear:1 plays:1 stands:1 gk:8 section:1 expressed:2 above:4 designing:1 satisfy:1 respectively:3 designed:1 equals:1 here:6 paz:1 plenio:1 china:3 τ1a:2 2kb:3 relaxation:4 change:1 great:1 involved:1 study:4 completely:1 suggests:4 published:1 suitable:1 spatially:6 apply:1 total:2 use:3 feb:1 working:1 remains:1 comparing:3 ψi:7 therefore:3 memory:1 type:3 more:5 treated:1 becomes:1 operators:3 site:1 berlin:1 normalized:1 particular:1 cases:1 hold:1 circumstances:5 high:1 springer:1 science:3 equation:1 modified:1 london:2 ρs:6 obvious:1 following:4 strategies:2 example:3 indicated:1 process:1 bennett:1 ψrs:9 states:6 indicates:3 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quant-ph9706021.txt |@word remarkable:1 rev:3 magnetic:1 results:3 leads:2 computation:2 consists:2 expressions:1 localized:1 whose:1 inverse:1 depend:1 description:1 γt:5 environment:16 anupam:1 those:1 stochastic:30 include:2 case:8 advantage:1 very:2 frequencies:3 rise:2 conditions:1 valued:1 2γt:2 difference:2 exact:1 condition:4 notations:1 hamiltonian:24 trc:1 solution:4 t1:4 math:2 indices:1 eigenvalues:1 optics:1 grateful:1 10b:2 10a:1 approximation:19 zero:8 correlator:1 rigorous:1 qualitatively:1 dynamics:9 volovich:2 canonical:1 spectral:14 established:2 what:1 appear:2 brackets:1 section:4 expressed:3 d3:1 version:2 ito:5 new:6 d1:1 method:5 satisfy:3 respectively:2 here:4 friedrichs:1 relaxation:1 consideration:1 table:2 deduced:1 obtained:3 institute:2 shift:3 inspired:1 vectors:6 allows:1 completely:1 survey:1 published:1 usually:1 resonance:3 studies:1 explained:1 unitarity:2 remnant:1 apply:2 total:1 tn:4 use:2 remains:1 positive:2 hudson:1 therefore:2 volterra:3 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quant-ph9706022.txt |@word represent:2 consider:2 limited:2 induces:1 focus:2 four:4 postponing:1 computation:7 contributions:1 alamos:2 technique:6 finally:1 program:1 device:1 those:2 caused:1 sent:1 ta:1 division:1 supported:1 straightforward:2 shifters:7 implicitly:1 wave:5 experimentally:1 difference:1 matrices:2 arrange:1 splitter:20 exits:2 presented:2 issue:1 cascading:1 large:2 convenience:2 vector:2 small:5 optics:5 upper:5 deutsch:1 translating:1 likely:1 dynamics:3 implemented:1 port:4 what:1 nonlinear:1 stands:3 apparatus:1 near:1 decoding:1 experiment:2 new:1 method:3 contrast:1 thin:1 submitted:1 ibid:2 respectively:1 error:1 component:2 teleportation:10 here:6 represented:3 path:10 observing:1 obtained:5 incoming:1 institute:1 involved:3 leaves:2 allows:1 exiting:1 suggests:1 resulting:2 action:1 unwanted:1 birefringent:1 composed:1 equivalence:1 useful:2 extra:1 requiring:1 explained:1 logical:1 outcomes:1 hadamard:14 singlephoton:2 use:8 reflected:3 would:1 prove:1 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quant-ph9706023.txt |@word represent:1 interpretation:1 consider:1 show:2 over:1 sources:1 iida:2 including:1 find:1 impact:1 sinθ:2 shifts:1 inclusion:1 spread:2 under:1 contrary:1 cosθ:2 h0:2 resolved:1 motivated:1 zagreb:1 very:1 evaluate:1 between:1 2rc:1 possible:1 introduce:1 geometrical:5 prog:1 new:1 noncontractible:2 immediately:1 boˇskovi:1 now:2 discuss:1 condition:1 resolve:1 particle:2 hamiltonian:3 fully:1 collective:1 arxiv:1 summary:1 croatia:1 mead:4 found:1 difficult:1 optics:1 valid:1 upper:1 because:1 khanna:1 energy:1 sin2:1 see:1 frequency:1 pφ:4 rc2:3 measurement:1 quantum:8 our:2 patch:1 eq:1 linear:1 even:1 phases:1 scale:2 inequalities:1 space:2 pattern:1 nuovo:2 measurements:1 rev:1 re:1 correctly:1 rc:13 evidently:1 formula:2 approach:1 consisting:1 terms:1 theory:1 proc:1 rlc:3 effect:8 explore:1 hypothesis:1 cos2:2 although:1 2m:1 represented:1 analyses:1 bz:1 box:1 derivation:1 institute:1 could:2 studied:1 parts:1 o:3 quantization:1 compatible:1 length:6 resulting:1 berry:7 introduced:1 cancellation:2 relation:2 first:1 diameter:1 soc:1 symmetry:1 bell:1 ca:1 within:1 three:1 semiclassical:1 pole:1 references:1 operator:1 estimate:1 aharonov:1 broadening:6 takes:1 imagine:1 indeterminate:2 system:5 tiny:1 assumption:1 treat:1 ph:1 hardly:1 theoretical:1 gives:2 suggested:1 corresponding:2 complete:1 successful:1 some:1 operators:2 jun:1 observe:1 elimination:1 foundations:1 line:5 level:2 present:1 he:2 p2:1 rotational:1 applying:1 rα:2 unlike:1 pacs:1 characteristic:1 cimento:2 us:3 theories:1 other:1 dφ:1 near:1 future:1 suppose:1 following:3 problem:1 define:1 example:1 mechanics:6 uncertainty:2 degenerate:1 give:1 almost:1 refs:1 measure:1 spectrum:6 ann:1 equal:1 states:5 sphere:1 single:1 palle:3 want:1 formalism:4 internal:2 physical:2 qα:2 nonvanishing:1 cm:2 qβ:2 no:1 when:1 point:1 note:1 field:1 nuclear:2 potential:1 quant:1 take:1 analogy:1 department:1 place:2 roy:1 conclusion:1 heisenberg:2 briefly:1 material:1 algebra:4 any:2 corrected:1 miscellaneous:1 collection:1 dpφ:4 levels:1 moving:1 necessity:1 phase:6 without:1 lower:1 task:1 consequences:1 assume:1 broadened:4 lines:1 theor:1 su:1 cosmology:1 bohm:1 insurmountable:1 bracket:1 principle:1 fundamental:5 mechanical:1 sc:1 quadratic:2 typical:1 physics:4 order:1 fact:1 dh0:4
