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quant-ph9807059.txt |@word fredenhagen:1 consider:10 rev:2 results:4 four:5 commute:2 follow:1 contributions:1 reynaud:5 careful:1 equivalence:1 quasi:10 tj:6 grabowski:2 excluded:1 under:3 norm:1 summarizes:1 case:2 g1:1 very:6 singularities:1 rise:2 springer:3 wave:4 every:1 rm:5 jacob:1 matrices:6 wick:1 condition:7 irreducible:3 notes:1 large:6 discrete:2 vector:5 math:3 small:9 der:2 unexpected:1 lecture:1 sign:1 approximation:1 second:1 zr:3 zs:1 even:3 index:9 spacetime:1 stands:1 incompatible:1 section:8 favour:1 above:2 new:4 increasing:1 boost:1 satisfy:3 impact:1 outgoing:1 component:1 here:2 understanding:1 localisation:1 xβ:1 along:1 strong:5 z0:2 change:1 obtained:3 incoming:1 minorant:1 study:2 larger:1 fνσ:5 permit:3 unwanted:1 makes:1 york:3 uniquely:1 useful:1 fand:1 replace:2 naimark:1 summation:1 should:1 planck:2 derivatives:1 use:1 takes:2 would:3 commun:1 covariant:11 positive:6 contains:1 kα:1 jaekel:5 hilbert:5 ψj:1 linear:2 therefore:1 m2:1 metric:1 more:12 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quant-ph9807060.txt |@word monte:1 partial:1 consider:3 results:3 leads:5 contributions:1 2r0:4 devoted:1 whose:1 θq:1 attracted:1 technique:1 monotonically:3 th:1 under:1 provides:2 far:1 wave:3 chooses:1 difference:2 exact:3 condition:10 entire:2 solution:9 large:4 dealt:1 indices:1 3b:1 equation:21 wronskian:2 sturm:2 10a:1 sign:2 jump:1 second:1 insertion:1 further:1 theory:5 even:6 what:7 fubini:1 trivial:3 section:3 giampiero:1 iκr:2 expressed:4 above:3 fractional:1 new:5 3a:1 contributes:1 jumps:2 contrast:2 coefficient:5 compact:1 full:1 exchange:1 respectively:2 never:1 equals:1 here:2 ranges:4 desired:2 simon:1 tangent:1 separation:1 consideration:1 standard:2 equations:4 eikr:1 logarithmic:4 obtained:1 scienze:1 involved:1 study:1 studied:2 periodic:1 products:1 action:1 suitable:1 changes:3 cancellation:1 involves:1 genuinely:1 via:1 useful:4 merely:1 substitution:1 summation:1 total:1 angelo:1 eψ:1 would:2 prove:2 remains:2 positive:6 whittaker:1 negative:2 hilbert:2 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quant-ph9807061.txt |@word nω:12 spaced:1 consider:3 show:3 vanishing:1 brownian:11 results:5 presence:2 soluble:2 thermal:1 relevant:1 relation:1 using:1 gn:7 gm:2 contributions:1 its:2 figure:5 previous:1 position:1 secondly:1 vs:4 parameters:1 decay:4 chosen:1 iii:2 point:1 tr:2 send:1 rel:1 ıa:2 finally:2 microscopic:1 coefficients:3 under:1 relevance:1 mail:1 argentina:3 main:1 equilibrium:4 them:1 factor:1 around:3 frequencies:1 secular:1 de:5 increases:1 macroscopical:1 obtain:2 game:1 cannot:1 ciencias:1 words:1 press:1 during:1 exact:8 condition:3 thermalizes:1 eigenvalue:1 evolution:5 theor:1 hereafter:1 particle:3 hamiltonian:2 conditions:1 arxiv:1 solution:5 us:1 sin:2 garcia:3 magnitude:1 yields:1 follows:2 analytical:1 found:1 about:1 fixed:1 decreasing:1 distinguishes:1 lorentzian:1 referred:1 population:3 smaller:2 variations:1 2re:2 play:1 related:1 ωt:4 see:5 frequency:1 sec:3 result:1 respect:2 quantum:3 damped:1 eq:5 eβω:1 after:2 canonical:1 emerges:1 shown:2 scale:2 suc:2 exponential:3 astronom:2 macroscopic:1 stemming:1 langevin:8 below:1 iht:1 state:1 amplitude:1 provides:1 between:2 ωm:3 ref:3 math:1 shows:1 coefficient:1 gives:1 numerical:4 theory:1 initially:1 sudarshan:1 view:1 ısica:3 given:5 