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quant-ph9810065.txt |@word consider:2 mns:3 preliminaries:1 commute:1 computation:1 consists:1 row:1 deterministic:2 languages:3 under:1 qacc:9 aris:1 norm:1 p2:3 very:1 denoted:1 corollary:4 matrices:4 t2:1 enon:3 t1:4 large:1 vector:1 small:1 lk1:2 smaller:2 mnn:2 odd:3 linear:2 what:2 lemmas:1 sum:1 expressed:1 goes:1 new:1 bn:1 contrast:1 respectively:1 divisor:5 institute:1 shift:20 study:1 vectors:1 t21:1 automaton:5 projection:2 unit:1 use:2 takes:2 would:2 prove:6 next:1 automata:9 m1:4 m0:4 m2:1 means:6 more:2 foundations:1 must:2 word:3 science:3 work:1 klj:3 mj:1 obvious:2 example:1 proof:3 f0:3 f1:3 compare:1 give:1 states:13 numbers:1 council:1 mn:12 needs:1 holds:4 maps:1 answer:1 product:2 after:2 fe:1 fn:3 o:1 qrej:10 element:1 complexity:1 over:2 qfas:7 symbols:1 paper:2 ieee:1 before:1 lf:1 ln:12 lj:7 lv:2 ls:2 lp:2 fij:1 mail:1 main:1 them:1 now:3 university:1 applied:3 latvia:2 l2:7 l1:1 eacc:3 modn:7 subset:1 ei:1 quantum:10 operation:1 special:11 shown:2 matrix:28 space:2 denotes:1 investigation:1 print:1 squares:1 induction:6 correct:1 weaknesses:1 theory:1 ambainis:2 vazirani:1 definition:4 language:3 starts:1 transition:3 hence:1 quadratically:1 generalizations:1 first:1 there:1 xn:2 probability:4 powerful:1 number:10 construct:2 another:2 given:1 introduction:1 riga:1 least:2 their:1 statement:1 siam:1 dfa:1 gives:1 tuple:1 rejected:1 x2:1 x0:5 x1:1 than:4 divisible:6 require:1 amplitude:2 38th:1 1n:1 rai:1 conjugate:1 any:4 mij:1 mappings:1 min:1 efficient:1 k1:7 strengths:1 regular:1 letter:1 accepting:3 class:1 observation:1 kj:6 kn:2 ks:2 proceedings:1 show:2 supported:1 halting:2 find:3 q1:19 q0:14 q2:5 situations:1 lemma:9 bernstein:1 oct:1 do:1 watrous:2 get:3 words:2 combinations:1 dt:1 prime:7 arxiv:1 common:5 qn:8 moduli:1 set:1 exists:1 observed:1 see:5 computer:2 rejecting:2 state:3 correctly:1 reading:2 transpose:1 multiplier:1 both:2 jt1:1 equal:5 0a:2 expression:1 qfa:8 otherwise:3 cj:1 ci:1 cn:1 ca:1 respect:1 conference:1 0a1:2 0a2:2 transformations:2 basis:2 equivalent:3 pmin:12 ai:1 pk:3 ph:3 define:1 aj:2 corresponding:2 observable:1 c3:3 c2:6 c1:7 c0:1 case:3 p1:3 value:2 will:3 property:18 va:8 vb:3 unitary:7 non:1 grammars:1 id:3 grant:1 alphabet:3 belong:1 complex:3 quant:3 finite:11 counterparts:1 identity:1 nevertheless:1 greatest:5 sets:1 left:2 2jt:2 less:1 integer:3 previous:1 recognizing:3 easy:3 input:4 transformation:3 possible:1 know:1 using:1 accepted:1 mod:1 like:1 follows:2 continue:1 steps:1 arbitrary:2 works:1 because:1 classical:1 some:1 b0:1 b1:1 b2:1 proper:1 happens:1 power:2 journal:1 each:4 bj:1 step:3 santa:1 integers:3 working:2 recognized:1 crutchfield:1 letters:5 dfas:1 h1:3 right:2 references:1 span:3 log:1 initial:1 way:14 was:1 function:3 considerably:1 elsewhere:1 form:2 regard:1 but:1 construction:1 collapses:1 us:1 called:5 proved:1 moore:1 computing:1 defined:2 abstract:1 describe:1 denote:1 na:1 multipliers:2 department:1 elements:5 superposition:6 a1:6 a0:8 a3:1 a2:4 implies:1 values:1 lanl:1 together:1 n2:1 starting:1
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quant-ph9810066.txt |@word secondly:1 precondition:3 consider:1 represent:1 skip:3 existing:1 andre:2 computation:8 edu:1 consists:1 reasoning:5 causes:1 inverse:1 calculate:5 graph:1 similarity:2 recurrence:1 tail:4 program:4 preserved:1 under:1 norm:1 case:9 predicate:7 amplitudes:3 rise:1 choice:2 unstructured:1 exact:1 høyer:2 condition:1 generalised:2 presented:3 cause:2 michael:1 solution:2 t1:2 deals:1 generalises:1 indices:1 says:1 deutsch:3 so17:1 sin5:2 sin2:2 sin3:3 elegant:2 zero:3 rigorous:3 further:1 machines:1 linear:1 even:1 section:8 expressed:1 sequential:5 3n:1 establishes:3 new:1 contributes:1 body:17 simultaneously:2 here:6 desired:7 expansion:5 others:1 represented:6 strong:1 equations:3 search:20 leaves:1 approaches:3 suggests:2 periodic:1 resulting:1 usually:1 had:1 suitable:1 makes:1 helps:1 involves:1 bounds:1 decrease:2 apply:5 establish:1 languages:1 use:6 superpositions:1 probabilities:3 positive:1 stated:1 soton:1 init:4 next:2 call:1 butler:1 25th:1 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quant-ph9810067.txt |@word epeau:1 consider:1 rev:3 global:1 grateful:1 go:1 follow:2 integrity:1 whose:2 referring:1 finally:1 asking:1 permanently:2 those:1 whatsoever:1 under:7 kwong:1 circumstances:1 worth:2 sent:7 ingredient:1 applied:1 digit:2 collaborate:1 very:6 choice:1 wishes:1 every:1 affect:1 24th:1 difference:1 securely:2 randomness:3 level:2 louis:1 unusual:1 applicable:1 leave:1 small:5 noted:1 concluded:2 smaller:1 computation:1 zero:2 street:1 perspective:1 further:1 implemented:4 even:1 transfer:1 what:1 plays:1 appear:1 blum:2 near:1 sequential:1 above:2 supplies:1 simultaneously:1 submitted:1 exchange:3 respectively:1 abstractly:1 here:2 agreement:1 subdivides:1 address:1 along:1 appears:1 box:4 sending:2 great:1 sender:1 suitably:1 receive:2 inspired:1 