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quant-ph9706024.txt |@word represent:2 concept:2 partial:3 consider:28 chain:1 varying:1 truncated:1 results:1 existing:1 leads:5 roy:1 quadrature:4 entropy:3 reinhold:1 consists:1 gn:38 expressions:1 excluded:1 gk:2 row:1 devoted:1 content:7 inverse:5 superpositions:1 paris:7 γp:4 orthonormalized:2 γu:4 kgl:1 does:3 squeezing:40 manifolds:1 th:13 under:6 details:1 analogous:1 hints:1 mehta:2 eliminate:1 p2:1 fax:1 infinite:2 provides:1 advantage:5 orthogonal:1 very:11 multi:1 choice:3 every:2 reordering:1 dispersions:1 zm:2 inequivalent:1 associated:1 difference:1 matrices:3 fan:1 dimensionality:2 smithey:4 exponential:1 level:2 did:5 knight:4 t2:3 scalar:2 t0:6 plotting:1 large:4 discrete:4 convenience:2 vector:4 minimal:1 splitted:1 regularizations:3 eigenvalues:4 regard:1 optics:7 equation:24 degeneracy:1 upper:1 zn:1 wronskian:2 tel:1 specially:1 completely:1 measurable:3 hillery:1 sign:1 approximation:3 second:5 progress:1 further:3 cat:1 odd:8 4x2:1 substitute:1 canonical:24 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quant-ph9706025.txt |@word stressed:1 consider:1 rev:6 results:1 four:1 scalar:2 grateful:1 follow:1 manfredi:3 whose:1 depend:1 calculate:1 pˆk:2 pˆl:1 anharmonic:1 orthogonal:1 very:2 lyapunov:1 ymh:15 mixing:1 matrices:4 hamiltonian:6 large:1 abµ:1 work:1 zero:5 dynamics:1 odd:4 theory:4 spectral:3 will:2 nonlinear:2 plays:1 sub:8 section:2 uniform:1 aaν:1 new:1 increasing:7 acknowledgments:1 nakamura:1 satisfy:2 degree:2 respectively:1 spacing:2 here:1 behaviour:4 q12:5 brambilla:1 equations:1 obtained:2 great:1 study:6 studied:3 periodic:1 poisson:7 published:1 makes:1 plotted:1 via:2 spatially:4 seligman:2 plot:3 use:4 positive:1 negative:1 next:1 classically:2 nucl:1 therefore:1 qcd:1 until:1 possible:2 more:1 separated:1 introducing:1 clearly:1 becomes:1 operators:1 curvature:10 berlin:1 particular:4 known:1 springer:1 science:1 equation:2 fµν:2 zirnbauer:1 theories:4 values:3 three:1 following:1 spontaneous:1 stimulating:1 initial:1 nearest:3 compare:1 figure:6 give:2 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quant-ph9706026.txt |@word represent:1 suny:1 crucial:1 dynamic:3 splitting:1 existing:2 four:4 maid:1 computation:4 consists:1 4e2:1 adjustment:2 millisecond:1 semiconductor:2 amplification:1 depend:2 violate:1 1µm:1 show:1 presents:1 charge:12 critical:4 present:1 under:1 analogous:1 include:2 applied:3 amplitudes:4 returned:1 advantage:3 very:4 rise:2 differently:1 induce:1 resistance:1 blockade:2 electron:6 herr:1 affect:2 difference:9 matrices:1 condition:7 squids:1 entire:1 jensen:1 exponential:3 level:17 positions:1 proposals:4 solution:1 large:8 solved:1 convenience:1 frequency:2 science:4 small:17 3b:1 c02:1 configurations:3 limitations:2 smaller:4 compensated:3 deutsch:1 miller:1 grover:1 estimates:1 direct:1 pulse:3 past:1 surrounding:1 rate:6 invention:1 design:6 arnold:1 go:1 realistic:2 chen:1 qualitatively:2 dynamics:26 implemented:2 zs:1 even:3 will:2 what:1 d2:1 dephasing:1 uniform:1 current:4 version:1 above:3 lifshitz:1 3c:1 new:4 3a:1 ground:4 ever:1 journal:1 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quant-ph9706027.txt |@word limited:1 concept:1 partial:7 consider:2 chain:1 caused:6 amplifies:1 founded:1 restated:1 consists:1 homomorphism:1 preserves:1 depend:7 calculate:1 longstanding:1 tr:34 braginsky:1 environment:1 uniqueness:1 grabowski:1 xta:1 under:3 norm:2 ta:73 case:9 supported:1 straightforward:1 every:3 summarized:1 ρe:6 condition:5 nonselective:17 school:1 tra:17 supports:1 notes:3 discrete:4 convenience:1 vector:4 eigenvalues:3 ueda:1 optics:2 concluded:2 lecture:2 second:9 concludes:3 rigorous:1 further:3 dynamics:1 substitute:1 linear:14 even:3 established:1 what:3 plays:1 stands:1 apparatus:39 section:4 m31:1 current:1 annals:1 above:17 sup:2 new:10 method:1 coefficient:1 focuses:1 notions:1 respectively:1 selective:1 represented:3 along:1 appears:1 change:25 obtained:3 remark:1 reason:1 usually:2 changes:1 involves:1 uniquely:5 formulated:1 projection:23 family:4 explained:2 association:1 plenum:1 outcomes:1 analyzing:1 logically:1 apply:2 operational:19 univ:1 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quant-ph9706028.txt |@word represent:1 casimirs:1 grobe:1 consider:4 rev:10 polish:1 scalar:1 generalize:2 disk:1 naukova:1 compact:1 depend:1 subjected:2 noncompact:2 passage:2 finally:1 squeezing:9 those:1 th:3 under:3 must:1 worth:2 kν:9 r12:1 orthogonal:2 far:1 2re:1 choice:2 every:1 hµν:3 difference:2 condition:2 2rp:1 irreducible:2 solution:1 standards:1 large:1 discrete:1 irreducibly:2 variances:1 indices:1 hνµ:2 warszawa:1 optics:2 noted:1 zn:5 zi:2 2k3:1 direct:2 literature:2 second:2 odd:6 zq:1 canonical:1 even:8 index:2 dr1:2 sum:2 expressed:1 above:8 overcomplete:10 new:3 satisfy:1 edited:1 simultaneously:1 here:9 hkj:1 desired:1 hkl:3 represented:2 luis:1 strong:1 equations:2 z1:7 z2:3 obtained:8 ekl:3 institute:1 studied:7 suggests:1 accomplished:1 drn:2 action:2 suitable:1 family:5 vij:2 summation:1 redefining:1 total:1 establish:2 denotes:2 unit:1 takes:1 prove:1 positive:2 contains:1 negative:4 properties:5 a51:2 a50:1 a53:1 noting:2 a54:1 ψl:1 robertson:3 zil:1 zij:6 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quant-ph9706029.txt |@word iǫ2:3 consider:4 12s2:1 lagrangian:2 varying:1 dynamic:1 results:2 types:1 expressions:4 research:1 whose:2 calculate:3 equivalence:1 canonical:2 presents:2 company:1 aus:1 squeezing:1 present:1 stable:2 worth:1 case:12 far:2 frequencies:2 2re:2 sons:1 difference:2 notations:1 presented:4 solution:14 solved:2 convenience:1 eigenvalues:1 refer:1 der:2 wronskian:2 force:1 carter:1 bo:1 foundation:1 sin2:2 direct:1 second:19 further:1 dynamics:2 theory:2 aim:1 nonlinear:11 plays:1 sub:1 brackets:2 section:5 resume:1 expressed:6 above:1 overcomplete:1 new:2 3a:3 waveguide:16 method:12 satisfy:1 full:1 lee:2 degree:3 respectively:5 here:6 cos2:1 sinh:5 represented:1 consideration:1 equations:27 implicit:1 obtained:4 great:1 institute:1 studied:2 products:1 poisson:2 published:2 hamiltoˆ:1 involves:1 zǫ:1 namely:1 substitution:8 replace:1 apply:4 establish:2 linearly:1 use:2 waveguides:4 prove:1 probabilities:1 etc:1 next:2 few:1 noting:1 therefore:2 taken:2 type:2 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quant-ph9706030.txt |@word measurements:1 consider:4 chain:1 rev:5 magnetic:2 focus:1 gg:1 grateful:1 foundations:1 follow:1 ψ1b:3 reasoning:1 inferences:1 gr:1 whose:2 inverse:2 depend:1 calculate:1 tp:1 does:2 th:2 meister:1 analogous:2 characterised:4 case:8 labels:1 provides:1 orthogonal:3 far:1 rise:1 geometrical:3 lynch:1 strand:1 generalised:4 squares:2 hamiltonian:2 forth:1 t2:1 solution:2 