departamento:1 step:1 hypothesis:1 key:1 become:1 re:1 coupling:1 equations:4 distribution:1 interpret:1 asymptotic:3 obtained:2 observable:1 instituto:2 hidden:1 survival:2 derivation:1 interesting:1 taking:1 discussed:1 according:1 greater:1 reduced:1 motion:3 probabilities:1 int:1 important:1 figures:2 universidad:1 departing:1 contribution:1 mean:3 peak:1 aires:4 ψm:2 contains:1 recurrences:1 modulates:1 probability:2 extra:1 into:2 fig:4 harmonic:2 reaches:3 bath:6 scaled:1 aa2:1 because:1 computing:1 iafe:1 captions:1 gn2:4 recurrence:3 use:1 perturbation:1 temperature:1 comparing:1 introduction:1 leading:1 eqs:2 initial:5 visualize:1 system:2 needed:1 master:7 damping:2 time:10 taken:2 alvarez:3 ph:1 was:2 until:1 reflects:1 2i:1 sort:1 only:1 through:1 irreversibility:1 form:2 centered:1 quantities:1 explanation:1 exactly:2 nonexponential:1 cos:7 jul:1 oscillates:1 unstable:1 pnm:4 profiles:1 values:2 particular:4 known:1 general:1 irreversible:2 than:3 naturales:1 observation:1 reconstruction:1 account:2 te:1 showed:1 pacs:1 equation:11 work:2 oscillator:6 second:2 value:5 while:1 minimum:1 del:2 behavior:3 ωn:27 following:2 fluctuations:4 problem:1 more:2 proof:1 detailed:2 function:1 compare:1 constant:1 zeno:2 espacio:2 process:1 allows:1 exactas:1 fax:1 iv:2 ii:2 oscillations:2 reads:1 ar:1 physica:1 guevara:1 seen:1 times:2 apparently:1 orders:1 regime:2 functions:1 ing:1 completeness:1 nm:2 nn:5 no:1 ψn:3 essentially:1 discussion:1 when:1 same:1 grows:1 unity:1 purely:1 quant:1 generalized:1 buenos:4 several:1 privileged:2 consequence:1 profile:1 independent:1 criterion:1 coming:1 replacing:1 oscillators:1 mechanical:1 reached:1 effect:1 prepared:1 algebraic:1 a2:1 uba:1 facultad:1 fits:1 choice:1 pωn:3 period:2 stress:1 short:1 natural:2 dynamical:4 resolution:1 min:1 correspond:1 together:1 misra:1 secs:1 solve:1 ative:1 correlation:1 firstly:1 observables:1 model:6 first:1 arising:1 order:3 fact:1 laws:1
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quant-ph9807062.txt |@word represent:1 cosines:1 partial:1 consider:11 switched:1 rev:5 davies:1 particular:1 brownian:13 results:7 although:1 know:2 entropy:1 grateful:1 consists:1 gn:31 gm:7 contributions:2 izt:7 devoted:2 increase:1 preserves:2 inverse:2 tz:1 integral:4 departing:3 tr:2 corrections:1 tp:9 containing:2 ıa:4 finally:3 alvarez:1 present:2 under:2 stochastic:1 necessary:3 ın:1 case:19 g1:2 encircles:2 very:11 frequencies:25 bm:3 keeping:1 subject:1 wave:1 indication:1 ultraviolet:1 figs:4 traced:1 summarized:1 associated:2 difference:2 exact:12 condition:9 identity:3 laura:1 convince:1 steeper:1 riemann:3 hamiltonian:13 t4:1 trb:3 t2:1 solution:6 damped:5 large:3 discrete:3 convenience:1 phase:1 succession:1 small:14 eigenvalues:2 shows:6 optics:1 kozak:1 upper:3 population:1 mn:7 force:1 oscillation:1 zk:4 const:1 zf:1 estimates:4 direct:2 literature:5 bω:5 approximation:6 located:1 second:11 n31:1 growing:1 dynamics:2 estimated:1 odd:1 expressions:1 oscar:1 theory:4 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quant-ph9807068.txt |@word positions:1 consider:5 magnetic:1 stems:1 results:1 leads:1 scalar:1 soni:1 edu:1 4e0:2 dϕ1:1 dϕ2:1 gi:1 whose:3 certainly:2 inverse:1 re:1 tw:1 tr:3 quasi:1 th:1 under:1 include:1 di1:4 eikonal:3 oberhettinger:1 sound:1 supported:1 g3:1 g2:1 g1:1 far:1 frequencies:3 wave:3 every:3 resonant:1 exact:1 condition:3 