claude:1 simultaneous:1 bob:13 makes:1 involves:1 genuinely:1 tasks:3 useful:4 secure:27 causal:1 use:2 cheating:2 would:4 probabilities:3 revelation:1 motivate:1 hilbert:1 distinct:1 until:2 taken:1 theoretical:3 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quant-ph9810068.txt |@word measurements:2 consider:2 springer:2 keep:2 global:1 results:1 founded:1 overlap:1 computation:2 go:5 follow:5 integrity:1 caveats:1 referring:1 aug:1 segments:1 send:3 finally:1 asking:1 present:3 th:1 under:2 kwong:1 must:8 worth:1 sent:7 advice:1 applied:1 charles:1 string:1 advantage:3 very:3 than:3 implicitly:2 keeping:1 fourth:1 wishes:1 lecture:2 24th:1 securely:2 governments:1 generalised:1 exponential:1 immediately:2 presented:1 transmission:2 forth:1 notes:2 list:3 solution:3 occurs:1 leave:1 solved:1 evades:1 shows:1 noted:1 20th:2 jeff:1 grateful:1 prediction:1 zero:1 street:1 further:1 implemented:2 even:1 what:1 plays:2 sub:1 advantageous:1 chicago:2 giving:1 section:1 near:1 supplied:1 3t:1 current:1 waiting:1 above:3 new:8 acknowledgments:1 developments:1 revealing:1 exchange:3 obviating:1 never:1 here:7 bi:6 possibility:2 separation:3 address:1 concluding:1 supplying:1 wait:1 arena:1 sending:3 receive:2 popescu:1 goldwasser:1 allows:2 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quant-ph9810069.txt |@word sch:1 magnetic:1 brownian:7 eds:1 expressions:4 consider:1 particles:1 inverse:1 groundstate:1 finally:1 does:1 helps:1 th:1 stochastic:2 analogous:1 summarizes:1 springer:1 every:1 markov:1 little:1 verrucchi:1 hamiltonian:4 cycon:1 vector:3 math:6 tognetti:1 optics:1 heckman:1 zj:1 zk:3 literature:1 approximation:1 second:1 rigorous:3 dynamics:3 tev:1 canonical:2 even:1 established:1 what:1 appear:1 itˆ:2 leschke:3 celebrated:1 symbolically:1 expressed:1 henceforth:1 bernhard:1 above:2 new:1 full:1 degree:1 respectively:1 here:4 courtens:1 dimensionality:1 path:19 strong:1 z1:3 z2:3 obtained:1 suitably:1 vectors:1 resulting:1 suitable:1 via:1 merely:1 replace:1 limj:1 apply:2 tools:1 unit:1 wealth:1 usa:1 prove:1 remains:1 positive:1 properties:1 therefore:1 relativistic:1 ib2:1 type:2 more:1 flat:1 operators:2 odinger:4 berlin:1 normalized:3 particular:2 ii:1 keeping:1 valued:2 pieri:1 simone:1 equation:1 following:1 example:1 proof:2 νr:2 process:1 expanding:1 sense:2 high:1 sphere:2 numbers:1 allowed:1 rescaling:1 regularization:2 write:1 how:1 ordinary:1 algebra:2 replacing:1 after:1 plane:4 physik:1 multiplication:1 fl:1 realized:1 dynamical:1 su:6 definitions:1 order:2 bodmann:2 ith:7 over:2 years:1 wiener:6 integrands:1 its:1 hundertmark:1 derive:1 kac:1 chosen:1 parts:1 systems:2 derivative:1 main:1 might:3 dyson:1 non:2 duhamel:1 processes:1 framework:1 they:1 arriving:1 now:1 hall:1 finite:1 university:1 presented:1 spinning:1 funahashi:1 l2:7 morandi:1 universit:1 2i:1 2j:10 square:2 fisk:1 energy:1 ercolessi:1 gaussian:1 related:1 extended:1 expect:1 measure:4 quantum:11 our:1 eq:1 shown:1 rs:1 furthermore:1 since:1 rev:3 denotes:2 diffusive:2 may:7 acting:2 formula:5 ref:8 interchanging:1 wiley:1 theory:1 limν:1 diagonal:1 approaches:1 york:1 e0:6 r2:8 napoli:1 florida:1 motion:5 kochetov:1 onto:1 symmetry:2 symbolic:2 number:2 duistermaat:1 obey:1 precisely:1 aharonov:1 given:4 perturbation:1 sakoda:1 similarly:1 introduction:1 adjoint:1 theoretische:1 relations:1 their:2 exponents:1 williams:1 continuous:4 employ:2 part:1 diffusion:1 namely:1 contravariant:2 states:3 contrary:1 were:1 pre:2 bridge:2 topics:1 manner:1 constrained:1 viewed:1 paths:5 genuine:1 zero:1 min:1 lim:4 self:1 able:1 ideas:2 phillips:1 coincide:1 heisenberg:1 formulas:1 boltzmann:1 germany:1 representation:6 phase:1 probabilistic:1 exponent:1 hj:3 rogers:1 later:1 feynman:3 proceedings:1 points:1 exp:13 mechanical:1 physics:1 thomas:1 casalbuoni:1 show:1 purely:1 relation:1 subtle:1 d2:3 ground:2 giachetti:1 based:1 knowledge:1 eigenspace:2 written:3 only:3 integrable:2 constant:2 hamiltonians:1 oct:1 hope:1 continuity:1 clarifying:1 means:1 expectation:1 firenze:1 cannot:1 nearly:1 words:1 ds:7 evolution:6 continuum:2 fields:1 arxiv:1 daubechies:3 analytical:1 fixed:1 kernel:1 reference:1 arrives:1 j3:5 see:3 result:6 quantizing:1 closer:1 commutation:1 definite:1 state:5 various:1 between:1 c2j:6 approach:2 terms:2 key:1 martingales:1 relying:1 adapting:2 essentially:1 limits:1 taking:2 contract:1 hψ:1 context:1 contribution:2 expression:4 finds:1 among:1 kirsch:1 vaia:1 dimensional:4 polynomial:3 respect:1 conference:1 pp:1 due:1 treat:1 interest:1 basic:1 ph:3 gerry:1 corresponding:1 covariance:1 coherent:12 denote:1 spin:19 present:1 associated:2 unlike:1 appearance:1 will:1 euclidean:4 while:1 ultra:2 planar:2 unitary:2 vol:1 refs:1 encountered:1 obeying:1 ih:3 claimed:1 make:1 same:1 complex:3 quant:2 widely:1 several:1 used:1 singapore:2 hand:1 parametrized:1 uses:1 purpose:1 frequently:1 identity:1 recent:2 schr:3 well:3 academic:1 contact:2 position:1 usual:1 spherical:1 diffusions:1 