large:1 vector:11 ml:1 small:2 configurations:2 consistent:1 direct:1 understanding:1 surrounding:1 second:5 street:2 ψ1a:8 incidentally:1 dynamics:2 remarkably:1 canonical:5 index:3 what:4 essence:1 appear:1 specification:1 axes:1 near:1 expressed:5 concisely:1 issues:1 above:4 lifshitz:2 international:1 consisting:1 coefficient:1 edited:1 led:2 exchange:1 dcb:1 component:1 here:5 analysed:1 ranges:1 address:2 represented:1 consideration:3 along:5 equations:1 change:1 obtained:2 study:3 vectors:5 controversy:2 resulting:1 changes:3 appropriately:1 formulated:1 inference:1 projection:1 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quant-ph9706031.txt |@word represent:1 todays:1 consider:8 rev:18 magnetic:1 global:1 results:8 leads:7 quadrature:3 gc:16 lewenstein:3 go:1 follow:3 gm:2 gl:19 γz:5 γy:8 γx:10 referring:2 preprint:1 presents:2 finally:2 squeezing:17 γn:1 γm:2 under:1 kλ:4 analogous:4 include:1 indicating:1 detect:1 2γn:1 nσ:1 amplitudes:1 g1:1 far:4 frequencies:4 rise:6 springer:1 engineered:3 wave:4 probability:1 p1:1 sidebands:5 resonant:2 exact:2 four:28 level:79 transmission:1 positions:5 erratum:1 solution:3 large:3 vector:2 microlaser:1 eigenvalues:3 markov:1 optics:2 still:1 upper:20 miller:1 ωag:1 direct:1 sign:1 approximation:5 dalton:1 rate:12 realistic:1 dynamics:10 quite:1 theory:3 spectral:1 employ:1 nonlinear:1 lindblad:1 stands:1 section:5 selected:1 dephasing:3 expressed:1 version:1 above:1 utkenhaus:1 new:2 gl2:8 increasing:1 equivalent:1 filled:1 coefficient:2 edited:1 full:7 κk:4 newyork:1 respectively:6 ficek:1 component:2 here:4 atoms:8 reported:1 identifications:1 replacements:1 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quant-ph9706032.txt |@word consider:2 rev:4 global:3 results:1 four:2 eds:1 entropy:3 computation:1 whose:1 preserves:1 γs:1 tt:23 tr:26 γt:27 uniqueness:1 preserved:2 under:2 proved:1 advantage:1 kraus:1 very:1 pascazio:1 wave:1 comm:2 putting:1 entries:1 experimentally:1 little:1 matrices:7 condition:6 hamiltonian:2 turns:1 notes:2 solution:1 large:1 vector:1 small:2 eigenvalues:6 equation:2 maiani:2 consistent:1 estimates:1 request:1 sign:1 zero:1 further:3 dynamics:7 theory:1 adds:1 appear:1 apparatus:1 sum:1 remain:1 above:2 new:3 increasing:1 evolving:1 full:2 respectively:1 never:2 alicki:1 mod:2 obtained:2 antisymmetric:1 parameters:6 technical:1 study:4 vectors:2 commonly:1 b389:1 situations:1 action:6 verri:1 conveniently:1 meson:1 planck:2 unit:1 would:3 remains:1 positive:33 negative:17 properties:1 nucl:4 call:1 therefore:8 fonda:1 taken:2 survive:1 means:1 type:1 vj:9 more:3 duality:1 thus:2 operators:6 tested:1 berlin:2 eλ:6 particular:1 factories:1 must:2 high:1 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quant-ph9706034.txt |@word limited:1 now:7 arrives:1 sch:4 remarkable:2 similarity:1 depends:1 magnetic:6 global:1 results:16 existing:1 leads:2 eds:5 overlap:1 during:1 go:1 follow:2 consider:7 griffin:1 depend:1 calculate:2 zeh:1 29b:1 baym:1 29a:1 environment:1 quasi:3 mediated:1 helps:2 th:1 under:6 analogous:1 must:3 2u0:1 wether:1 proved:1 straightforward:2 outside:1 far:5 frequencies:3 sufficiently:3 ψk:2 induce:1 wave:5 esry:2 electron:1 maali:1 figs:4 summarized:1 resonant:2 tridiagonal:1 difference:14 exact:7 conserved:1 cool:1 tri:1 europhys:1 34a:1 34b:1 level:9 positions:1 solution:10 bohn:1 large:3 solved:3 differential:1 shenoy:1 burke:1 small:3 eigenvalues:1 referred:1 optics:11 der:2 degeneracy:1 andrews:4 employing:1 lewenstein:2 10b:1 dealing:1 10a:1 direct:1 approximation:20 second:15 growing:1 further:1 dynamics:1 cat:39 odd:1 substitute:1 linear:3 even:6 aim:2 nonlinear:7 developed:1 trapping:3 stoof:2 indicated:1 section:12 evaporative:3 joos:1 macroscopically:1 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quant-ph9706040.txt |@word represent:1 consider:2 similarity:1 rev:1 magnetic:2 global:1 results:9 invent:1 proposition:9 computation:4 follow:1 expressions:1 adjustment:3 compact:1 whose:1 preserves:1 inverse:1 tv:1 tq:2 tn:4 charge:5 those:1 γm:2 under:2 tg:1 worth:1 applied:1 rise:2 lecture:1 condition:2 dim:20 hamiltonian:10 irreducible:2 notes:1 t2:2 pullback:5 vector:23 indices:1 relation:1 div:3 haar:2 bψ:1 direct:2 ωab:4 second:2 canonical:11 what:1 plays:3 brackets:1 section:5 expressed:3 version:2 intersect:1 new:1 apply:1 method:3 coefficient:1 guillemin:3 choquet:1 here:3 reported:1 tangent:1 expansion:1 xν:1 consideration:1 appears:2 gaµ:1 obtained:1 remark:1 weinstein:3 technical:1 vectors:2 ignoring:1 suggests:1 symp:1 resulting:1 poisson:2 action:18 involves:1 uniquely:1 orthonormality:1 projection:10 claim:1 specifics:1 unitary:1 equivariant:5 sgn:1 pulls:1 total:1 univ:1 derivatives:1 use:1 covariant:8 positive:1 dnn:2 dni:8 ψt:5 dnj:1 morette:1 ψi:2 indiana:1 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quant-ph9706042.txt |@word represent:5 consider:5 limited:1 rev:21 desirable:1 results:3 illustrated:3 scalar:11 tξ1:1 computation:1 edu:1 consists:1 reynaud:1 inverse:1 calculate:2 re:1 tr:8 young:1 veb:1 berstein:1 under:2 tf:2 dramatically:1 orthogonal:1 very:2 edn:1 connects:1 wave:4 overcomes:1 difference:1 exact:1 condition:17 entire:1 tra:1 knight:2 trb:1 guo:2 large:1 trs:3 optics:3 mahler:9 smaller:1 says:1 deutsch:1 consistent:2 coefficient:7 direct:1 zero:4 deutscher:1 depression:1 canonical:3 subscripts:1 index:2 3y:1 nonlinear:2 plays:1 inputoutput:1 d2:4 section:5 expressed:4 experiment:1 above:3 shared:1 satisfy:2 evanescent:1 degree:1 respectively:4 gener:1 teleportation:1 here:1 believed:1 plenio:2 china:3 represented:1 ratio:1 strong:1 equations:1 box:2 spontaneous:1 larger:1 schumacher:1 domains:1 formation:2 proof:3 der:1 klyshko:2 explained:1 counts:1 total:4 derivatives:1 use:4 indicated:1 remains:3 give:1 next:1 linear:2 therefore:2 aperture:3 more:1 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quant-ph9706043.txt |@word secondly:1 