entire:2 quantized:1 solves:1 presented:1 did:4 turns:2 applicable:2 correct:1 large:1 vector:5 magner:1 small:1 eigenvalues:5 degeneracy:1 application:1 employing:1 zi:2 nthu:1 consistent:2 arnimallee:1 direct:1 sign:4 approximation:10 fold:1 second:6 value:1 primes:1 spectral:1 index:3 nonlinear:1 plays:3 g23:1 sum:14 axes:1 expressed:2 agrees:1 current:1 ˆe:1 above:1 expresses:1 contributes:1 acknowledgments:1 component:1 here:2 understanding:1 china:1 ansatz:1 address:1 concluding:1 path:3 along:3 extrema:2 equations:1 balian:2 obtained:4 convert:1 hamiltonian:1 shift:1 study:1 vectors:2 allows:1 periodic:15 resulting:1 characterizing:1 poisson:2 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quant-ph9807070.txt |@word represent:2 consider:4 scratch:1 magnetic:2 comparatively:1 results:3 existing:1 roy:1 computation:4 edu:2 whose:2 boghosian:1 depend:1 calculate:6 re:1 alamos:1 technique:3 finally:4 under:2 include:3 applied:2 labels:1 amplitudes:2 very:1 frequencies:1 choice:3 electron:2 wishes:1 vastly:1 matrices:3 severely:1 hamiltonian:13 turns:1 t2:2 ffts:1 large:6 solved:2 vector:3 small:7 eigenvalues:15 solutions:1 approximately:1 force:1 estimates:1 approximation:1 second:4 implemented:6 even:2 index:5 what:3 errors:1 appear:3 sum:2 near:1 above:8 new:3 increasing:1 consisting:1 body:1 edited:1 evolving:1 full:3 explosion:2 exchange:1 error:1 component:2 desired:4 possibility:1 represented:2 invented:1 respect:1 appears:1 change:1 obtained:1 naval:2 involved:1 elaborate:2 vectors:2 reason:2 commonly:2 accomplished:3 resulting:2 suggestion:1 usually:1 resonance:2 implement:1 fourier:1 via:1 useful:2 extra:1 vij:3 requiring:1 merely:1 attraction:1 private:2 apply:3 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quant-ph9807078.txt |@word consider:4 magnetic:3 roy:1 grateful:1 follow:1 amplified:1 whose:1 acting:8 presents:1 finally:1 under:1 case:3 orthogonal:1 very:3 entries:1 resonant:1 experimentally:1 matrices:1 hamiltonian:1 accidentally:1 large:1 small:1 computation:2 deutsch:1 so17:1 pulse:1 sign:2 likely:1 pass:9 further:2 errors:2 rate:1 experiment:1 ˆf:7 method:2 led:1 penultimate:1 here:3 represented:3 consideration:1 observing:1 search:7 involved:1 leaves:1 larger:1 resulting:1 action:2 control:17 followed:6 extra:1 readily:1 use:1 would:2 distinct:1 soton:1 pedagogical:1 next:1 survive:1 jonathan:1 minor:1 becomes:2 operators:4 site:1 reversible:1 particular:1 known:1 grassl:2 challenge:1 work:1 grover:11 values:4 hansen:1 example:5 f0:11 nearest:2 process:1 states:3 effectively:1 acm:1 occur:1 united:1 end:1 s2:1 s0:2 ωres:2 write:1 located:1 pure:2 gate:6 sin:7 brassard:1 inputs:1 product:1 algebra:1 may:8 after:2 applications:1 produce:1 fl:4 realized:1 register:32 separations:1 si:2 negligible:2 sf:1 operations:3 restriction:1 acts:1 pretending:1 produces:1 displayed:1 course:2 through:10 still:2 before:2 maps:1 exact:1 persist:1 non:1 return:2 combination:3 propose:1 practice:1 introduce:1 i0r:4 effects:1 dar:1 symposium:1 now:5 discuss:2 easily:1 university:1 sufficiently:3 magnitude:1 each:4 2l:4 initialised:1 used:4 inverted:1 frequency:2 static:1 measurement:3 quantum:1 eq:1 out:3 biham:4 jul:1 matrix:3 rev:2 particles:2 rf:1 adapt:1 ref:1 shows:1 theory:1 interactions:3 given:2 standard:1 unwanted:1 jozsa:1 interaction:2 could:6 times:1 4th:1 lth:2 onto:2 first:1 initial:3 probability:3 