gainesville:1 identify:2 atomic:1 klauder:4 alternative:1 eigenstates:1 stratonovich:1 heuristic:1 conjugates:1 preprint:1 lebesgue:2 similarities:1 theorem:2 mod:1 real:3 2j3:1 warzel:2 rules:1 breaks:1 stereographically:1 world:2 formal:1 semiclassical:1 inomata:1 follows:1 serves:1 consensus:1 dµz:5 yields:1 integrals:6 pointwise:1 stationary:1 calculus:2 sketch:1 right:1 often:1 some:2 certain:1 understood:1 gilmore:1 b1:1 pev:1 integration:2 comments:2 dz1:1 dz2:1 refer:1 semigroups:1 scientific:2 bl:2 agreement:1 expansion:1 bk:3 although:1 imaginary:2 hilbert:6 projector:1 about:1 kinematical:1 freedom:1 discussed:1 o:2 side:1 characterized:1 introduced:1 equally:1 into:1 within:1 integral:15 functional:1 three:1 down:1 weyl:1 references:1 pathintegral:2 arecchi:1 operator:12 institut:1 there:2 way:1 function:1 form:1 urnberg:1 regard:1 but:3 erlangen:2 illuminating:1 convergence:1 line:2 volume:1 he0:3 regularized:2 ur:1 projecting:1 limit:7 mechanics:1 froese:1 taylor:1 proved:1 defined:4 recognize:1 general:1 fujii:1 single:1 exist:1 formalism:1 check:1 functions:3 no:1 when:1 casher:1 other:1 details:1 department:1 mathematics:1 chichester:1 symbol:2 convincing:1 kashiwa:1 generated:1 bounded:2 simon:2 using:2 requires:1 space:8 pseudo:1 paper1:1 time:9 starting:1 itˆo:1 restored:1
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quant-ph9810070.txt |@word sci:1 consider:3 results:5 leads:5 roy:6 consists:1 anggi:1 hole:1 terms:2 paris:1 subjected:1 finally:1 program:1 those:5 th:1 stable:5 stochastic:8 applied:5 belonging:1 advantage:1 far:1 rise:3 springer:1 witten:1 condition:2 enjoyable:1 basics:1 presented:4 proc:3 solution:7 large:3 discrete:1 small:1 eigenvalues:12 sturm:1 ten:2 approximation:2 go:1 second:1 design:1 further:2 dynamics:4 spectral:5 index:1 revised:1 appear:1 giving:1 trivial:1 section:3 expressed:3 find:3 above:3 designing:1 new:13 increasing:1 method:5 confluent:2 degree:3 fiz:1 respectively:5 here:15 desired:1 ansatz:2 razavy:1 represented:1 xγ:2 invented:1 equations:1 logarithmic:1 obtained:4 search:2 involved:1 study:1 larger:3 allows:1 reason:1 resulting:1 hospitality:1 suitable:1 plotted:3 via:3 family:1 hermite:1 plenum:1 circumvent:1 planck:10 plot:1 additive:1 working:1 remains:1 positive:8 negative:1 next:2 nucl:1 noting:3 ψn:18 therefore:4 type:1 until:1 more:4 initiated:1 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quant-ph9810071.txt |@word monte:1 concept:1 customary:1 consider:2 pointing:1 crucial:5 magnetic:5 global:2 desirable:1 results:12 leads:1 jawaharlal:1 scalar:1 entropy:1 comments:1 computation:1 follow:1 monroe:1 mesons:1 contributions:1 issues:1 row:1 increase:1 exercised:1 berry:2 depend:1 violate:6 leung:1 concerned:1 acting:1 factoring:1 coincide:1 environment:2 charge:1 critical:1 present:3 whatsoever:1 under:9 osterwalder:3 nodes:2 characterised:1 norm:1 ingredient:2 p2:2 labels:1 amplitudes:9 provides:2 straightforward:1 mabuchi:1 linked:1 could:1 rise:4 springer:1 choice:3 witten:4 every:1 chuang:1 entries:1 ithaca:1 air:1 difference:3 matrices:1 condition:1 room:1 adjective:2 riemann:1 pancharatnam:1 hamiltonian:3 did:1 positions:1 unusual:1 fewer:1 correct:2 discrete:1 vector:6 section:2 small:2 gauge:2 optics:1 lines:1 illustrating:1 grateful:1 excited:1 dealing:1 consistent:3 among:2 direct:1 crop:1 sign:1 approximation:2 second:6 enclosed:1 corner:1 rigorous:1 dynamics:4 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quant-ph9810073.txt |@word represent:1 partial:1 consider:4 remarkable:1 illustrates:1 magnetic:5 results:1 four:2 ga:1 peshkin:1 depend:1 calculate:1 graph:2 charge:1 excluded:1 under:1 analogous:1 divergent:1 shielding:1 wave:4 wishes:1 difference:2 condition:4 leads:2 presented:2 accidentally:1 large:2 convenience:1 science:1 small:1 inspection:1 consistent:1 sin2:18 direct:1 zero:1 concludes:1 further:1 dynamics:1 odd:1 quite:1 even:2 barrier:5 section:15 brief:1 goes:1 new:3 respectively:2 equals:1 here:2 cos3:2 cos2:1 strong:1 ctu:1 ˇt:2 studied:1 suggests:1 periodic:1 procedure:2 ˇa:1 family:2 translational:1 total:2 plot:2 use:2 asymptotic:1 would:3 sake:2 eφ:1 finally:1 few:1 call:1 means:1 type:1 theoretical:1 more:5 flat:1 incident:1 initial:2 operators:3 basically:1 particular:4 known:1 cases:3 rotational:4 recall:1 setup:1 det:5 values:2 thin:1 following:1 arrive:1 compare:1 figure:6 relativistic:1 involve:1 indicates:1 minimum:1 allowed:1 occur:3 rather:5 discussion:1 six:1 feature:2 arrangement:1 write:1 pure:7 parameter:1 sin:14 simplicity:1 may:1 after:1 derived:2 plane:2 faculty:1 choice:1 parallel:1 correspond:1 provide:1 ones:1 so:3 prefactor:1 restriction:1 interpretation:1 indeed:1 over:1 insight:1 interpreted:1 course:1 paper:1 through:1 2v:1 mentioned:2 existence:1 still:1 its:2 tending:1 ıc:2 acknowledge:1 chosen:1 interesting:1 coordinates:1 actually:4 fig:2 main:1 non:6 combination:1 introduce:1 hamilton:3 altogether:2 now:4 discuss:1 2u:1 term:1 equality:2 oppositely:1 2m:1 