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quant-ph9711021.txt |@word code:1 consider:3 rev:5 dynamic:1 results:2 computation:2 whose:1 preserves:1 knill:1 technique:1 presents:1 th:4 under:1 analogous:1 include:1 p2:2 straightforward:1 wave:1 p1:2 subsystems:2 hamiltonian:5 occurs:2 noiseless:1 discrete:8 convenience:1 small:3 chuang:1 equation:3 work:1 ρl:2 second:1 compensates:1 qmn:6 dynamics:6 what:4 nonlinear:4 rate:4 feedback:1 brief:1 version:1 above:6 new:3 boost:1 method:4 slotine:1 here:4 modular:4 others:1 box:1 convert:1 institute:1 popescu:1 allows:4 leaving:2 accomplished:3 resulting:2 loop:1 permutation:1 scales:3 inducing:1 apply:5 ipx:4 unit:2 alamitos:1 environment:2 use:2 takes:2 codewords:3 distinct:2 laflamme:3 comparing:4 going:1 call:1 taken:1 theoretical:1 more:1 composite:3 operators:5 corrected:4 occurred:4 reversible:1 particular:3 foundations:1 hold:1 easiest:1 must:1 science:5 originally:1 mn:3 modified:1 nine:4 following:4 spontaneous:1 example:5 numbers:2 compare:1 process:1 bennett:3 states:11 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quant-ph9711022.txt |@word secondly:1 consider:5 rev:2 results:3 leads:3 eds:2 expressions:3 depend:3 calculate:4 iii:1 nonlocal:6 spirit:1 tj:4 present:1 ti:5 indicating:1 applied:1 amplitudes:7 straightforward:1 implicitly:1 choice:18 corollary:1 every:1 decide:1 difference:1 condition:2 splitter:10 morley:1 presented:1 did:1 progress:1 metaphysics:1 optics:1 equation:4 upper:1 rohrlich:1 measurable:3 imply:2 value:9 further:3 even:3 appear:2 anton:1 sum:8 expressed:1 consistently:1 experiment:28 new:3 increasing:1 inertial:4 movement:2 coefficient:3 led:1 notions:2 channeled:1 respectively:1 realizations:1 agreement:1 cos2:1 represented:1 path:5 change:1 box:1 institute:1 involved:1 inspired:1 timings:1 leaving:2 resulting:2 suggestion:1 makes:9 involves:2 figure:1 forbid:1 polarizers:2 private:1 outcomes:4 herzog:1 formulates:1 counts:1 total:3 establish:1 scarani:2 takes:1 would:13 probabilities:22 chooses:2 eσ:1 therefore:6 expanding:1 means:1 entails:1 today:1 more:2 separated:7 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quant-ph9711027.txt |@word concept:2 partial:1 rev:1 focus:1 roy:1 commute:4 gl:1 inverse:1 concerned:1 equivalence:1 quasi:10 present:1 include:1 straightforward:1 far:4 seemingly:1 wave:1 matrices:4 dim:2 accompanying:1 solution:1 try:1 vector:1 trw:2 keiji:1 estimates:1 second:2 plays:1 stands:1 apparatus:6 section:4 new:2 fujiwara:1 equals:1 here:4 sld:6 along:5 logarithmic:2 differential:2 obtained:2 remark:1 allows:1 simultaneous:1 changes:1 private:1 kobayashi:1 conventional:2 asymptotic:1 would:1 sake:1 positive:4 negative:2 vol:2 theoretical:1 more:1 introducing:1 becomes:1 operators:2 curvature:1 eθ:3 particular:1 known:1 foundations:1 hold:1 must:1 me:1 tokyo:2 equation:3 infinitesimal:1 following:4 root:1 example:1 proof:3 indicated:1 process:1 expanding:1 states:4 unbiased:4 assumptions:1 sense:1 conversely:1 information:4 holds:2 estimator:4 pure:1 significance:1 optimal:2 parameter:6 simplicity:2 4tr:1 wiley:1 minimum:1 confirmed:1 plane:1 coming:1 