number:1 directly:2 zalka:1 little:1 unknown:2 system:12 construct:1 returns:1 bits:8 hoyer:1 exactly:1 july:1 representing:1 than:1 coefficients:1 target:17 namely:2 project:2 amplitude:2 minus:1 explicit:1 argument:1 sf0:2 unlikely:1 close:2 need:2 seen:1 any:2 convenient:1 note:2 take:1 so:5 begin:1 multiple:1 though:1 molecule:1 firstly:1 encodes:1 phase:1 acknowledgements:1 measured:1 southampton:2 richard:1 consequences:1 considered:1 later:1 order:3 realised:1 physics:2 fact:1 quantity:1 optimal:1 registers:3 chuang:1 find:2 tapp:1 just:1 written:5 should:3 only:3 explicitly:1 employed:1 means:2 overall:1 cannot:1 words:1 arxiv:1 yield:1 consisting:1 london:1 discussing:1 set:1 achieved:1 depends:1 result:3 discussions:1 unaltered:1 subsequent:1 currently:1 sites:1 state:28 unable:1 between:4 terms:1 uk:1 nature:1 however:2 both:1 cos:4 annual:1 equal:5 experimental:1 simple:1 dimensional:2 simply:1 tony:1 addition:1 invert:1 three:1 been:1 workshop:1 ph:4 direction:2 corresponding:3 subspace:2 generalization:1 repetition:1 spin:11 applied:1 hughes:1 value:9 will:12 suppose:3 error:3 situation:1 manner:1 polymer:1 unitary:1 played:1 almost:1 refs:1 thus:2 them:1 envisages:1 different:3 author:1 perhaps:1 same:2 unity:1 quant:4 modification:4 solution:1 extended:1 see:2 i0:9 effect:1 hand:2 moment:1 purpose:1 identity:2 database:6 idempotent:1 without:1 boyer:1 clears:1 usual:1 proposed:3 being:1 obtain:8 actions:1 stored:2 using:1 useful:1 λl:3 field:2 except:1 initialise:1 lett:2 input:1 ross:1 kingdom:1 haux:1 repetitions:1 sˆf:1 integer:4 bit:20 projects:1 rotate:1 necessary:3 particle:1 follows:1 arbitrary:2 some:1 searching:1 28th:1 shall:2 proc:3 nmr:1 step:3 hadamard:2 integers:3 most:1 o:8 practical:1 soc:1 into:3 device:14 references:1 operator:11 proportional:1 removing:1 there:4 hey:1 fast:3 lidar:2 was:1 function:8 jones:2 but:3 consist:1 wish:2 flip:3 devices:3 owing:2 iterated:1 distribution:2 uf:11 similar:1 called:1 ac:1 defined:1 abstract:1 measure:1 single:1 sˆ0:5 check:1 constructed:1 mosca:1 compared:1 no:1 whereas:1 when:2 detail:1 application:5 other:7 role:1 department:1 1bj:1 elements:1 superposition:1 oracle:2 generalized:1 astronomy:1 searches:1 auxiliary:12 algorithm:12 assume:1 required:5 sˆ2:2 together:1 time:2 far:1 decoherence:1 original:1
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quant-ph9807079.txt |@word limited:3 monte:1 consider:5 represent:2 crucial:1 both:5 focus:2 zoller:4 leads:13 scalar:6 gb:2 computation:3 francesco:1 follow:2 expressions:2 gk:14 gr:2 compact:1 whose:3 inverse:1 depend:5 calculate:19 re:4 iii:37 deterministic:12 vs:1 contained:1 environment:42 finally:6 squeezing:18 those:2 under:9 hermann:1 stochastic:54 analogous:1 norm:1 unnormalized:2 case:8 belonging:2 random:2 expressing:1 straightforward:2 orthogonal:1 very:5 frequencies:1 straße:1 springer:3 wave:12 rl:3 ical:1 every:1 summarized:1 resonant:1 little:1 exact:7 fakult:1 condition:24 hdr:11 propagating:1 presented:10 evaluation:3 notes:2 t2:21 solution:18 t0:263 t1:41 large:4 solved:1 vector:3 demonstrated:1 small:5 eigenvalues:4 markov:19 rk:1 optics:9 grained:2 still:1 heinz:1 const:1 ψi:2 consistent:1 direct:3 literature:1 cosh:3 approximation:18 limǫ:1 second:21 lines:5 davis:1 equal:5 further:9 dynamics:24 estimated:4 carlo:1 dψ2:3 dψ1:5 linear:10 displacement:2 index:1 