differential:16 detect:1 energy:3 related:3 elementary:1 owing:1 quantum:2 our:2 shown:1 matrix:2 since:1 rev:2 looking:1 re:2 formula:7 math:2 theory:1 ıˇcek:1 divergence:1 given:2 standard:4 keep:1 motion:1 length:1 place:1 hence:2 first:1 origin:2 already:1 features:2 symmetry:6 directly:2 fluxes:2 quality:1 angular:2 aharonov:5 illustrate:1 differ:1 πk:2 least:1 anyone:1 assumption:1 reexamine:1 centered:1 explanation:1 somewhat:1 than:1 specify:1 determines:1 sections:1 namely:3 were:1 treated:1 φjk:1 ann:2 mind:1 argument:1 4uv:2 need:3 forced:1 strength:1 angle:5 lim:4 latter:2 able:2 oriented:1 potential:5 take:1 concern:1 multiple:1 electric:1 shall:3 4u2:1 simplify:2 regular:3 significant:2 formulae:4 acknowledgements:1 eı:2 don:1 takes:1 considered:1 clear:1 traditional:1 graphs:5 principle:1 exp:1 fact:2 quantity:1 particularly:3 show:1 violation:4 gauge:1 inconsistent:1 rough:1 trivial:1 find:1 parameters:7 should:2 prolong:1 only:2 explicitly:1 integrate:1 local:2 oct:1 do:1 get:2 da:1 joint:1 cannot:1 closely:2 2me:1 arxiv:1 rotationally:2 common:1 fixed:1 view:1 set:2 reference:1 prague:1 depends:1 radius:1 result:1 talmi:1 subject:1 visualize:1 αw:1 ways:1 nuclear:1 symmetric:1 enough:1 between:1 invariant:1 boundary:15 conditions:11 solenoid:3 nature:1 importance:1 weak:1 however:3 gratefully:1 vanishing:1 distinguish:1 dependance:3 cos:22 equal:2 figures:1 passing:1 expression:4 finds:1 minima:1 nonrelativistic:1 simple:1 corresponds:9 dimensional:1 diverges:1 exhibits:1 moreover:2 specializing:1 described:1 solenoids:1 addition:1 three:4 been:3 basic:1 ph:1 direction:2 corresponding:1 quantities:1 concerning:1 observe:1 angles:1 general:2 case:9 pacs:1 solid:2 examine:1 value:4 will:2 while:2 behavior:2 situation:1 characterizing:2 thus:2 them:1 reads:1 im:1 vanish:1 different:1 grant:1 make:1 cross:16 same:1 another:1 complex:1 quant:1 dimensionless:1 difficult:2 independent:1 see:2 numerical:1 effect:11 compared:1 purpose:1 infinite:1 recent:1 kept:1 proceed:1 well:3 analysis:4 obviously:1 bohm:5 convenient:1 model:1 usual:3 generally:3 obtain:1 shape:2 immediately:2 scattering:10 singularity:1 note:3 enters:1 point:3 character:1 interested:1 lett:1 remaining:1 momentum:3 real:2 rescaled:1 spinless:1 read:1 possible:2 five:1 integer:1 depicts:1 mod:4 imposed:3 particle:5 reduces:1 shapes:1 flux:6 either:2 arbitrary:1 adami:1 mathematical:1 because:1 picture:1 czech:2 some:5 respect:1 nonzero:1 provided:1 describing:2 dimensions:1 though:1 manipulations:1 demonstrated:1 simpler:1 discussed:1 dependence:5 o:1 range:1 introduced:1 contains:1 letter:1 into:1 integral:1 due:1 references:1 determine:1 operator:1 significantly:1 comparing:1 support:1 there:4 u2:10 way:2 forward:2 was:4 assumes:1 function:7 form:2 but:3 idealized:1 line:5 removed:1 true:2 observation:1 2πk:6 uv:9 maximum:1 us:8 below:2 limit:3 demonstrate:1 problem:4 ab:8 constant:2 defined:1 abstract:1 describe:1 denote:1 dashed:3 conserved:2 dθ:20 physical:2 again:2 nk:1 no:1 fixing:1 when:4 field:1 setting:1 republic:1 department:1 mathematics:1 conclusion:1 polar:2 resembles:1 peak:1 included:1 nonintegrable:1 independently:1 implies:1 interval:1 dσ:10 together:1 mass:1 dot:1 time:1 teta:1 backward:4 starting:1 original:1
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quant-ph9810074.txt |@word limited:1 magnetic:1 desirable:1 emch:1 entropy:57 consists:5 localized:1 violate:1 under:2 every:1 affect:1 internally:1 convenience:1 unrelated:2 succession:1 pragmatic:3 concise:1 consistent:9 second:15 persuade:1 even:7 established:3 specification:1 above:3 new:6 seeks:1 evolving:1 simultaneously:2 never:2 here:1 represented:4 path:1 balian:1 interpret:1 obtained:1 elaborate:1 changed:1 suitable:2 settled:2 projection:1 highly:1 stern:3 total:2 univ:1 unit:1 would:10 chooses:1 kinematics:2 therefore:10 until:1 fractions:2 tolerated:1 brings:1 odinger:2 hole:2 hold:1 blocking:2 must:17 word:2 pursue:1 setup:21 work:2 theories:1 suggestive:2 itself:14 concepts:2 example:8 give:3 preserving:2 involve:4 indicates:1 caution:1 want:3 end:1 thing:1 feature:2 how:14 significance:1 ordinary:1 description:5 beauty:1 replacing:2 after:12 wrong:2 summarize:2 law:2 parallel:1 attempt:2 third:5 acknowledged:1 complexity:1 order:3 operations:1 interpretation:13 over:9 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quant-ph9810084.txt |@word concept:1 partial:1 consider:7 pointing:1 interference:1 magnetic:2 lack:1 leads:1 roy:1 disc:3 entropy:13 comments:3 parameterization:12 consists:2 disk:1 contributions:1 gr:3 compact:1 whose:1 simon:5 depend:3 calculate:1 tx:1 segments:1 equivalence:1 tr:4 byrd:3 including:1 removal:1 finally:2 spain:1 under:4 te:1 worth:1 case:7 unsatisfying:1 orthogonal:2 very:2 rise:2 utexas:4 geometrical:4 electron:2 sons:1 little:8 matrices:31 condition:1 arrange:1 entire:2 basics:1 trm:1 higgins:2 hamiltonian:3 turns:1 having:1 list:1 solution:1 travels:1 convenience:1 vector:2 generalize:1 optics:2 