concept:5 sci:1 consider:15 remarkable:1 priori:1 rev:12 φp2:22 theoretical:1 results:12 gy:2 existing:1 leads:5 received:1 philosopher:1 plays:1 c2:1 follow:1 expressions:2 ρˆp:6 looking:2 certainly:8 careful:1 depend:2 violate:1 albrecht:1 irrelevant:1 description:5 vattay:1 posteriori:1 environment:4 german:1 uniqueness:1 wants:1 those:8 th:10 stable:1 analogous:4 circumstances:1 worth:2 summarizes:1 case:12 incorporate:1 collapsing:1 tudor:1 very:2 rise:1 translations:1 springer:1 tacitly:1 wave:10 stat:1 every:1 ullman:1 lecture:1 telling:1 experimentally:2 emphasized:3 difference:4 exact:1 tri:1 notations:1 disturb:1 obvious:1 solves:2 presented:3 did:2 irreducible:1 notes:1 t0:4 occurs:1 leave:1 solved:1 zeh:2 small:2 eigenvalues:7 hospitality:1 optics:1 noted:1 degeneracy:2 favoured:1 strongly:1 approximately:1 mi:5 consistent:3 among:1 prediction:3 4p:2 past:8 grant:1 zero:6 fiber:1 annihilation:1 rigorous:1 further:2 dynamics:9 cat:3 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quant-ph9706044.txt |@word 2nπ:3 magnetic:7 global:1 results:2 leads:4 certainly:3 inverse:5 λn3:2 squeezing:1 those:1 analogous:1 case:10 orthogonal:3 induce:4 choice:2 nieto:1 matrices:1 condition:5 indicate:1 presented:1 turns:1 t2:1 solution:4 try:1 solved:3 vector:2 small:2 enforce:1 illustrating:1 direct:2 zero:2 value:1 pass:1 dynamics:1 functioning:1 will:11 sum:1 axes:2 uniform:1 aperiodic:1 international:1 method:1 simultaneously:2 spacing:2 here:1 rosas:1 behaviour:1 ramsey:1 possibility:1 directions:2 along:5 equations:3 implicit:1 obtained:3 study:3 vectors:1 sx:1 periodic:3 usually:1 resonance:6 makes:2 named:1 formulated:1 useful:1 projection:1 inducing:2 fig:1 ipn:1 editors:1 rχ:1 decrease:1 names:1 circumvent:1 unit:1 use:2 would:7 commun:1 eχ:3 going:1 taken:1 associated:1 rabitz:1 today:1 more:1 formally:1 oscar:1 odinger:1 curvature:1 rigid:1 particular:1 known:2 projective:2 cases:1 aligned:1 evolves:1 springer:1 deformed:1 equation:2 work:1 oscillator:1 zhao:1 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quant-ph9706045.txt |@word limited:2 secondly:1 obstruction:1 entropy:1 consists:4 saved:1 localized:2 whose:1 under:7 every:1 summarized:1 experimentally:1 school:1 solution:10 unrelated:1 math:5 heading:2 consistent:8 approximation:2 second:4 chem:1 selected:1 sheeted:1 above:11 new:6 ever:1 consisting:8 coefficient:2 never:6 here:16 asymmetry:1 mev:2 represented:10 path:36 obtained:8 suitably:1 study:1 stressed:1 suitable:2 settled:1 york:2 yamada:8 projection:3 slices:2 julia:1 total:1 propagators:2 linearly:1 reflected:1 would:3 negative:2 d54:1 therefore:21 m2:1 type:10 brings:1 odinger:3 hold:1 must:2 kumar:1 permits:1 pursue:1 work:4 concepts:1 mx:5 wang:1 give:3 relativistic:8 involve:1 degenerate:1 end:2 provide:1 feature:4 how:8 lundqvist:1 symposium:2 replacing:1 oscillators:4 after:4 analagous:3 summarize:3 law:1 types:3 attempt:3 effective:1 ρnn:2 ρeiθ:4 complexity:2 green:2 enter:3 order:16 operations:1 restriction:1 interpretation:5 over:28 satisfied:6 london:1 japan:1 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quant-ph9706046.txt |@word precise:1 axes:2 protocol:7 proposed:1 show:3 cheat:2 indeed:2 random:3 satisfied:4 four:1 including:1 computation:4 integer:1 existence:1 still:1 oblivious:1 qbc:5 perfect:1 symmetric:1 peres:1 signal:1 han:1 how:1 interesting:1 enough:1 young:1 should:1 only:4 ardehali:1 lett:9 compares:1 might:1 sent:3 non:1 his:2 greater:1 cryptography:1 means:1 mor:1 possible:2 investigated:1 obtain:1 sided:2 test:2 cannot:3 entangled:11 they:2 new:1 report:6 experimentally:1 bit:8 qkd:2 him:1 advanced:1 particle:1 presented:1 follows:1 university:1 arxiv:1 alice:15 try:2 fuchs:1 qc:3 europhys:1 chau:2 she:6 each:4 told:1 macchiavello:1 noted:2 concluded:1 parity:3 because:2 exists:1 supporting:1 sends:1 correlations:1 mail:2 proc:1 used:2 noise:1 value:1 pass:2 quantum:20 our:1 ieee:2 even:1 shown:4 multiparty:1 although:1 announces:1 performs:2 since:1 rev:10 quantph:1 particles:4 state:2 won:1 correctly:1 conjectured:1 biham:1 shared:1 ref:5 occurs:3 side:1 satisfy:1 core:1 sz:1 korea:3 recently:1 never:1 however:1 asymmetrical:3 mayers:2 asymmetry:1 them:3 york:1 key:1 news:1 along:1 deutsch:1 distribution:1 bz:1 both:4 pairs:3 griffiths:1 sanpera:1 applications:1 institute:1 certainty:1 besides:1 according:1 honest:3 creates:1 int:1 present:1 due:1 receives:2 insecurity:2 hence:1 symmetrical:1 bob:19 hwang:2 top:1 first:1 among:1 muller:1 tasks:2 secure:5 simple:1 powerful:1 commitment:4 outcomes:7 another:1 parties:1 impossible:5 bangalore:1 koh:1 given:1 cheating:1 los:4 probabilities:3 transfer:1 support:1 there:5 three:1 been:2 next:2 defined:1 much:1 popescu:1 therefore:1 way:1 ph:4 scheme:2 was:4 final:3 more:1 qsc:1 bennett:3 sending:2 jul:1 gyu:1 too:1 authors:1 known:2 taejon:1 maximally:8 spin:3 than:1 protocols:1 he:3 case:2 randomly:1 keeping:1 alamos:4 wiesner:1 science:1 work:1 nonmaximally:1 us:1 will:3 while:2 determined:1 crepeau:1 following:1 problem:2 outcome:12 could:1 gisin:2 mechanics:1 storing:2 ac:2 computers:1 processing:1 give:1 predict:1 measurement:5 thus:2 conjecture:2 states:10 say:1 itself:1 exist:3 conf:1 further:1 jozsa:1 technology:1 occur:4 axis:1 requirements:1 lo:3 mermin:1 no:7 make:1 tossing:14 invalid:4 tells:1 application:2 ideal:1 other:4 quant:4 build:1 department:2 party:5 coincide:1 zbinden:1 brassard:3 yeong:1 sure:3 users:3 may:1 kaist:1 insecure:1 published:2 systems:1 hand:2 most:2 important:1 prepares:1 end:2 coin:14 data:1 why:1 niu:1 prescribed:1 realized:1 implies:1 computations:1 consequently:1 clear:1 well:1 without:1 thought:1 kr:2 impossibility:1 ones:1 honestly:4 sigact:2 physics:2 ekert:3 fact:1 know:4