horizontal:4 choice:1 data:4 parallel:8 natural:4 imply:1 element:1 so:7 representation:2 order:2 interpretation:2 hiroshi:1 over:3 move:1 lsj:19 satisfied:1 lsi:21 matsumoto:1 lst:6 experiments:1 through:1 statistical:4 during:1 japan:1 satisfies:2 its:4 before:1 derive:1 thank:1 fij:8 derivative:2 easier:1 non:2 evolution:1 introduce:1 they:2 nov:1 now:1 bigger:1 eigenvalue:1 term:3 several:1 equality:4 hereafter:1 always:1 university:1 hermitian:8 iff:8 inequality:1 side:1 characterized:1 mean:1 subset:1 holonomy:2 energy:1 related:1 parallelity:5 measurement:4 quantum:24 our:1 operation:1 matrix:13 space:6 rep:2 helstrom:3 holevo:1 denoted:1 rm:2 get:1 ref:4 math:4 fiber:2 theory:19 free:1 mapping:1 approaches:1 york:2 estimate:5 dimm:2 definition:2 geometry:2 counterpart:2 δij:1 hence:2 first:2 indebted:1 major:1 xi:1 probability:3 omitted:1 omission:1 done:1 clarity:1 aharonov:1 manuscript:1 given:3 necessarily:1 surement:1 introduction:1 unknown:2 system:2 john:1 stinespring:1 continuous:1 part:2 anandan:1 uhlmann:14 detection:1 holland:1 cyclic:1 zero:2 classes:2 f12:1 treated:2 argument:1 generalization:1 say:1 need:1 any:19 symmetrized:1 lie:1 min:1 efficient:1 note:1 sciences:1 generalized:1 analogy:2 accuracy:1 trace:1 though:1 trρ:1 arena:1 definitions:1 pair:1 acknowledgements:1 probabilistic:1 why:1 consequences:1 calculated:1 adopt:1 points:1 analogically:1 mechanical:1 physics:1 implying:2 carefully:1 inspiring:1 knowledge:1 writes:2 only:1 factor:2 attained:1 local:1 his:1 viewpoint:1 means:1 dependent:1 expectation:1 words:1 dw:3 dt:6 dr:2 produced:1 processes:1 arxiv:1 paper:4 queries:1 london:1 set:1 notational:1 relative:2 see:7 geometrically:2 w0:3 discussions:2 close:2 best:1 closer:1 fails:1 said:4 definite:2 jts:1 state:1 closed:3 between:4 theta:1 conditions:5 a392:1 terms:1 statistically:1 however:2 vanishing:3 key:1 jk:1 distinguish:1 both:2 reverse:2 equal:1 connection:2 berry:2 estimation:27 point:2 corresponds:2 whatever:1 coincidence:1 nomizu:1 rpf:12 respect:2 throughout:2 pr:1 pp:6 described:1 addition:1 skew:1 locally:9 three:1 change:1 ph:1 algebras:1 pn:3 terminologies:1 corresponding:2 25a:1 covariance:2 lift:3 spin:2 θt:7 case:5 subsets:1 harder:1 value:3 optimization:1 error:1 unbiasedness:1 loop:5 unitary:2 played:1 almost:1 refs:3 thus:2 ii:1 characterize:2 ij:1 vanish:3 different:1 fibers:1 same:1 quant:1 finite:1 yung:1 independent:1 used:2 hand:2 purpose:1 identity:3 lower:4 well:1 obviously:1 academic:1 model:10 left:1 just:1 being:2 obtain:1 reviewed:2 press:1 ozawa:1 λk:1 λi:1 previous:1 letting:3 akio:1 density:5 conclude:1 except:1 belongs:1 lett:3 theorem:7 real:1 aspects:1 checking:1 possible:1 know:1 vθ:3 using:1 helpful:1 like:1 reduces:1 adiabatic:1 works:1 quantal:1 mathematical:1 because:4 classical:17 some:1 back:2 transport:4 provides:1 proc:2 measuring:3 equivalent:1 bi:3 bj:1 hilbert:2 about:1 theorems:2 o:2 misleading:1 mixed:1 introduced:3 soc:2 communication:1 bound:6 phase:5 appropriate:1 square:1 references:1 estimators:1 amsterdam:1 statistics:1 θt1:4 θt0:4 assumed:2 strictly:2 long:1 nagaoka:3 dispersion:1 way:1 