der:1 posta:1 degeneracy:1 aρa:2 edu:3 sin2:8 discover:1 understanding:1 approximation:3 go:1 zero:3 further:1 dynamics:4 chem:1 odd:1 theory:5 even:1 will:12 what:1 appear:1 specification:1 brief:2 expressed:1 current:1 experiment:1 above:7 new:2 row:1 method:1 satisfy:2 zaragoza:2 christian:1 degree:1 respectively:1 kendrick:1 component:1 khanna:1 here:5 diagonal:12 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quant-ph9811003.txt |@word limited:1 concept:1 consider:2 rev:24 roc:1 results:2 existing:1 illustrated:2 eds:2 entropy:7 gb:16 computation:1 consists:4 expressions:4 research:2 gi:7 soc:1 whose:1 terms:3 calculate:7 technique:1 tr:1 γt:1 tn:25 γi:2 does:3 under:5 kλ:9 γb:1 γa:1 norm:1 odinger:1 amplitudes:2 presently:3 orthogonal:1 very:1 springer:2 idealised:1 sons:1 resonant:1 experimentally:3 difference:1 exact:3 condition:4 gkλ:3 europhys:1 exponential:1 level:4 opt:3 knight:7 notes:1 t2:1 solution:1 t0:7 standards:1 large:4 detected:10 microlaser:1 small:5 eigenvalues:2 markov:1 optics:3 noted:1 upper:1 ga:18 dealing:2 pulse:2 feasibility:1 zero:2 manipulating:1 dynamics:6 linear:1 even:2 index:1 what:1 trapping:2 section:7 experiment:2 goes:1 new:5 contributes:1 method:2 counters:1 elect:1 respectively:1 never:1 component:2 equals:1 here:4 atoms:33 plenio:10 free:2 relaxation:3 represented:1 strong:2 appears:2 trans:1 spite:1 larger:5 allows:4 through:13 amount:3 resulting:1 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quant-ph9811004.txt |@word shor:1 measurements:1 consider:1 popescu:1 show:1 violation:2 indeed:1 suggests:1 obtain:3 interpreted:1 produced:1 gda:7 via:1 london:1 argued:1 statements:1 question:1 still:1 its:1 effect:4 massar:1 peres:1 conjunction:1 thank:1 how:1 true:4 regarded:1 point:2 seems:1 pawel:2 nonlocal:2 should:5 better:1 whether:1 only:2 extracting:2 lr:5 systems:1 theorem:4 employed:1 analogous:1 main:1 local:5 momentum:1 details:1 applied:1 his:1 orthogonal:2 read:3 mor:1 zurek:1 reader:1 impossible:1 possible:4 anyway:1 framework:1 cannot:3 entangled:2 they:3 instead:1 report:1 using:2 nov:1 now:2 pacs:1 name:1 polish:1 impressive:1 particle:1 podolsky:4 did:2 cause:1 university:2 arxiv:1 alice:8 try:1 realistic:1 wooters:2 conflict:1 science:1 found:1 probably:1 qm:12 noted:1 realism:2 view:1 concluded:1 different:1 set:1 marek:1 violated:1 einstein:4 stronger:2 lett:3 distantly:1 translating:1 become:1 see:3 aquire:1 measure:1 quantum:5 compatible:1 theoretic:2 nonlocality:10 best:3 out:2 even:1 deals:1 what:1 inequalities:1 difficult:1 position:1 univ:2 since:2 rev:4 particles:4 numerous:1 state:2 version:1 provides:4 between:3 operationally:1 completness:2 formula:1 correct:1 demonstrated:1 find:1 who:1 recently:2 nature:3 dieks:1 error:1 communicate:1 however:3 here:2 quite:2 ryszard:1 believed:1 reason:1 enters:2 refuting:1 will:2 imagine:3 represented:1 wanted:1 come:1 properties:3 bz:1 both:2 about:1 cqm:3 hard:1 carried:1 language:1 gratefully:1 institute:1 could:5 acknowledge:1 messages:1 counterpart:3 turn:1 zukowski:1 statement:2 ilr:4 context:1 divincenzo:1 bob:8 argue:1 first:1 does:2 raised:1 nsk:4 spatially:1 mail:3 bell:15 sentence:1 communication:1 into:3 within:1 predictions:9 scene:1 system:2 first:1 pair:2 written:1 global:1 send:2 parties:1 pairs:1 message:2 operational:2 tools:1 signals:1 described:1 would:5 extraction:2 assumed:2 support:1 there:3 mermin:1 three:1 been:1 parallel:1 classically:1 going:1 call:1 pg:1 way:4 astrophysics:1 ph:3 scheme:1 was:3 theoretical:1 pl:3 more:2 separated:1 correlations:3 complete:2 form:2 sending:1 ch:1 smolin:1 exactly:1 michal:1 needed:1 authors:2 tacitly:1 careful:1 spin:1 than:5 he:1 case:2 ii:2 account:1 wootters:1 mif:1 showed:3 horodecki:1 fuchs:1 type:1 efficient:1 when:1 single:1 us:2 preparation:1 technical:1 while:1 rains:1 nine:2 were:1 following:2 problem:1 treated:1 called:2 address:3 result:1 mechanics:4 claim:1 reduces:1 certain:1 bennett:5 am:2 argument:6 accept:1 states:6 discussions:1 say:4 numbers:1 allowed:1 recover:1 apparently:1 any:1 physical:1 cloning:1 information:7 subsystems:1 paradox:9 able:1 refute:1 rather:3 verify:1 latter:1 means:3 rosen:4 negation:1 same:1 apply:1 note:2 located:1 other:1 quant:3 arguments:1 mathematics:1 awaits:1 proof:1 conclusion:2 status:1 product:2 used:3 entanglement:15 description:1 coming:1 superluminal:3 measurement:1 knew:1 took:1 replace:1 wrong:1 produce:2 purpose:1 faculty:1 prepares:1 revealed:2 why:1 foundation:1 coupling:1 famous:1 charlie:5 poland:2 no:2 epr:13 roughly:1 like:1 provide:1 without:14 so:7 incomplete:1 very:1 observables:2 stapp:1 physics:3 original:2 fact:3 know:1