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quant-ph9807080.txt |@word represent:2 concept:1 consider:3 gq:2 results:2 leads:1 scalar:1 generalize:1 gl:4 whose:2 replacements:1 calculate:2 deterministic:4 environment:1 γi:6 tj:1 th:1 ti:3 hermann:1 stochastic:34 te:1 ta:1 g2:3 straightforward:1 orthogonal:1 very:1 straße:1 percival:2 wave:8 herder:1 exact:2 fakult:1 condition:10 four:1 level:4 ref:6 notes:2 t2:17 solution:11 t0:44 t1:32 large:1 vector:4 optics:4 correct:1 consistent:1 measurable:1 jump:9 second:1 further:2 dynamics:2 estimated:4 dψ0:2 even:1 sub:1 brackets:1 expressed:1 uniform:1 above:2 new:4 contributes:1 method:5 simultaneously:1 malized:1 respectively:2 realizations:1 component:1 here:3 ansatz:1 alone:2 quite:2 equations:1 alicki:1 obtained:5 remark:1 vectors:5 resulting:1 procedure:1 resonance:2 fourier:1 uniquely:2 castin:4 compare:3 replace:1 select:1 tn:7 use:1 would:1 distinct:1 positive:1 finally:1 next:1 calculation:13 type:4 until:1 operators:17 under:1 odinger:4 berlin:4 appendix:1 normalized:3 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quant-ph9807081.txt |@word consider:2 leads:1 roy:4 tricomi:2 consists:1 follow:1 gj:1 gi:1 devoted:1 whose:1 c0:7 terms:4 essentials:1 technique:1 groundstate:1 recurrence:1 finally:1 those:4 under:1 fh2:1 applied:1 orthogonal:1 very:2 rise:2 witten:1 nieto:4 parameter:1 exact:1 condition:1 generalised:3 entire:1 hussin:1 hamiltonian:1 turns:1 eigenvalues:3 dutra:1 sign:1 second:1 gn:3 further:1 dψ0:1 spectral:2 nonlinear:3 appear:1 giving:1 d2:1 section:5 expressed:2 indian:1 above:5 new:4 method:3 contrast:1 body:1 dψn:1 degree:1 respectively:2 here:6 inverse:2 ansatz:1 groups:1 xγ:1 respect:1 transformation:4 obtained:5 remark:1 singapore:1 institute:1 involved:1 usually:1 suitable:1 varshni:1 via:6 replace:1 resolutions:1 unit:2 plot:2 proceed:1 would:3 positive:5 properties:7 few:1 call:2 therefore:2 more:7 lowering:3 becomes:2 operators:12 berlin:2 particular:2 known:4 cases:1 iii:2 springer:1 deformed:2 recall:2 oscillator:8 salam:1 erd:2 fock:4 values:4 following:5 making:1 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quant-ph9807082.txt |@word represent:1 consider:2 rev:7 excellent:1 results:1 leads:1 scalar:1 computation:2 francesco:1 whose:2 calculate:1 deterministic:2 tr:1 quasi:3 preserved:1 stable:2 hermann:1 stochastic:22 norm:1 straße:1 percival:3 wave:7 exact:1 fakult:1 condition:2 hamiltonian:2 notes:1 solution:15 t0:6 vector:4 optics:4 heinz:1 jump:4 estimated:2 even:1 established:1 qsde:1 uniform:1 above:6 new:3 method:3 thin:1 respectively:1 realizations:5 dψt:2 equations:8 obtained:4 vectors:1 suggests:1 resonance:2 suitable:1 plotted:2 castin:1 replace:1 glance:1 readily:1 use:1 takes:1 remains:1 positive:1 ψt:32 calculation:6 more:2 started:1 operators:13 berlin:3 appendix:1 particular:3 unraveled:1 springer:3 valued:1 integrating:2 equation:25 work:1 reproduce:1 values:1 ρt:2 following:2 example:3 compare:1 figure:2 2lj:4 process:7 preserving:1 numbers:3 verlag:3 end:1 pure:1 product:1 description:2 may:1 hence:2 physik:1 summarize:1 short:1 dynamical:1 lines:3 element:5 correlation:7 order:5 superscript:1 ito:2 developed:2 stability:1 wiener:1 through:2 mentioned:1 its:1 lc:1 lj:33 choose:1 lq:1 rabi:1 motivated:1 propose:1 φˆt:1 processes:1 framework:2 walls:1 now:1 drop:1 each:3 universit:1 mean:3 differential:14 formulate:1 idea:1 extended:5 