function:3 north:1 form:1 but:1 russian:1 attainable:3 line:1 true:6 he:1 up:1 us:1 called:5 eigenvector:1 proved:1 defined:5 certain:1 abstract:1 measure:2 am:2 engineering:1 dθ:8 distributions:1 metric:1 physical:1 functions:1 no:1 when:4 vanishes:7 tight:2 other:2 role:2 department:1 tie:2 briefly:1 uniformly:1 bundle:2 important:2 fisher:2 structure:1 independently:1 implies:3 geometrical:3 factors:1 curve:3 dρ:1 parallelism:1 observables:1 starting:1 original:1 virtue:1
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quant-ph9711028.txt |@word ibid:1 exponentiation:1 rev:7 results:2 leads:2 eds:1 commute:1 consists:1 follow:1 gm:3 contributions:1 calculate:1 uniqueness:1 squeezing:3 th:7 divergent:1 division:1 ured:1 g0:1 putting:1 affect:1 nieto:2 difference:4 matrices:5 condition:7 solves:1 irreducible:2 nagel:3 solution:8 large:1 solved:1 vector:2 truax:1 indices:4 eigenvalues:1 refer:1 optics:2 upper:1 slower:1 hillery:3 cosh:1 fold:1 zero:2 further:1 implemented:2 odd:3 expressions:1 canonical:1 even:6 giving:1 section:2 expressed:5 above:5 new:3 increasing:2 method:1 coefficient:3 confluent:1 degree:2 respectively:1 here:4 b2m:1 ansatz:1 sinh:1 equations:2 differential:1 obtained:2 institute:1 study:2 studied:1 leaving:1 suitable:2 orthonormality:2 family:1 9n:1 hermite:2 explained:1 analyzing:1 apply:1 linearly:1 use:2 takes:1 would:2 positive:6 next:1 comparing:1 bases:1 m0:1 iℓ:1 taken:1 robertson:3 type:3 theoretical:2 possible:5 more:3 operators:9 odinger:3 correspondingly:1 normalized:5 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quant-ph9711037.txt |@word consider:1 rev:5 results:1 leads:1 houches:1 follow:2 expressions:1 reasoning:1 particles:1 certainly:1 catastrophe:3 ıa:2 finally:1 does:2 γn:11 th:2 breach:1 proved:1 orthogonal:1 very:16 rise:3 wave:16 stays:1 trouble:1 bringing:1 condition:6 entire:1 unlike:1 hamiltonian:4 turns:1 solution:5 large:6 admissible:1 math:1 small:11 eigenvalues:1 accumulation:1 work:1 neighborhood:1 approximation:1 located:2 rate:4 rigorous:1 situated:2 nonuniform:1 what:3 opaque:1 trivial:1 section:9 poles:6 lifshitz:1 new:2 net:1 increasing:1 method:6 contrast:1 satisfy:2 edited:1 κn:1 ibid:1 respectively:2 equals:1 here:2 reported:1 olica:1 free:1 address:1 represented:1 obtained:1 instituto:2 delimited:1 study:2 studied:1 muenster:1 chemical:1 action:2 see:2 although:4 assertion:1 addressed:1 clockwise:2 select:1 use:1 takes:1 would:2 commun:1 positive:4 whittaker:1 give:3 next:1 comparing:1 ψn:7 therefore:9 usp:1 flaw:1 hermitean:1 becomes:2 corrected:1 odinger:8 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quant-ph9711038.txt |@word concept:1 consider:3 commute:1 edu:1 gn:1 whose:1 compose:2 εp:1 equivalence:1 must:1 pathria:1 marks:1 eβ:3 degeneration:1 sorkin:3 case:4 g5:2 implicitly:1 wave:5 probability:1 should:1 difference:1 bringing:1 deformations:1 condition:3 hamiltonian:1 convenience:1 vector:1 eigenvalues:1 configurations:1 ze:2 approximation:1 rate:1 displays:1 odd:2 eigenspaces:1 canonical:2 even:2 nonlinear:1 sun:2 sum:2 expressed:1 d3:1 ˆa:1 above:5 fractional:2 new:7 ˆj:1 ˆn:1 satisfy:2 