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quant-ph9811005.txt |@word represent:5 code:9 consider:9 limited:2 rev:2 rob:1 invent:1 concept:1 computation:7 edu:1 consists:1 follow:1 issues:1 increase:2 depend:1 nonlocal:8 presents:1 preserved:1 under:1 dramatically:1 applied:3 shielding:1 straightforward:1 evolves:1 very:2 baton:1 every:1 affect:1 1s:2 matrices:1 newly:1 entire:1 exponential:1 solution:1 solved:1 small:6 smaller:3 nearing:1 rate:6 cost:1 perspective:1 further:1 odd:1 even:3 errors:52 apparatus:1 expressed:1 decoding:4 cell:1 paying:1 localized:1 above:1 values:2 method:2 proliferation:2 simultaneously:1 degree:1 doubt:1 error:53 component:4 residual:1 here:2 understanding:1 desired:1 objects:1 operating:1 others:2 represented:4 equations:1 appears:2 change:4 approaches:1 example:1 spheres:1 suitable:1 useful:1 total:2 unit:1 environment:3 use:1 would:2 codewords:4 probabilities:1 few:2 going:1 therefore:4 memory:1 taken:1 type:1 more:1 knows:1 flying:2 corrected:6 reversible:2 controlling:1 foundations:1 cases:4 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quant-ph9811008.txt |@word optimal:1 partial:1 sch:1 represent:1 enl:3 accurate:2 authors:1 obtain:2 leads:2 known:1 ge:1 paper:2 2tα:1 montr:1 computation:1 using:2 differentiation:1 expressions:1 research:1 find:2 consider:1 x10:2 tables:1 now:3 number:1 nasser:1 kluwer:1 λx2:2 chosen:1 graph:2 show:1 hall:2 only:4 valid:2 location:1 maisonneuve:1 might:1 transformation:2 momentum:4 real:5 applied:1 non:1 perturbation:2 above:2 eigenvalue:14 press:1 de:1 results:6 expectation:1 bound:6 test:1 figs:1 they:2 instead:1 oxford:1 provided:1 nov:1 replace:2 exact:6 gen:3 convexity:1 occurring:1 ebec:1 ǫnl:4 increasing:1 qu:1 follows:1 university:2 arxiv:1 t2:2 solution:1 e00:6 correct:1 discrete:2 spiked:4 minimal:1 arbitrary:3 2l:2 eigenvalues:11 x12:2 fixed:1 page:9 solutions:2 upper:4 en:7 financial:1 methods:4 our:1 renormalized:1 smooth:3 energy:4 lebanon:1 approximations:1 ǫn:2 approximation:4 grant:1 namely:1 used:2 result:1 convex:1 tˆ:5 tmin:1 approximated:1 eq:5 purposes:1 canada:2 gol:3 dimensions:9 richard:1 bottom:2 since:1 integration:3 reasoning:1 may:1 lifshitz:1 provides:1 monotone:2 formula:7 problems:1 saad:2 ref:2 method:3 math:3 notice:1 numerical:5 recently:1 theory:1 extend:1 respectively:2 wavefunctions:2 radial:1 dman:3 given:3 here:2 however:1 gratefully:1 statistics:1 illustration:2 hypervirial:1 address:1 along:1 xα:2 respect:2 2n:6 problem:2 log:1 obtained:8 both:2 last:1 similar:1 could:2 discussed:1 according:1 acknowledged:1 greatly:1 positive:5 expression:4 other:1 first:4 mechanics:3 followed:1 unnormalized:3 conclude:1 simple:6 pergamon:2 wave:1 potentials:1 harmonic:6 dinger:1 dimensional:3 references:1 landau:1 operator:1 table:6 open:1 angular:4 seeding:1 use:4 boulevard:1 described:1 transformations:4 prove:1 west:1 support:1 there:1 approximate:1 acknowledgment:1 natural:1 relativistic:1 scope:1 ph:1 was:1 knowledge:1 dame:1 function:1 corresponding:4 eal:1 form:1 some:1 under:1 odinger:7 but:1 direct:4 tential:1 particular:4 x2:18 implies:1 x1:1 present:4 case:3 showed:1 pacs:1 science:1 equation:8 work:1 oscillator:6 bounds:19 us:1 po:1 dordrecht:1 minimum:1 values:3 were:2 following:1 mensions:1 property:1 root:5 example:3 london:1 exhibit:2 concave:1 fig:2 h3g:1 do:1 lines:1 abstract:1 thus:1 spectrum:1 general:2 helped:1 quantum:3 engineering:1 concordia:1 formulae:1 allowed:1 indeed:1 functions:3 develop:1 exploratory:1 min:2 provide:2 s2:8 discussion:1 di:1 when:2 same:1 sciences:1 potential:10 quant:1 generalized:1 spatial:1 department:2 mathematics:2 beirut:1 priori:1 extended:2 immediate:1 singular:1 replacing:1 notre:1 earlier:1 derived:1 top:2 extending:1 generated:1 purpose:1 faculty:1 exercises:1 nl:1 geometrical:1 data:1 class:1 µx:1 lower:4 no:1 schr:7 e21:6 council:1 considered:1 consequently:1 interval:3 well:1 order:1 4n:3 academic:1 4f:1 meanwhile:1 tˆα:1 dimension:3
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quant-ph9811009.txt |@word concept:1 consider:4 chain:1 2c0:1 lack:1 commute:1 offdiagonal:1 grateful:1 go:3 follow:1 expressions:1 gr:1 whose:2 c0:2 concerned:1 nonlocal:3 passage:1 ıa:2 finally:4 does:5 ny:1 spain:4 kε:5 under:6 stochastic:18 analogous:3 barcel:1 bilocal:1 global:1 hibbs:1 straightforward:1 outside:1 far:1 induce:1 readout:3 sons:1 every:1 redefinition:1 difference:2 condition:5 ρi0:1 randomness:3 dαp:1 hamiltonian:12 positions:1 solution:3 large:5 discrete:4 math:1 dealt:1 small:4 entropy:1 though:3 optics:1 der:2 measuring:1 smaller:4 ornstein:1 approximation:7 imply:2 dissipation:4 equal:2 further:2 substitute:1 linear:1 even:7 index:1 what:3 errors:25 adds:1 appear:1 clock:75 deeply:1 section:2 dephasing:2 cell:3 consistently:1 version:1 above:1 new:3 dtα:1 increasing:1 preserved:1 satisfy:1 edited:2 valle:1 respectively:1 realizations:1 component:1 here:1 diagonal:5 following:1 asymmetry:1 inverse:2 galilean:2 separation:1 fulfill:2 represented:1 luis:1 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quant-ph9811010.txt |@word emch:2 consider:2 similarity:1 caused:1 both:2 results:3 leads:3 nottingham:1 commute:7 kato:3 go:1 gn:3 gm:1 contributions:2 egles:1 factorizing:4 simon:1 depend:3 disposal:1 tr:6 environment:16 charge:3 monotonically:1 γm:3 