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quant-ph9706047.txt |@word limited:1 partial:2 consider:5 chinese:2 caused:1 dynamic:1 kanai:5 generalize:1 expressions:2 inverse:1 calculate:1 young:1 γt:10 finally:2 those:1 stochastic:2 applied:1 supported:1 straightforward:1 very:5 brownian:5 wave:28 sons:1 difference:1 exact:1 presented:1 solution:4 large:5 small:2 optics:1 force:2 renormalized:3 direct:6 approximation:3 second:4 dynamics:1 chem:1 canonical:6 even:1 nonlinear:1 appear:1 sun:5 version:1 above:3 overcomplete:1 new:2 method:4 chose:1 newyork:1 respectively:3 realizations:1 component:4 here:3 china:4 represented:3 along:1 coupling:11 equations:1 obtained:3 institute:2 shift:1 study:2 studied:1 approaches:1 action:12 resonance:1 modifying:2 total:9 conventional:1 prove:2 visit:1 quasi:1 hong:4 a51:2 calculation:1 therefore:1 vj:8 reflects:1 eiωj:3 introducing:1 formally:1 becomes:1 operators:8 odinger:2 varying:1 known:2 cases:3 evolves:2 account:1 defines:1 quantized:1 equation:2 work:1 oscillator:7 zhao:1 widths:1 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quant-ph9706048.txt |@word represent:2 consider:3 caused:1 magnetic:2 varying:1 results:1 four:1 gc:3 contributions:2 whose:1 certainly:2 inverse:1 zone:1 tr:2 behave:1 contours:3 under:4 worth:1 case:11 straightforward:1 far:1 springer:1 wave:54 naka:1 exact:7 condition:2 leads:1 level:2 transmission:8 turns:3 developing:1 solution:13 large:1 solved:2 section:1 3b:1 der:1 upper:1 measurable:1 sign:2 second:7 evaluated:1 estimated:1 bold:2 even:8 dissertation:1 froissart:1 stands:1 sum:2 poles:6 above:7 supplies:1 3a:1 contrast:1 satisfy:2 outgoing:1 respectively:3 component:1 here:1 okubo:1 following:1 others:1 represented:5 consideration:1 along:5 strong:1 equations:3 appears:1 change:1 obtained:5 waseda:2 incoming:1 shift:2 larger:1 completely:4 fourier:1 makes:1 composed:1 via:1 spatially:1 2δp:2 ipx:2 total:2 use:1 asymptotic:14 would:5 remains:2 positive:4 give:5 negative:6 iq:7 depicted:1 program:1 therefore:3 m3:1 endowed:1 taken:1 survive:1 more:2 separated:1 definition:1 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quant-ph9706049.txt |@word code:2 consider:2 probl:3 entropy:11 kato:1 calculate:1 technique:1 tr:1 presents:1 g4:1 g2:1 g1:1 orthogonal:6 very:2 sons:2 encounter:1 visualized:1 presented:1 transmission:1 posts:1 solution:1 large:3 eigenvalues:3 upr:1 upper:2 maximization:4 rate:9 will:3 sub:1 uniform:1 version:5 above:5 sup:1 international:1 neq:1 satisfy:1 here:6 represented:1 study:1 larger:1 schumacher:3 useful:2 apply:2 conventional:6 probabilities:2 optimize:1 ψj:1 a53:1 ψi:3 a54:2 more:1 introducing:1 becomes:1 operators:3 tamagawa:1 known:1 cases:1 account:2 word:1 tokyo:1 ρi:2 equation:1 remain:1 ρr:1 westmoreland:1 following:2 trans:2 root:3 example:3 compare:1 figure:4 give:4 calculation:1 states:10 sense:1 information:12 needs:1 provide:2 how:1 enr:1 pure:4 priori:10 tried:1 may:1 max:6 wiley:2 derived:1 fa:1 burnashev:1 natural:2 effective:1 sr:6 davies:2 order:4 typical:2 pointed:1 symbols:2 paper:3 mentioned:1 existence:1 ieee:2 its:1 massey:1 derive:1 group:1 sξ:6 ln:15 condition:2 them:1 greater:1 fig:11 they:1 finite:2 university:1 ensemble:3 2e:1 2f:4 inequality:1 transmitted:1 found:7 inserts:1 osaki:4 square:3 connect:1 measurement:5 quantum:47 our:1 eq:5 special:1 out:1 shown:3 matrix:7 space:1 rev:4 holevo:10 research:2 formula:1 shows:1 theory:15 clarify:2 estimate:1 jozsa:1 r0:1 ministry:1 length:1 hence:1 teor:1 first:4 features:1 probability:11 coding:6 directly:1 given:6 introduction:1 eqs:2 eqr:1 system:3 relations:1 scheme:4 gives:1 exactly:1 part:1 july:1 than:2 john:1 showed:1 fuchs:2 second:4 future:1 were:1 distinguished:1 published:2 rewrite:1 any:1 zero:3 lim:1 take:1 so:5 channel:12 play:2 shall:1 systems:3 most:1 coded:2 average:3 sometimes:1 cover:1 exp:2 fact:2 thomas:1 show:4 random:2 discovered:1 relation:1 find:2 based:4 state:4 should:1 only:2 surveyed:1 achieve:1 means:2 cannot:2 words:2 arxiv:1 schemes:1 gram:4 ban:4 set:2 ary:6 detection:4 result:5 japan:1 optimum:3 capacity:8 µr:1 symmetric:1 enough:2 αe:1 between:1 recently:3 nature:1 attention:1 however:1 jon:1 received:1 many:1 taking:1 conclusions:1 according:1 figures:2 com:1 simple:1 wootters:1 corresponds:2 respect:6 telecommunications:1 ps:7 addition:3 much:1 treat:1 pe:6 ph:3 define:4 corresponding:1 photon:2 gap:1 c1:8 those:1 case:8 solid:1 reliable:1 value:3 employ:1 while:1 optimization:2 replaced:1 error:6 property:2 procedure:1 almost:2 von:12 thus:1 non:1 equal:3 examined:1 binary:4 make:1 same:4 quant:3 several:4 difficult:2 used:1 numerical:6 mutual:2 hand:1 purpose:1 gallager:12 off:8 center:1 well:1 eps:7 λj:1 stratonovich:3 cut:8 density:1 momose:1 signals:7 source:2 other:1 theorem:9 input:2 gave:1 opt:1 psk:4 additivity:1 mod:1 necessary:3 like:1 sk3:1 sk2:1 follows:6 signal:18 communications:1 output:1 essential:1 because:2 neumann:12 classical:2 sequence:1 some:5 examples:6 minimax:1 per:1 does:1 2en:1 ξr:1 power:2 super:1 properties:3 comparison:3 extension:1 theorems:1 o:5 covariant:1 introduced:1 communication:6 into:3 bound:3 en:2 references:1 operator:2 next:3 a51:1 there:1 way:2 kurokawa:2 was:4 function:31 jun:1 line:2 true:2 maximum:6 us:6 un:2 problem:1 called:1 detailed:1 pij:1 proved:3 defined:3 abstract:1 general:1 peres:1 engineering:1 reliability:31 file:7 laboratory:1 inf:3 formalism:1 sasaki:3 inc:2 functions:3 compared:1 no:1 dashed:1 when:2 application:1 valid:1 role:2 shannon:4 ns:7 αei:1 symbol:2 problems:3 ξi:4 important:3 bounded:1 assume:2 ternary:5 hirota:5 4f:4