edited:1 exchange:9 here:1 believed:1 china:1 represented:1 laughlin:1 november:1 change:2 obtained:1 my:1 study:2 larger:1 experience:1 eigenequation:1 p2:1 products:1 permutation:5 emerge:1 via:3 useful:3 projection:1 qˆ:66 marked:2 decrease:1 summation:2 total:3 unit:3 would:1 commun:1 probabilities:1 negative:1 intense:1 ψk:4 linear:1 ψi:7 call:1 associated:1 type:2 reflects:1 more:5 solitons:1 operators:2 under:1 correspondingly:1 nkt:1 hole:1 fermionic:1 high:1 none:2 deformed:1 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quant-ph9711043.txt |@word 1st:1 logarithms:1 concept:1 consider:9 results:2 existing:2 leads:5 circuitry:1 computation:5 consists:2 amplified:1 seemed:1 adjust:1 whose:2 preserves:2 simon:3 calculate:1 disposal:1 technique:3 ts:39 factoring:1 presents:3 finally:1 helps:1 th:1 under:1 include:1 norm:1 adapt:1 alternating:1 func2:1 memorandum:2 amplitudes:8 string:1 advantage:2 orthogonal:2 very:1 choice:2 print:6 ical:1 entries:1 difference:1 matrices:1 rn:1 condition:1 entire:2 presented:8 solution:5 fewer:1 large:1 item:1 vector:11 small:3 enhance:1 boyer:1 smaller:1 occurrence:1 deutsch:1 olds:1 approximation:1 go:7 zero:5 design:6 evaluated:1 substituting:1 dynamics:1 estimated:5 machines:1 what:2 xor:2 power:2 iterating:1 28th:1 section:19 selected:1 near:1 rithm:1 experiment:4 above:12 scientists:2 3c:1 polylogarithmic:3 consisting:2 margolus:1 full:1 simultaneously:1 a400:1 component:2 lem:1 diagonal:2 desired:5 explore:1 selective:5 represented:5 consideration:1 wait:1 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quant-ph9711050.txt |@word partial:1 consider:5 roc:1 results:1 eds:2 proposition:4 comments:1 expressions:1 viceversa:1 λij:3 depend:1 tr:2 finally:3 behave:1 kλ:2 stochastic:11 analogous:1 include:1 orthogonal:2 very:2 2re:1 springer:2 choice:1 every:4 resonant:1 matrices:2 condition:2 trh:4 level:6 turns:3 notes:1 trf:2 large:4 anelastic:1 annihilates:1 small:1 optics:3 zj:3 consistent:1 direct:2 literature:1 approximation:3 surrounding:1 zero:3 value:1 dynamics:1 canonical:1 appear:1 section:17 ito:1 expresses:1 outgoing:3 full:4 exchange:1 respectively:1 component:1 diagonalises:1 atoms:2 behaviour:2 free:1 directions:1 along:1 strong:1 alicki:1 change:2 obtained:6 remark:1 barchielli:4 incoming:1 parameters:1 shift:4 study:1 vectors:1 allows:2 eberly:1 resulting:1 resonance:3 studi:1 via:1 projection:1 classification:1 extra:1 contrarily:1 limt:1 names:1 total:4 unit:1 use:2 asymptotic:2 would:3 commun:1 intense:1 positive:1 hudson:5 semigroups:3 therefore:4 taken:3 type:2 more:3 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quant-ph9711051.txt |@word concept:2 partial:1 consider:7 rev:3 results:1 existing:1 scalar:2 abelian:1 computation:1 inverse:1 quadruple:1 finally:2 exit:1 norm:1 p2:19 straightforward:1 orthogonal:1 very:1 springer:3 choice:1 every:1 lecture:1 difference:1 convexity:1 school:1 presented:3 notes:1 convenience:1 vector:6 small:2 λi2:1 meccanica:1 noted:1 zi:2 approximation:1 rigorous:3 dynamics:1 implemented:1 haag:2 theory:12 spectral:2 what:1 plays:1 stands:1 invertible:1 xσ:1 sum:1 