multitime:4 measurement:1 quantum:38 eq:3 special:1 shown:3 matrix:23 space:7 since:2 crucial:2 denotes:3 acting:1 herder:1 lecture:1 ref:5 linear:3 gardiner:3 free:1 standard:2 completely:1 york:3 ρij:2 generate:1 milburn:1 could:1 times:1 motion:3 δij:1 freiburg:1 first:4 directly:1 thick:2 open:4 given:3 necessarily:1 system:9 master:10 realization:3 show:1 scheme:4 petruccione:4 albert:1 part:1 superoperator:1 believe:1 than:1 diffusion:17 determines:1 unfortunately:1 accordance:1 breuer:4 fig:4 any:1 efficient:1 latter:1 note:2 performance:1 bernd:1 accuracy:1 heisenberg:11 dθt:1 reach:1 extending:2 propagate:2 but:3 kappler:2 2tr:1 pair:1 ludwigs:1 measured:1 deviations:1 surprising:1 calculated:2 steady:2 physics:2 fact:3 restriction:1 random:3 solutions:2 longer:1 lindblad:4 based:5 dalibard:1 only:2 notation:1 means:1 expectation:3 cannot:1 propagated:1 during:1 dt:12 carmichael:1 evolution:7 arxiv:1 doubled:6 analytical:5 qj:1 view:1 parkins:2 computed:2 correlations:1 relative:2 see:1 individual:1 result:2 closer:1 federal:1 state:25 various:1 correctly:2 diamonds:3 drawn:1 approach:5 recently:1 transpose:1 however:2 unnormalized:1 fluctuations:2 problem:1 both:1 equal:1 point:3 simply:1 respect:2 throughout:1 proceeded:1 dum:1 basis:1 addition:1 due:1 been:1 immense:1 much:1 interest:1 outweighed:1 ph:1 systems:4 corresponding:1 quantities:1 sufficient:1 covariance:3 coherently:2 systematic:1 θt:11 applied:1 pacs:1 solid:3 value:2 will:1 error:2 procedure:4 real:1 larger:1 coupled:2 thus:1 ih:1 vs:2 im:1 regression:4 φt:15 unity:2 complex:1 quant:1 mølmer:1 regime:1 used:1 numerical:13 hand:2 driven:2 relies:1 obviously:2 model:15 proposed:5 accurate:1 obtain:3 proposes:2 alternative:1 zoller:2 density:9 seems:1 ψˆt:1 lett:3 samples:1 theorem:4 heidelberg:3 resolved:1 dφt:1 vacuum:1 using:6 mod:1 necessary:1 sizes:2 alternatively:2 specific:1 yields:1 reduced:2 some:3 unraveling:3 peter:1 describing:1 integration:3 per:2 unstable:1 demonstrated:1 inserting:1 noise:1 seconds:1 jumps:1 agreement:2 step:3 although:2 described:4 hilbert:7 about:1 extension:1 piecewise:1 simulation:6 practical:1 ensure:1 germany:1 introduced:1 computational:1 letter:2 into:1 within:2 hermitian:1 square:2 references:1 operator:7 initial:5 start:1 accordingly:2 way:3 was:1 θˆt:5 function:10 complete:1 form:1 governs:1 jul:1 construction:2 link:1 atom:2 line:4 level:3 he:1 applying:1 evident:1 smooth:1 up:3 ur:1 frequency:1 demonstrate:1 distribution:1 define:4 similar:2 gisin:7 constant:1 defined:2 abstract:1 specified:1 general:3 single:1 av:1 constructed:2 functions:4 compared:1 dashed:2 whereas:1 other:1 republic:1 deviation:4 picture:10 draw:1 elements:8 models:1 symbol:1 dissipation:1 m18:1 faster:1 algorithm:6 governed:2 cpu:1 eθ0:1 time:14 observables:1 original:1
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quant-ph9807083.txt |@word consider:2 rev:2 results:1 contributions:1 causes:1 simon:1 does:3 under:4 case:7 fax:2 springer:1 ieice:1 wave:10 electron:15 summarized:1 mixing:1 affect:2 exact:1 condition:16 disturb:1 level:3 solution:3 mπx:1 fourier:1 small:17 eigenvalues:5 sidelengths:1 mishima:2 strongly:2 smaller:1 force:2 findings:2 direct:2 approximation:2 gθ1:1 further:1 dynamics:3 estimated:2 mπ:1 nonlinear:1 rectangles:1 section:2 current:1 above:1 new:2 body:1 full:1 degree:1 respectively:3 promising:1 component:2 