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quant-ph9706050.txt |@word represent:1 concept:2 remarkable:1 secondly:1 gz:4 leads:2 eds:1 mile:1 broader:1 stochastically:1 remarkably:1 gh:1 rmki:1 depend:1 chain:1 4ns:1 fellowship:2 equivalence:2 tr:1 presents:1 under:1 stochastic:59 norm:1 supported:1 advantage:1 percival:3 coloured:4 electron:2 redefinition:1 exact:6 condition:1 osi:4 hamiltonian:1 knight:1 solution:1 vector:3 markov:6 optics:4 der:1 configurations:1 concluded:1 force:4 strunz:3 za:6 approximation:8 zero:3 further:1 dynamics:3 expressions:1 theory:4 aim:1 nonlinear:1 adds:1 advantageous:1 trivial:1 expressed:1 current:1 version:2 ˆi:2 method:1 ρt:1 satisfy:1 realizations:1 here:1 δza:2 believed:1 plenio:1 2kb:1 represented:1 path:8 equations:2 appears:1 change:1 box:1 institute:1 vectors:4 allows:3 matacz:1 suggests:1 published:2 action:2 mz:6 changes:1 pearle:1 via:1 merwe:1 iz:1 total:10 establish:2 propagators:2 linearly:1 ψz:15 environment:13 use:2 takes:2 would:1 prove:1 next:1 few:1 memory:5 taken:2 ψa:11 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quant-ph9706054.txt |@word consider:4 results:2 gy:2 leads:1 shimony:2 follow:1 displaying:1 particles:2 certainly:2 calculate:3 finally:1 otv:1 th:3 under:1 analogous:1 include:1 case:6 very:1 wave:1 pression:1 condition:1 four:1 gov:2 obvious:1 turns:1 occurs:1 try:4 item:4 indices:1 eigenvalues:1 inserting:1 past:1 imply:3 displays:1 rigorous:1 further:1 dynamics:1 what:4 circumstance:1 expressed:1 experiment:1 above:9 new:5 learned:1 d1:9 multitude:1 edited:1 simultaneously:4 respectively:6 applies:1 here:2 change:4 violate:1 obtained:1 institute:1 items:1 larger:1 contradiction:3 hospitality:1 dyad:1 suitable:3 changes:1 uniquely:7 via:1 mea:1 extra:4 logical:1 hardy:4 logically:1 apply:2 unit:3 readily:1 use:1 would:2 ψr:2 positive:2 predictions:1 few:1 call:1 therefore:4 m2:18 taken:1 themselves:1 type:1 more:3 formally:1 becomes:3 operators:2 odinger:2 everywhere:1 normalized:2 particular:2 account:1 recall:1 equation:2 work:2 mi:4 mk:1 mj:10 reproduce:1 values:1 following:3 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quant-ph9706055.txt |@word spherical:1 manifold:1 phenomenon:1 spectral:1 obtain:1 leads:1 scalar:4 spaces:4 through:1 looks:1 c2:3 4rµν:1 expressions:1 d2:2 its:2 d0:3 consider:1 compact:1 calculate:1 parameters:1 field:6 ln:9 hab:2 perturb:1 gab:2 forms:1 source:1 only:2 harmonics:1 versa:1 extensive:1 main:1 kaluza:1 rµνρσ:2 divergent:3 dm:1 rαβ:2 taα:2 klein:1 means:2 df:1 greiner:1 combination:3 introduce:1 results:2 aα:1 vα:3 vβ:1 should:1 background:1 vacuum:10 press:1 integer:1 emphasized:1 tbd:2 formal:1 finite:2 dowker:1 2k:1 fields:13 university:2 arxiv:1 invariants:1 ηab:3 2z:4 harmonically:1 specific:1 vector:2 follows:3 2l:1 eigenvalues:4 2n:8 works:1 out:1 hαβ:1 constraints:1 spinor:3 set:1 compensated:2 computed:2 counterterms:1 series:1 energy:9 some:1 birmingham:1 olp:5 calculated:1 second:1 weinberg:1 radius:1 value:2 quantum:4 invariant:1 odd:2 kinetic:1 subject:1 even:2 vol:1 throughout:1 tensor:12 space:12 electromagnetic:1 rep:1 rev:1 expressed:1 research:1 symmetric:2 arbitrary:1 state:1 poles:2 tαβ:10 αi:2 rm:7 d1:2 evaluation:2 grangian:1 terms:2 theory:4 degree:1 respectively:1 irkutsk:1 contain:1 however:1 expansion:2 lichnerowicz:1 det:3 convolutions:1 demonstrate:1 vtn:3 dubna:1 appears:1 mod:1 topology:1 r4:2 degeneracies:1 ref:3 r1:2 r2:3 geometry:1 toms:1 according:1 traceless:1 place:1 ltf:1 casimir:2 corrections:1 contribution:2 introduced:1 expression:2 relation:1 yαβ:3 muller:1 initial:1 presence:1 lims:1 birrell:1 compare:1 contributions:1 latter:1 dimensional:10 references:1 operator:2 cp:2 rµν:2 sen:1 contractions:1 vef:1 given:3 takes:1 degenerations:2 contains:1 they:1 negative:2 been:1 properties:1 int:1 nucl:2 manifolds:1 therefore:2 jinr:1 robertson:2 ph:1 was:2 theoretical:1 ensured:1 function:3 obtained:1 rαβγδ:2 corresponding:1 tµν:1 form:1 comparison:1 becomes:1 jun:1 curvature:3 gravitational:2 part:2 external:3 known:1 projective:1 representing:1 analogous:1 present:1 reflection:1 case:2 made:1 coefficients:2 evident:1 regularized:1 anomaly:1 equation:2 work:1 appearance:1 zero:1 evaluated:1 euclidean:2 determined:2 values:4 were:2 following:1 fluctuations:1 di:1 rbd:1 conformal:1 russia:1 loop:4 candelas:1 va:1 rad:1 ab:3 give:1 defined:3 abstract:1 argument:2 ann:1 general:1 tad:1 sphere:3 performed:1 tab:2 turns:1 yα:2 curved:3 orthogonal:1 property:1 metric:2 absolute:1 regularization:1 plunien:1 us:1 rβγ:1 whereas:1 acts:1 davies:1 hβγ:1 instance:1 nontrivial:3 potential:5 quant:1 la2:1 bogolubov:1 department:1 additional:1 massless:3 massive:1 simplicity:1 used:1 may:2 ξr:1 object:1 effect:1 hγβ:1 sc:1 hγα:1 due:1 coming:1 cambridge:2 representations:2 evaluations:1 chang:1 expand:1 λ2i:1 constructed:2 coupling:1 effective:4 vice:1 considered:1 underlies:1 sp:1 well:1 d27:1 tα:1 peculiarities:1 without:1 so:7 principle:1 components:1 time:1 walker:2 representation:1 model:1 physics:1 order:1 fact:1 quantity:1
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quant-ph9706056.txt |@word ali:1 lagrangian:5 forbidden:1 global:3 blanchard:1 results:4 scalar:1 whose:2 equivalence:1 timedependent:1 alberta:2 case:3 wave:2 every:1 exact:10 condition:1 solution:11 eigenvalues:1 direct:1 integrability:1 further:1 dynamics:5 linear:1 spectral:2 what:1 expressed:1 method:1 satisfy:2 q1:2 lee:2 degree:1 respectively:1 growing:1 address:1 equations:3 institute:2 study:1 p2:3 action:1 studies:1 br:1 family:1 namely:1 imaginary:1 select:1 use:2 would:3 distinct:1 classically:1 therefore:1 theoretical:1 ψe:9 operators:3 odinger:8 berlin:2 normalized:2 separates:1 known:6 springer:2 science:1 equation:14 oscillator:10 theories:1 mv:3 following:1 example:1 states:2 indicates:1 verlag:2 needs:1 rather:1 discussion:1 parameter:1 circular:2 riesenfeld:2 seoul:1 may:1 oscillators:13 after:1 dx2:1 applications:1 demonstrating:1 fl:1 ω2e:4 outline:1 order:4 se:2 pointed:1 its:1 le:4 interesting:1 lai:1 coordinates:1 mail:1 non:1 outlined:1 introduce:1 they:1 easily:3 university:2 2m:5 side:1 differential:1 another:3 formulate:1 energy:1 reduce:1 idea:1 frequency:6 obtains:1 quantum:5 eq:4 special:1 out:1 canada:1 shown:3 rev:2 denotes:1 investigation:1 ref:2 math:2 theory:3 enforcing:1 standard:3 difficulty:1 could:1 motion:3 hence:1 generalizations:1 features:1 