expressed:2 above:2 consisting:1 respectively:3 here:4 understanding:1 modular:1 represented:2 respect:1 obtained:2 remark:1 institute:1 study:1 vectors:3 contradiction:1 products:2 hospitality:1 uniquely:2 family:2 explained:1 addressed:1 rσ:1 univ:1 causal:1 use:3 projector:1 would:3 prove:1 positive:5 contains:4 nagoya:2 properties:1 selfdual:1 m1:10 therefore:4 m2:10 taken:1 scope:1 theoretical:1 more:4 linden:1 main:1 composite:8 operators:6 berlin:1 carrying:1 normalized:1 particular:4 states:39 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quant-ph9711055.txt |@word monte:2 wigner:17 proposed:4 show:1 characterisation:1 probe:14 resolution:2 polish:1 course:1 shape:1 relation:1 statistical:3 using:3 superimposed:1 interpretation:2 d2:2 issues:1 sampled:1 photodetector:1 teoretycznej:1 calculate:1 parameters:1 preprint:1 supported:1 only:2 does:1 corresponds:1 fig:2 factor:2 partially:1 eugene:1 alternating:1 rescaled:3 non:2 photocount:1 above:1 advantage:1 means:1 quasidistribution:4 expectation:3 kbn:1 resent:1 beam:1 krzysztof:1 reconstruct:1 nov:1 exact:1 wp:4 mod:1 2t:1 splitter:1 smithey:2 fizyki:1 transmission:1 fields:2 signal:8 arxiv:1 patch:1 large:1 imposed:2 deleterious:1 yields:1 demonstrated:1 each:1 found:1 shows:2 uniwersytet:1 essential:1 multiplying:1 physically:1 series:1 direct:3 decreasing:1 understood:1 zero:1 towards:1 value:5 measure:2 quantum:7 terms:1 beyond:1 eq:3 special:1 techniques:1 ˆp:3 fails:1 ˆs:4 appear:1 space:16 events:1 furthermore:1 selected:1 rev:3 expressed:2 case:1 state:5 experiment:2 provides:1 formula:1 newly:2 gov:1 scanned:1 method:1 contrast:1 mode:5 measuring:1 warszawski:1 intensity:1 recently:2 amplitude:1 power:1 easily:2 fock:2 squeezed:1 approaches:2 ws:4 references:1 banaszek:3 directions:1 rapidly:1 rigorous:1 interpret:1 observable:3 limitation:1 ref:1 efficiency:2 region:1 uncertainty:2 allows:1 realistic:1 simulations:1 wallentowitz:1 contribution:1 introduced:1 consequently:1 experimental:1 first:1 origin:1 point:6 within:2 integral:4 homodyne:1 sampling:4 simply:1 least:1 directly:1 issue:1 operator:1 unit:2 illustrate:1 given:1 statistics:3 reflected:1 vogel:1 area:1 ordering:1 positive:1 there:1 due:1 been:1 error:2 their:1 depicted:1 therefore:2 goes:1 ph:1 scheme:4 pn:2 lett:2 function:18 setup:2 complete:2 both:1 quantities:1 operators:1 xxx:1 photon:9 odkiewicz:2 coherent:3 exploding:1 particular:1 parameterisation:1 must:1 applied:1 reconstructed:1 novel:1 intuitive:1 grant:1 was:2 wodkiewicz:1 work:2 up:1 tomographic:2 will:2 compensation:2 determined:1 superposed:1 evaluating:1 were:1 following:2 outcome:1 rescaling:1 poland:1 result:1 detailed:1 opt:1 lanl:1 ordered:2 abs:1 figure:2 scan:1 defined:1 discussed:1 measurement:3 thus:1 states:2 effectively:1 single:2 konrad:1 laboratory:1 limit:4 counting:6 any:1 calculated:1 physics:1 functions:2 formalism:3 us:1 depending:1 carlo:2 discussion:1 when:1 feature:1 field:3 complex:1 quant:1 take:1 moves:1 becomes:1 schematically:1 sured:1 detector:1 p03b:1 parameter:1 tool:1 product:2 used:3 http:1 may:1 numerical:3 effect:1 generated:1 important:1 instytut:1 purpose:1 additionally:1 phase:17 changing:1 analytically:1 measured:3 class:1 stress:1 correlated:1 attempt:1 modes:1 assume:1 light:2 clear:1 required:1 analysis:1 picks:1 delta:1 without:2 algorithms:2 principle:2 exp:3 mechanical:1 representation:2 normally:1 quantity:1