under:3 norm:13 divergent:1 g2:3 g1:3 orthogonal:3 very:2 continues:1 choice:1 puzzles:1 markov:1 cook:1 condition:2 illustrated:1 exponential:1 presented:7 tre:16 solution:2 large:7 discrete:3 math:2 small:5 eigenvalues:1 trs:7 upper:1 strongly:2 smaller:2 consistent:2 estimates:5 measurable:1 second:2 evaluated:1 7th:1 specker:1 theory:14 spectral:9 plays:1 ihe:1 sum:1 uniform:7 experiment:1 subspaces:5 values:6 increasing:1 method:1 contrast:2 satisfy:8 full:1 ihβ:1 respectively:1 ihα:1 spacing:1 here:3 behaviour:2 objects:2 represented:3 affiliated:2 stamatescu:1 coupling:3 remark:2 technical:1 involved:1 vectors:4 periodic:2 definitively:1 fourier:1 uniquely:1 appropriately:1 formulated:1 projection:12 family:7 limt:2 weaker:1 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quant-ph9811011.txt |@word ψ1x:3 limited:2 φn2:1 φn1:1 secondly:1 magnetic:1 reversibility:9 consists:2 whose:5 calculate:2 γt:3 aus:1 γn:2 under:3 rise:3 experimentally:5 disturb:2 vibrational:21 ref:10 solution:4 steinbach:4 convenience:1 specially:1 deutsch:1 pulse:57 approximation:8 second:20 implemented:3 even:4 aim:3 nel:1 trapping:2 ˆx:15 ˆy:9 supplied:1 ˆd:1 above:26 ˆg:2 new:1 ˆj:9 coefficient:1 evolving:1 simultaneously:3 κi:2 never:3 equals:1 here:28 met:1 plenio:4 active:3 obtained:3 elaborate:2 suitable:1 appropriately:1 buˇzek:1 projection:2 explained:2 highly:2 turchette:2 counts:2 total:1 unit:1 would:7 abbreviations:1 m1:1 therefore:5 type:6 berlin:1 reversible:10 aligned:15 must:4 springer:1 mf:6 work:3 mj:5 concepts:2 akin:1 hansen:1 example:5 transition:41 wang:1 indicated:9 give:11 involve:1 degenerate:1 feasible:2 shelving:1 feature:1 how:18 hot:1 significance:1 gate:1 description:2 after:14 10mhz:3 speculatively:1 summarize:1 law:1 types:3 occurence:1 effective:2 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quant-ph9811012.txt |@word concept:1 partial:1 consider:1 ceases:1 crucial:1 forbidden:2 lack:1 focus:3 perelman:1 eds:1 ge:1 grateful:1 go:3 primes:1 denotes:1 contributions:1 localized:2 scr:1 increase:2 depend:6 ahmedabad:1 concerned:1 sines:1 vs:7 ts:1 finally:1 those:2 marks:5 anharmonic:11 straightforward:2 very:2 stroud:3 results:4 figs:5 govern:1 difference:2 exact:2 look:3 obvious:3 hamiltonian:1 mirror:1 fewer:1 discrete:1 eigenvalues:9 optics:2 trv:38 strongly:2 smaller:1 occurrence:1 dealing:2 estimates:1 nearing:1 pulse:1 likely:1 evaluated:1 further:1 dynamics:28 estimated:1 odd:8 addition:1 even:8 index:1 what:2 nonlinear:2 superlattices:1 giving:1 section:4 near:12 expressed:2 fock:1 causes:1 goes:2 fractional:11 new:2 increasing:2 waveguide:1 contrast:2 full:7 respectively:1 never:2 equals:1 here:7 understanding:2 behaviour:20 squeezed:8 asymmetry:2 address:2 extrema:1 equations:2 appears:4 obtained:1 2mπ:2 great:1 antisymmetric:1 study:8 studied:3 allows:1 culminate:1 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quant-ph9811014.txt |@word represent:1 consider:2 secondly:1 results:2 leads:1 quadrature:8 expressions:2 contributions:1 kowalski:1 technique:3 finally:1 those:1 analogous:1 worth:1 supported:1 hough:1 engineered:1 wave:3 resonant:1 experimentally:1 modulator:5 transmission:1 2κl:4 solution:1 large:1 detected:2 small:2 optics:2 sign:1 rate:2 evaluated:1 linear:1 adds:1 sub:1 giving:1 sum:1 consequent:1 experiment:2 above:6 capital:1 new:2 method:2 κl:2 respectively:1 mcclelland:2 equations:1 allows:1 commonly:1 lightwave:2 published:1 fourier:2 via:2 useful:1 extra:1 vin:5 modifying:1 brought:1 aˆν:2 logically:1 achievable:1 total:1 readily:1 conventional:1 would:5 comparing:1 noting:1 therefore:6 australian:3 theoretical:1 preserved:1 operators:5 normalized:1 ward:1 must:1 sample:1 springer:1 stabilized:3 locked:1 science:1 equation:4 work:1 oscillator:2 values:1 control:2 figure:4 mirrors:1 calculation:1 neglected:1 high:5 indicates:2 performed:1 council:1 linearized:1 verlag:1 arrangement:1 opt:1 description:1 may:2 after:1 designed:1 faculty:1 improving:1 readout:3 constants:1 effective:1 light:5 so:4 order:2 feedback:19 laboratory:1 radiation:13 stability:1 thermal:14 experiments:1 through:2 lasers:1 affect:1 its:1 jacobs:1 thank:1 chosen:1 absence:1 systems:1 suspension:2 non:2 photodetection:1 greater:1 practice:1 walls:2 front:1 nov:1 now:1 hall:1 matched:4 represents:3 term:1 fully:2 university:1 sufficiently:1 transmitted:1 mode:7 κin:4 acoustic:2 domain:5 series:1 energy:1 reduce:2 harb:2 frequency:6 entering:2 measurement:13 quantum:11 our:2 huntington:1 eq:6 out:1 shown:3 tombesi:1 rev:7 research:1 re:1 rf:2 daniel:1 drever:1 electronics:4 ref:3 shows:3 aˆl:1 tildes:1 theory:1 gardiner:1 free:1 standard:1 york:1 milburn:2 benefits:2 derivation:1 could:1 david:1 motion:2 turn:2 undesirable:1 assumed:1 consequence:1 first:1 already:1 shapiro:1 reflected:11 simplified:1 relations:1 suspended:1 ring:1 clarity:1 squashed:1 timothy:1 given:4 limited:2 their:1 system:11 approximately:1 indicate:1 rates:1 scheme:2 national:1 gives:3 imperfect:1 inefficient:1 