variables:1 timeindependent:1 done:1 directly:1 precisely:1 given:1 similarly:1 system:1 construct:1 variational:3 liang:1 relationship:1 exactly:1 because:1 authors:1 x2:4 july:1 coefficients:1 dynamical:6 uning:1 unfortunately:1 second:1 contrary:1 generality:1 constrained:1 apparently:1 clearly:1 viewed:1 able:1 note:2 sciences:1 subjects:1 generalized:1 switching:1 play:3 most:1 claims:1 class:2 interacting:1 observation:3 implications:1 physics:2 fact:1 show:4 lewis:2 solutions:8 d2:1 ualberta:1 q2:1 knowledge:1 integrable:1 hamiltonians:2 local:1 do:2 means:1 dependent:18 ko:1 remedy:1 dx:8 dt:1 gen:1 prime:1 arxiv:1 yield:4 snutp:1 view:3 requirement:1 national:1 see:1 college:1 recently:1 awaits:1 phases:1 eigenfunctions:2 between:1 invariant:1 geometric:1 approach:2 korea:1 terms:1 however:1 jr:1 ji:4 multiplier:1 article:1 kirsten:1 region:1 hψ:1 uni:1 simple:1 ca:1 corresponds:1 dimensional:7 lagrange:1 hω0:1 arts:1 described:1 due:1 been:1 interest:1 basic:1 ph:3 define:1 corresponding:3 derivative:1 those:1 applied:1 euclidean:1 squeezed:2 identical:1 played:1 refs:2 ir:1 ugge:1 technology:1 same:1 parts:1 quant:3 higher:1 independent:1 used:2 trajectories:1 hand:1 driven:1 purpose:1 kim:5 normalization:1 schr:8 well:1 analysis:1 without:1 solve:1 position:2 being:1 edmonton:1 obtain:1 actions:1 identify:1 uller:1 preprint:2 vψ:1 character:1 potential:2 relevance:1 solvable:1 real:5 2j1:1 eigenvalue:13 harmonic:18 advanced:1 prominent:1 loss:1 appearing:1 performing:1 indication:1 arbitrary:1 become:1 δe:1 mathematical:1 right:1 methods:1 classical:13 some:2 choosing:1 demonstrates:1 integration:1 unit:2 turkey:1 june:1 equivalent:4 unusual:1 although:1 relating:1 about:1 central:2 constraint:3 practical:1 consequently:1 presence:1 h2:1 soh:1 functional:2 square:2 references:1 operator:1 utility:1 there:2 iq2:1 way:1 form:3 jun:1 construction:2 made:1 us:2 ωn:2 problem:12 ωe:1 mechanics:2 constant:1 certain:4 abstract:1 general:1 physical:1 again:1 functions:2 istanbul:1 no:2 mostafazadeh:1 reality:1 field:2 other:1 role:4 department:1 mathematics:1 conclusion:1 zhou:1 preceding:1 problems:2 includes:1 variable:2 mω0:1 t6g:1 algebraic:1 dψ:1 assume:1 mass:3 time:20
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quant-ph9706057.txt |@word secondly:1 concept:2 sci:1 consider:3 pairing:21 illustrated:1 cooperative:1 expressions:1 dimensionality:1 tw:1 quasi:2 c5:7 th:4 tc:1 applied:2 schrieffer:1 very:1 baton:1 exact:2 condition:2 treating:1 dim:1 hamiltonian:8 irreducible:1 solution:1 leave:1 small:1 eigenvalues:2 degeneracy:1 sign:1 approximation:2 zero:2 odd:1 even:1 what:1 giving:1 xρ:1 cheng:1 ˆj:1 increasing:1 method:2 satisfy:1 simultaneously:1 respectively:2 orbitals:1 behaviour:1 china:1 equations:2 study:1 products:1 studies:1 useful:1 summation:2 total:1 takes:1 finally:1 few:2 nucl:2 therefore:3 taken:1 type:1 becomes:1 operators:1 blocking:1 must:1 high:1 deformed:2 science:1 equation:1 following:4 example:2 numbers:3 chosen:1 xcj:1 allowed:1 suggestions:1 lombard:1 states:3 indicates:1 assumptions:1 sn2:1 bk1:3 sn1:1 yang:1 s0:5 feature:1 write:1 significance:1 cjj:3 product:1 mat:1 algebra:5 snn:1 applications:1 fd:1 wave:2 realized:1 sx:4 6th:3 sj:7 negligible:1 sn:5 sm:8 enter:1 representation:1 2sm:1 holds:1 ruckenstein:1 indeed:1 mainly:1 coll:1 through:1 differs:1 satisfies:2 its:1 blocked:1 rapidly:1 la:1 energies:1 affine:1 fig:2 clusters:1 yi:4 yk:1 diagonalize:1 nonorthogonal:1 effects:1 eigenvalue:1 always:1 university:2 traced:1 each:1 2m:1 weight:2 energy:9 measure:1 quantum:1 seniority:3 shown:2 dominates:1 kerman:1 matrix:1 restricted:1 furthermore:1 since:1 rev:6 particles:2 ajm:3 suffices:1 foundation:1 theory:2 pairs:2 interaction:4 determining:1 irrep:1 consequence:1 uses:1 first:4 xk:1 major:1 xi:8 xn:1 vacua:1 pines:2 number:8 long:1 rink:1 given:2 5th:3 system:1 relations:2 too:1 percentage:1 scheme:2 shell:12 draayer:1 x2:2 x1:3 than:2 coefficients:3 determined:5 dalian:1 ann:1 need:1 seen:1 occupied:1 clearly:1 lie:1 strength:2 k3:1 k2:4 k1:1 generalized:6 normal:1 pair:1 considered:1 ki:2 metal:1 kp:4 principle:1 typically:1 lying:1 show:1 supported:1 spaces:1 relation:1 solutions:3 rouge:1 feng:1 highest:1 parameters:1 state:4 only:3 bases:2 generators:1 intractable:1 notation:1 spurious:1 nonconservation:1 yielded:1 barranco:1 bardeen:1 arxiv:1 racah:2 analytical:1 fixed:1 coefficient:2 set:1 national:1 correlations:1 up:1 talmi:2 satisfying:2 commutation:1 written:2 difficulties:1 between:1 c2j:8 diagonalized:2 c2m:2 however:1 jm:4 jj:1 group:1 configuration:2 come:1 suggested:1 restrictions:1 successes:1 equal:2 etc:1 cj:15 ci:2 reasons:1 dimensional:2 simply:1 belyaev:2 cs:1 table:4 basis:1 due:1 been:3 quickly:1 int:1 treat:1 ph:1 louisiana:1 hernandez:1 corresponding:1 zeng:1 c3:7 c1:7 spin:1 those:1 case:7 pacs:1 ǫj:2 expanded:2 value:1 while:2 applies:1 unitary:1 non:1 duan:1 greater:1 orbital:1 different:3 hubbard:1 grant:1 recursion:1 same:2 any:3 complex:1 quant:1 pauli:3 largest:1 c7:1 defines:1 pan:1 difficult:1 numerical:1 randeria:1 driven:1 levels:6 liquids:1 infinite:2 positives:1 normalization:1 eigenvectors:2 well:2 eps:1 bohr:2 model:1 dimension:1 left:1 spherical:1 proposed:2 less:1 underlying:1 atomic:1 eigenstates:1 λm:1 lett:3 easy:1 c11:1 excited:1 real:2 fys:1 increases:1 vacuum:1 using:1 unique:1 particle:5 follows:3 schmitt:1 δn:1 arbitrary:1 nucleons:1 essential:1 because:3 methods:1 truncated:1 some:2 back:1 examples:1 diagonalizing:1 xn1:2 xn2:2 cooper:2 lead:1 agreement:1 expansion:2 negatives:1 simpler:1 integers:1 valence:1 introduced:3 slightly:1 xnn:1 conserving:1 shieh:1 down:1 liaoning:1 operator:1 shells:3 support:1 there:1 specifically:1 low:1 was:2 lowest:6 form:1 phenomena:2 differences:2 jun:1 level:1 truncation:1 made:1 instructive:1 verma:1 maximum:1 ωj:8 limit:1 problem:3 detailed:1 constant:1 defined:1 abstract:1 aj:2 proven:1 general:2 single:7 formalism:2 physical:1 ni:4 functions:2 no:3 whereas:1 when:3 application:1 other:1 mottelson:2 department:2 superconductivity:3 deriving:1 generated:1 important:1 nucleus:1 astronomy:1 acknowledgment:1 medd:1 physics:4 d22:1 orbit:1 serious:1 nuclei:5 bcs:3