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quant-ph9711056.txt |@word consider:1 rev:2 brownian:2 existing:1 illustrated:1 eds:1 perturbations:1 localized:1 increase:1 subjected:1 finally:1 does:1 under:3 stochastic:4 nodes:2 ingredient:1 supported:1 very:2 wave:8 experimentally:1 difference:1 presented:2 knight:1 large:6 phase:2 small:3 configurations:2 consistent:1 measurable:1 approximation:2 elegant:1 copenhagen:1 cat:2 nonlinear:1 experiment:2 above:2 new:2 jumps:3 contrast:1 notions:1 degree:1 here:3 relaxation:4 quite:1 equations:1 alicki:1 logarithmic:1 obtained:1 institute:1 allows:2 approaches:1 extra:1 important:1 analyzing:1 planck:1 unit:1 superpositions:3 contains:1 pedagogical:1 few:1 live:1 doubt:1 therefore:2 theoretical:1 more:1 separated:1 israel:1 freedom:4 odinger:4 normalized:1 particular:3 foundations:1 cases:1 producing:1 topic:1 springer:1 extension:1 thanks:1 equation:7 work:1 theories:2 macroscopically:2 obvious:1 universe:1 following:4 example:1 dedicated:1 cosmological:1 process:1 discussed:1 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quant-ph9711057.txt |@word represent:1 concept:2 partial:1 consider:3 rev:2 magnetic:1 global:1 brownian:3 results:3 leads:3 roy:2 entropy:7 grateful:1 expressions:2 compact:3 inverse:1 depend:1 essentials:1 spin:2 concerned:1 equivalence:1 characterises:2 gab:3 finally:2 edward:1 manifolds:2 under:1 stochastic:12 characterised:2 applied:1 dwti:4 advantage:1 far:1 rise:1 conditions:2 choice:1 balancing:1 lynch:1 γabc:2 affect:1 exact:2 strand:1 generalised:1 hamiltonian:6 solution:5 vector:5 eigenvalues:2 upper:1 kibble:1 sin2:1 direct:1 ωab:5 second:4 street:2 arnold:1 dynamics:15 canonical:3 what:1 nonlinear:6 plays:1 refractory:1 sum:1 foregoing:1 uniform:3 poles:1 above:3 international:1 satisfy:1 edited:2 measurements:1 respectively:1 pushing:1 here:10 agreement:1 tangent:2 address:2 represented:1 consideration:1 along:1 equations:4 interpret:1 obtained:1 great:1 antisymmetric:1 study:4 vectors:1 allows:1 approaches:1 resulting:5 studies:1 involves:3 projection:3 vii:1 marcel:1 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quant-ph9711058.txt |@word limited:3 externally:1 partial:2 pointing:1 rev:9 comparatively:1 gz:1 indicates:1 roy:1 supplement:1 york:1 consists:1 2r2:1 8e:2 whose:1 fronts:1 bremsstrahlung:1 calculate:1 zone:1 alamos:1 flash:11 tail:1 according:2 device:1 excluded:1 under:1 worth:1 sound:1 presently:1 zhang:1 far:1 frequencies:1 conjectured:1 geometrical:1 ultraviolet:1 fall:1 chodos:2 experimentally:2 ln:2 difference:3 enter:1 pre:1 incoherent:2 eds:1 cause:1 shock:3 large:3 shuryak:1 settle:1 small:4 equation:1 inserting:1 heinz:7 eberlein:1 direct:5 pulse:10 sign:1 approximation:6 zero:2 value:4 correlator:27 further:1 dynamics:7 estimated:2 scotto:1 spectral:1 will:9 what:1 developed:2 