here:2 okubo:1 ranges:1 ρav:7 gesztesy:1 ratio:1 strong:11 appears:2 changes:1 suitably:1 larger:1 krohn:1 published:1 suitable:1 makes:1 examining:1 yamada:1 family:1 summation:1 apply:1 prove:1 contains:1 monotonically:1 ψm:3 inner:1 formally:1 naive:1 validity:2 phone:2 dirichlet:1 normalized:2 known:1 cases:2 iii:1 high:1 keeping:1 equation:7 work:2 following:2 trans:1 transition:2 give:1 discussed:1 neglected:1 conjecture:1 states:3 indicates:2 conversely:1 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quant-ph9807084.txt |@word limited:1 dewitt:1 consider:3 rev:3 results:2 four:1 scalar:3 abelian:1 computation:2 expressions:1 contributions:8 whose:1 irrelevant:1 concerned:1 tq:2 tn:1 alvarez:2 aut:1 breach:1 te:2 worth:2 divergent:12 applied:1 unrenormalized:1 amplitudes:1 rescue:1 straightforward:2 far:1 rise:2 wave:2 wishes:1 ultraviolet:12 tmi:1 difference:1 logarithmically:5 leads:2 hamiltonian:8 turns:2 t2:1 make:2 t1:1 large:3 vector:1 dealt:1 small:5 inertial:2 programme:1 employing:2 zi:6 renormalized:8 consistent:2 direct:3 matrices:2 rate:3 analogue:2 linear:4 residue:1 employ:1 what:1 stands:2 sum:3 contracted:1 henceforth:1 above:3 capital:1 new:5 principal:1 edited:1 divergence:1 here:5 behaviour:9 governing:1 others:1 represented:1 appears:1 rigorously:1 study:2 involves:1 york:4 uniquely:1 boundedness:1 useful:2 elaborated:2 contrarily:1 integrations:1 replace:3 aph:10 apply:1 glance:1 total:3 linearly:2 readily:2 conventional:2 feb:1 would:3 sake:1 positive:2 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quant-ph9807085.txt |@word jason:1 consider:6 gp:3 varying:2 splitting:1 four:1 roy:1 contributions:1 devoted:1 inverse:3 depend:1 alamos:1 deterministic:6 interactions:1 under:8 analogous:2 case:1 random:1 amplitudes:3 g2:5 g1:4 orthogonal:1 far:1 frequencies:8 conditions:2 g9:2 bratislava:4 gou:1 maali:1 figs:1 sidebands:2 resonant:5 condition:2 leads:2 vibrational:20 hamiltonian:13 turns:1 solution:2 vector:7 small:1 optics:4 application:1 smaller:2 second:2 design:1 further:1 dynamics:2 subscripts:1 established:1 what:1 abc:12 cˆj:3 trapping:4 advantageous:1 ˆx:1 diag:2 section:1 axes:1 expressed:1 sequential:1 subspaces:7 3b:2 ˆj:7 ˆk:1 method:1 3d:11 pˆa:1 respectively:2 realizations:2 component:22 here:3 atoms:1 desired:6 replacements:1 free:1 address:2 represented:2 consideration:2 along:1 quite:1 observing:1 obtained:3 great:1 institute:2 involved:2 studied:1 eberly:2 twamley:2 resulting:1 action:11 resonance:3 king:3 matos:2 buˇzek:2 via:5 projection:1 scales:1 turchette:1 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quant-ph9807086.txt |@word concept:1 consider:1 rev:10 results:1 four:7 tapping:1 research:1 depend:2 alamos:8 swap:2 amplitudes:7 bratislava:3 print:8 affect:1 difference:1 condition:1 swapping:4 presented:6 ref:3 vector:3 optics:1 hillery:8 elegant:1 perspective:1 estimated:1 machines:3 what:2 appear:1 expressed:1 networks:2 new:3 bruß:3 simultaneously:4 here:4 plenio:1 address:1 represented:2 extreme:1 cerf:6 generalizing:1 institute:2 involved:1 study:1 vectors:2 allows:1 prior:1 situations:1 action:2 bob:10 suitable:1 emerge:1 buˇzek:13 via:7 followed:1 griffiths:2 family:1 logical:3 scaled:3 apply:1 would:3 massar:4 generate:1 classically:2 explicitly:1 therefore:1 ib1:1 type:1 theoretical:1 preserved:1 sharing:1 composite:2 outputs:1 operators:3 controlling:1 