enhancing:1 optical:1 authors:3 than:1 modes:1 detection:1 ben:1 showed:1 require:1 see:1 limiting:1 annihilation:1 amplitude:12 were:1 impinge:1 minus:1 pre:1 fluctuation:6 reduction:4 spectrum:4 any:2 efficient:1 isolated:1 performance:3 detector:2 10hz:1 added:1 significant:1 retaining:1 measured:2 considered:2 intrinsic:1 steady:2 highlight:1 part:2 mechanical:1 physics:1 fact:2 show:1 diode:1 probe:1 relation:2 substituting:1 analogue:1 find:6 based:1 parameters:2 commutators:1 state:7 peculiar:1 penalty:2 only:3 explicitly:1 factor:3 local:1 do:1 notation:1 expectation:1 beam:6 aν:3 gray:1 fields:2 arxiv:1 yield:1 acknowledgments:1 gravitational:1 satisfy:1 reference:3 achieved:1 sensitivity:2 relative:2 intensity:24 sec:2 result:1 discussions:1 close:1 optimum:1 best:1 ralph:3 written:2 use:1 between:2 justified:1 terms:2 nature:2 buchler:2 however:3 efficiency:3 incident:1 fluctuations:12 come:1 improve:1 taking:1 variance:1 expression:1 comes:1 reasons:1 perot:2 malcolm:1 applicability:1 described:1 suppressed:3 due:11 been:1 detuning:4 reflective:1 ph:1 territory:1 fig:1 corresponding:1 coherent:6 present:5 case:4 laser:10 value:1 will:12 while:1 ain:5 evaluating:2 error:3 squeezed:5 loop:17 va:7 pzt:1 demolition:2 make:1 locking:4 parts:1 quant:1 units:2 dimensionless:1 electro:2 infer:1 development:1 independent:1 used:7 optic:2 singapore:1 upon:1 effect:2 hand:1 saulson:1 user:1 vref:2 suitable:1 reflection:4 bachor:3 well:2 without:1 experimental:1 dashed:1 firstly:1 position:1 model:2 just:1 being:1 photo:1 obtain:2 gravity:2 sources:2 bandwidth:2 world:1 yamamoto:1 speed:1 josa:1 improvement:1 source:3 other:5 easy:1 poissonian:2 input:11 wiseman:3 excited:1 real:3 australia:1 increased:2 squashing:2 haus:1 department:1 vacuum:6 using:9 rear:1 loss:6 like:1 δx:3 signal:5 manual:1 always:1 output:3 because:2 methods:1 classical:4 back:2 mirror:7 provided:2 realistic:1 cavity:55 measurements:1 does:2 provides:2 assuming:2 demonstrated:1 measuring:1 noise:62 obey:1 power:2 fed:1 qnd:2 pressure:13 substituted:1 although:1 found:4 super:1 about:1 mixer:1 collett:2 carrier:1 ensure:1 introduced:1 soc:1 letters:1 presence:1 into:2 within:2 ηk:2 three:1 phase:25 stabilisation:2 operator:15 aref:3 statistics:1 additional:1 transfer:2 there:1 vaf:4 transform:1 long:1 width:1 appl:1 low:3 was:1 naturally:1 function:4 considerably:1 form:3 enough:1 fundamentals:1 ford:1 gain:5 impedance:4 line:1 yag:1 evident:1 inside:4 below:2 limit:6 pumped:1 demonstrate:1 agree:1 later:1 ad:3 defined:2 detectors:3 measure:2 am:1 scientific:1 formulation:1 intra:17 compared:3 dotted:1 no:3 corporation:1 whereas:1 nd:1 detail:1 field:21 interested:1 2db:1 test:1 interferometric:2 commutator:1 important:1 fabry:2 suppression:2 linearization:1 seismic:2 assume:1 typically:1 required:1 time:1 requires:1
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quant-ph9811015.txt |@word limited:2 sci:1 amplifier:7 results:6 quadrature:23 amplified:3 causes:1 amplification:8 ts:11 finally:1 efficiencies:1 analogous:1 include:1 indicating:1 division:1 downstream:1 far:1 rise:1 mixing:1 experimentally:2 difference:4 modulator:4 presented:1 transmission:1 noiseless:6 convenience:1 adjust:1 small:1 postdoctoral:1 optics:2 originally:1 upper:1 sin2:3 zero:1 video:2 further:1 rivera:1 linear:1 employ:1 appear:2 giving:1 d2:4 exactly:1 current:3 ˆa:1 experiment:5 goes:1 capital:1 new:1 method:3 exercise:1 coefficient:1 od2:1 component:5 teleportation:3 agreement:1 behaviour:1 cos2:2 excess:1 path:1 mcclelland:1 equations:2 obtained:4 trans:1 rigorously:1 losses:1 action:1 fourier:2 cancellation:2 plotted:1 garreau:1 via:1 convolution:1 extra:1 explained:1 achievable:2 traversing:1 total:1 plot:3 use:1 would:3 positive:2 transmissivity:1 arms:1 therefore:6 pzt:2 australian:5 theoretical:5 more:4 successful:1 becomes:1 operators:4 visibility:1 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quant-ph9811016.txt |@word 8d:1 limited:1 partial:1 remarkable:2 rev:1 results:1 fluids:1 gd:2 go:1 sci:1 saved:1 plasmas:1 localized:1 whose:2 ıs:1 inverse:1 nonlocal:1 does:4 under:2 discovering:1 include:1 far:1 ifsc:1 exception:1 wave:8 exact:1 condition:3 hamiltonian:1 turns:1 solution:15 large:1 math:3 small:2 relation:1 equation:27 possibility:1 cosh:2 zero:7 even:3 index:1 nonlinear:28 expressed:1 mycielski:2 current:2 goes:3 new:6 contrast:1 coefficient:2 edited:4 respectively:1 equals:1 free:6 making:1 strong:1 equations:4 appears:1 interpret:1 trans:1 shift:1 studied:2 completely:1 permit:1 suitable:1 studies:1 zhdanov:1 via:1 spatially:1 although:2 family:7 glance:1 derivatives:4 use:1 would:1 commun:1 positive:3 negative:1 a28:1 bialynicki:2 a54:1 usp:1 taken:1 type:2 until:1 more:1 ambiguity:1 solitons:9 odinger:7 berlin:1 normalized:1 particular:2 cases:3 must:2 account:1 valued:1 thanks:1 deformed:3 fls:12 modified:1 values:4 following:1 im:4 arrive:2 example:2 f0:2 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