appear:1 invertible:1 brackets:1 putterman:1 pandey:2 expressed:2 access:1 turnaround:1 above:4 mq:1 increasing:1 method:2 emitters:1 body:1 gsi:1 q0:20 respectively:4 component:1 proc:1 here:6 water:4 contemplate:1 pratt:1 intercept:15 ansatz:1 active:1 ratio:1 strong:3 logarithmic:1 extreme:1 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quant-ph9711061.txt |@word reproduced:1 parker:1 wigner:1 consider:2 show:1 september:1 indeed:1 govern:1 perelman:1 distortion:1 tcl:5 atomic:1 y2:1 ithaca:2 its:1 fifth:1 scr:1 perfect:4 depend:4 zoller:2 cornell:2 striking:1 evanston:2 than:1 forms:1 simple:1 only:1 colby:3 treatment:4 under:1 derivative:2 tsr:4 alber:2 applied:1 supported:1 around:2 modulate:1 repeats:1 showing:1 possible:1 wave:30 define:1 bluhm:8 lett:5 international:1 using:1 nov:1 commensurabilities:1 yu:2 condition:1 northwestern:2 term:3 particle:9 presented:2 university:6 arxiv:1 acknowledgments:1 discrete:1 demonstrated:1 each:3 periods:1 references:1 cycles:1 mean:1 en:7 classical:4 sequence:1 series:1 energy:6 some:1 packet:12 second:1 college:2 examples:2 respect:1 quantum:25 recently:1 chem:1 eigenstates:1 subject:1 shown:2 scale:1 multidimensional:1 pattern:1 robert:1 rev:10 research:1 current:1 case:1 state:1 proof:1 t12:1 fractional:9 new:3 commensurate:1 occurs:3 porter:2 ulicke:1 schleich:1 foundation:1 condensed:1 full:5 terms:1 august:1 rep:1 selecting:1 however:2 expansion:2 atoms:1 analytical:1 reason:1 complicated:1 free:1 ratios:1 based:1 therefore:2 box:10 both:2 usa:4 beck:2 studied:1 but:1 dependence:2 times:4 motion:6 energies:9 accomplished:1 periodic:2 resulting:1 usually:1 trev:4 first:2 strongly:1 there:3 features:1 classification:5 scales:3 rydberg:4 averbukh:1 tudose:4 period:2 system:3 dimensional:10 austria:1 because:1 accounts:1 stark:1 national:1 associated:1 ellipse:1 macdonald:1 conventional:1 described:3 tuning:1 revival:22 width:1 introduction:1 create:1 initial:4 three:3 long:3 next:1 their:1 linear:1 much:1 structure:13 time:7 bloomington:2 ph:1 molecular:2 type:7 quadratic:2 systems:20 controlled:1 commences:1 form:2 am:1 formed:1 alan:1 volume:1 here:1 en1:2 pulse:1 indiana:2 2n2:1 hold:1 collapses:1 present:2 must:2 me:2 multi:2 laser:1 permits:3 science:1 work:1 oscillator:1 beats:3 value:1 matter:1 harmonic:1 squeezed:1 vienna:1 solely:1 example:8 numbers:6 exhibit:8 taylor:1 proved:1 chosen:1 defined:3 certain:2 describe:1 grant:1 mixed:1 regularity:1 general:1 states:1 weighting:1 examine:2 examined:1 il:2 seen:1 vanish:1 occur:1 collapse:1 different:2 depends:1 variety:1 generic:3 sh:1 kosteleck:9 when:1 length:1 same:1 chemical:1 ny:2 ideal:2 other:2 quant:1 department:8 symposium:1 several:1 parameter:1 particular:1 exactly:2 superposition:2 separate:1 after:2 stroud:1 most:2 phy:1 levels:1 moving:1 keplerian:1 unpublished:1 n1:2 revivals:22 fl:1 class:1 types:8 peaked:1 short:1 third:3 considered:1 no:4 well:4 packets:18 analysis:1 order:1 more:2 number:1 part:1 proceedings:1 fact:1 mechanical:2 definitions:1 n2:4 carpets:1 physics:9 section:2 talk:1 ritsch:1