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quant-ph9706062.txt |@word neighbors:1 represent:2 logarithms:1 allowed:6 consider:14 remarkable:1 skip:2 results:1 four:2 clear:1 computation:5 edu:2 go:9 follow:1 localized:3 row:3 whose:7 depend:2 superpositions:3 γs:1 concerned:1 technique:1 γt:2 tn:70 answered:1 edward:1 device:1 c5:1 excluded:3 under:2 nodes:68 kθ:3 ingredient:1 continues:1 supported:1 amplitudes:2 string:2 far:8 rise:6 connects:6 seemingly:1 choice:3 sons:1 every:2 figs:1 decide:1 entries:1 affect:3 papadimitriou:1 exact:6 condition:5 look:1 indicate:3 level:90 transmission:13 suffices:1 yˆn:2 list:2 solution:3 fewer:3 t1:3 try:3 solved:5 convenience:2 pba:13 pbc:2 science:1 small:9 eigenvalues:3 markov:5 lines:12 proof:1 lloyd:1 smaller:1 force:1 cooperative:1 zj:2 consistent:1 grover:3 sin2:5 discover:1 cosh:2 matrices:2 consists:1 zero:5 chopping:2 traveling:2 run:1 defines:1 ci1:5 odd:6 substitute:1 theory:1 even:15 index:1 what:4 sub:1 w5:1 xˆk:1 section:10 bc:1 expressed:1 current:1 paragraph:2 a52:1 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quant-ph9706063.txt |@word concept:1 consider:1 results:2 consists:1 follow:1 expressions:1 calculate:1 deterministic:2 finally:2 under:1 ontological:2 p2:1 amplitudes:1 string:11 straightforward:2 wave:16 electron:1 condition:2 dim:1 hamiltonian:2 proc:1 small:1 optics:1 oscillation:3 consistent:2 hillery:1 sign:1 approximation:1 discriminated:1 second:1 dynamics:1 even:4 section:1 expressed:3 above:1 new:1 net:1 exchange:1 respectively:1 never:1 wrapping:1 here:1 separation:1 eikx:4 represented:2 interpret:2 brilliant:1 study:1 studied:1 reports:1 usually:1 fourier:1 followed:1 brought:1 summation:1 total:1 use:3 prove:1 coupled:1 negative:1 calculation:1 call:1 therefore:2 reflects:1 more:1 duality:1 operators:2 odinger:5 clue:1 cases:1 must:1 me:1 word:1 equation:5 infinitesimal:10 following:4 averages:2 example:2 figure:1 process:2 relativistic:8 cited:1 accept:2 assumptions:1 o:2 how:1 ensemble:7 tried:1 derived:3 mapping:1 corrections:1 waves:5 geometrical:1 plank:2 constants:1 natural:1 remember:1 light:2 so:3 fundamental:1 representation:4 wigner:9 words:1 insight:1 satisfied:1 entity:4 paper:3 through:7 statistical:3 mentioned:1 kinetic:2 its:1 before:1 symmetry:4 chosen:1 relativity:2 coordinates:1 actually:2 forms:1 choose:3 might:1 non:8 presupposed:1 they:1 rotation:1 now:3 represents:1 february:1 name:3 university:1 mode:1 each:5 2m:4 characterized:1 mental:1 energy:7 hard:1 related:3 used:2 expect:2 quantum:14 special:2 description:1 ultimately:1 space:45 furthermore:2 since:6 particles:16 print:3 dxdp:2 theory:4 interactions:4 mapped:1 free:1 imagine:1 definition:5 interaction:7 could:1 motion:1 ordering:2 length:1 hence:3 first:1 separable:1 xn:11 probability:13 variables:1 number:4 directly:1 carry:1 law:1 antiparticles:1 introduction:1 system:13 relations:1 their:1 eqn:16 wrapped:1 tool:1 continuous:2 transverse:1 corresponded:3 translation:2 distance:1 zero:2 limiting:1 supposed:5 amplitude:14 were:1 distinguished:1 bridge:1 generality:1 any:5 relatively:1 genuine:1 newtonian:5 self:1 connell:1 isolated:1 instance:1 internal:14 attempted:1 though:3 rhs:1 object:12 propagate:1 phase:17 especially:2 considered:2 average:3 phil:1 definitely:1 electrons:2 principle:4 exp:1 velocity:3 kx:1 physics:4 came:1 relation:2 interpretation:1 find:2 explain:1 should:3 analytic:4 only:1 local:1 equilibrium:1 means:3 express:1 expectation:1 cannot:4 dx:16 interpreted:4 dp:1 arxiv:1 summary:2 experiments:1 ut:1 view:4 ignored:1 set:1 connections:1 wonder:1 interacting:1 review:2 propagates:1 szilard:1 between:1 propagated:1 nature:2 however:2 moyal:6 problem:3 exclusion:1 many:1 density:5 equal:1 etc:2 connection:1 became:1 berry:1 among:2 point:6 corresponds:1 pop:2 dimensional:10 scully:1 respect:1 described:1 addition:7 px:2 copies:1 been:2 pc:1 change:3 ph:4 abstract:1 define:5 direction:1 dimesional:1 propositions:1 subspace:4 understand:2 spin:1 former:2 those:6 case:3 conception:1 value:1 eik:1 slc:1 ix:5 uncertainty:1 vg:1 phenomenological:1 thus:4 them:1 characterize:1 itself:1 disappear:1 confirmed:2 same:2 complex:18 quant:4 pauli:1 independent:2 investigated:1 infinity:2 effect:3 hand:2 kim:2 pδx:1 infinite:3 schr:5 without:2 coordinate:13 model:4 chemistry:1 left:1 proposed:1 being:1 abbreviation:1 using:5 regardless:1 macroscopic:3 yet:1 integer:1 conclusions:1 except:1 thermodynamics:1 potential:1 choice:1 versa:1 theorem:1 transformation:8 momentum:13 real:13 loss:1 couple:1 utah:1 possible:3 know:1 vacuum:20 world:4 like:3 skeptical:1 necessary:1 δx:6 particle:13 alternatively:1 specific:1 mathematical:1 because:4 classical:13 people:1 some:2 oscillations:4 conventionally:1 scale:1 dimensions:1 electromagnetic:2 unavoidable:1 integration:1 closely:1 conventional:1 substituted:1 although:1 imaginary:8 ontology:1 properties:1 about:1 pλ:4 recognized:1 nothing:1 connected:2 soc:1 cambridge:1 functional:1 variable:1 appropriate:1 right:1 references:1 operator:4 proportional:1 statistics:6 assumed:2 there:4 long:1 way:2 was:10 function:20 complete:2 form:1 phenomena:6 jun:1 but:6 made:2 characteristic:4 up:1 us:2 liouville:1 distribution:6 pm:10 mechanics:11 constant:2 defined:5 universal:1 describe:3 general:1 multiparticle:1 pˆ:7 formalism:4 archive:3 physical:27 again:2 no:4 when:3 detail:1 reality:1 other:2 department:1 mathematics:1 out:1 superposition:1 photon:1 searched:1 meaning:4 a2:1 included:2 vice:1 assume:1 kinetics:1 rule:2 mass:2 fact:1 time:3 starting:1 strings:1 once:4
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