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quant-ph9711067.txt |@word customary:5 consider:1 pth:1 varying:2 results:7 leads:3 quadrature:6 entropy:3 ǫi:6 devoted:1 subjected:2 γna:1 tr:10 γt:1 finally:2 monotonically:1 squeezing:9 under:2 dramatically:1 applied:1 fax:1 advantage:1 very:2 frequencies:1 rise:1 ieice:1 rth:2 figs:5 associated:2 difference:1 condition:1 level:1 transmission:4 who:1 fragile:1 list:1 solution:1 manifestly:1 iopt:2 unconditioned:1 originally:1 upper:5 unexpected:1 occurrence:1 direct:6 rate:1 enhancement:1 further:1 theory:2 even:5 giving:2 beaten:1 analogously:1 decoding:1 current:1 ˆa:1 homodyning:2 ǫp:6 above:2 ˆi:1 increasing:3 method:3 coefficient:1 full:1 respectively:3 never:1 equals:1 here:2 desired:1 others:1 ratio:1 along:2 strong:6 table:5 obtained:1 great:1 losses:1 allows:2 approaches:1 yˆ:14 action:2 studi:1 narrow:1 makes:3 numerical:5 plotted:4 recursion:3 via:1 bounds:1 namely:3 yuen:2 integrations:1 achievable:1 total:6 estimate:1 bra:1 plot:2 use:3 additive:2 sacchi:1 would:1 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quant-ph9711068.txt |@word emch:1 maximum:3 brownian:1 results:2 eds:1 computation:7 inverse:1 depend:2 deterministic:1 finally:1 γn:2 stochastic:1 p2:1 belonging:1 orthogonal:2 very:5 2re:1 choice:1 lyapunov:11 figs:1 entries:1 difference:3 exact:2 condition:3 narnhofer:1 hamiltonian:2 turns:1 notes:1 t2:1 large:5 admissible:2 vector:3 small:5 eigenvalues:2 measurable:2 carefully:2 second:2 dynamics:2 implemented:1 haake:1 even:3 established:1 what:1 plays:2 rate:3 xφ:1 expressed:2 uniform:2 birkhoff:1 version:1 goes:1 sup:7 new:1 3a:2 supporting:3 condensed:1 kicked:5 reliably:2 degree:1 here:5 behaviour:1 tangent:2 departamento:1 separation:2 directions:2 along:2 standard:1 obtained:7 instituto:1 study:3 studied:1 resulting:1 action:2 fourier:2 uniquely:1 useful:2 projection:1 explained:1 weigert:4 apply:1 should:1 univ:1 unit:1 derivatives:1 use:1 additive:1 would:1 prove:1 distinct:3 positive:4 hilbert:1 definiteness:1 3b:1 therefore:3 bochner:1 theoretical:2 flat:2 initial:6 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quant-ph9711071.txt |@word neighbors:1 represent:2 tjz:9 consider:1 chain:47 secondly:1 directions:1 spie:1 results:8 leads:2 roy:1 scalar:1 lewenstein:1 go:1 fawcett:1 expressions:2 rot:1 layers:1 depend:7 calculate:1 neighbours:4 does:1 tj:1 those:1 th:5 kλ:18 analogous:2 ckλ:8 amplitudes:4 ϕd:4 very:6 frequencies:1 wave:8 every:3 refractive:4 matrices:1 fakult:1 discovered:1 gkλ:10 riemann:1 level:8 did:1 positions:4 solution:6 t0:1 large:3 integro:6 vector:9 small:5 hospitality:1 optics:4 c1x:4 zl:2 zh:2 dealing:1 sin2:2 approximation:8 konstanz:5 eλj:2 substituting:6 situated:2 substitute:1 linear:18 even:1 will:15 interatomic:9 nonlinear:1 brackets:2 section:7 rlj:2 near:3 uniform:1 t2y:2 t2x:5 t2z:1 above:4 ωk2:1 new:3 increasing:1 method:3 devoted:1 creation:2 give:1 evanescent:3 exchange:2 respectively:3 modify:1 here:5 atoms:38 behaviour:4 growing:1 ansatz:2 address:1 represented:2 strong:2 equations:22 appears:1 change:2 aud:1 obtained:8 remark:2 seek:1 hamiltonian:2 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