normalized:1 known:2 cases:1 iii:1 account:1 der:1 values:1 following:1 fulfill:1 proof:2 control:7 process:2 allowed:2 states:9 performed:7 sense:1 inseparability:1 information:19 s1:21 s0:21 how:3 pure:7 optimal:9 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quant-ph9807087.txt |@word camacho:2 barone:1 consider:3 represent:2 results:2 leads:1 eds:2 scalar:1 diss:1 go:1 localized:3 scott:3 γy:2 careful:1 depend:1 superpositions:1 unanswered:1 environment:6 answered:1 finally:1 aut:1 stochastic:1 interacting:1 very:8 wave:17 puzzles:1 electron:20 every:2 decide:1 exact:1 condition:6 look:2 osi:2 level:1 issue:3 t2:1 solution:12 large:1 integro:1 small:7 relation:6 optics:2 der:1 smaller:2 supression:1 approximation:1 fold:1 konstanz:3 deutscher:1 traveling:1 fong:1 further:1 salam:1 theory:11 even:7 employ:1 nonlinear:6 plays:1 appear:2 macroscopically:1 d3:2 current:2 goes:2 new:8 solitonic:9 body:3 respectively:1 never:1 certainly:1 here:4 behaviour:3 objects:2 possibility:1 situation:2 along:1 sine:2 equations:10 appears:1 obtained:4 search:3 wesley:1 involved:3 study:2 experience:1 example:1 changes:1 broglie:1 holmes:2 emerge:1 addresses:1 extra:2 substitution:1 plenum:2 assertion:1 addressed:2 approches:1 readily:4 proceed:1 would:3 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quant-ph9807088.txt |@word partial:1 consider:2 rev:5 magnetic:1 amplifier:2 results:1 leads:2 zˆj:2 scalar:1 ga:10 gj:2 localized:1 whose:2 inverse:1 violate:2 aug:1 subjected:1 presents:1 finally:1 does:2 squeezing:1 present:4 under:2 tc:2 indicating:1 confirmation:1 far:3 maximized:1 springer:1 wave:9 electron:1 manipulated:3 resonant:3 treating:2 hamiltonian:5 evaluation:1 guo:1 solution:3 large:8 small:1 eigenvalues:3 referred:1 optics:7 linearizing:1 upper:5 consistent:3 direct:2 past:1 rate:2 enhancement:1 sustaining:1 further:1 dynamics:1 theory:1 even:1 nonlinear:1 wavenumbers:1 appear:1 section:1 remain:1 find:1 current:1 ˆa:1 experiment:1 gi:4 new:2 ever:1 contrast:2 satisfy:1 edited:1 degree:1 exchange:1 respectively:2 component:6 here:5 atoms:5 amplification:1 consideration:1 strong:6 equations:1 obtained:1 almost:1 naval:1 study:1 studied:2 periodic:1 resulting:1 usually:1 resonance:1 studies:1 controled:1 involves:1 followed:2 vij:1 vik:1 vio:1 vapors:1 decrease:1 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quant-ph9807089.txt |@word consider:1 rev:8 avalanche:1 transmittances:1 calculate:3 paris:1 γk:12 tj:1 th:1 under:2 td:1 worth:1 norm:1 overlaps:1 advantage:1 far:1 mixing:1 condition:2 rα:1 splitter:13 guo:1 large:1 solved:1 vector:1 succession:3 zn:1 10a:1 zero:5 traveling:10 dynamics:1 what:1 goes:1 designing:1 new:1 increasing:1 method:6 edited:1 led:1 degree:1 d1:3 respectively:1 here:3 atoms:4 desired:3 address:1 strong:2 equations:1 obtained:1 suitably:1 leaving:2 resulting:1 adopting:1 transmittance:7 appropriately:1 via:1 projection:2 greenbelt:1 highly:1 summation:1 fed:1 shepard:1 commun:1 probabilities:1 abbreviations:1 comparing:1 noting:1 ψn:1 more:1 operators:1 aware:1 particular:1 producing:5 bagnato:1 recall:1 setup:1 work:1 oscillator:2 mk:2 fock:9 values:4 following:1 γkl:1 control:1 dn:1 figure:2 mirrors:1 calculation:1 states:27 performed:2 tab:1 absolute:2 straightforward:1 kwiat:1 rather:1 write:2 pure:2 opt:2 displacements:1 undergoing:1 algebra:2 may:4 max:1 after:6 hong:1 produce:1 man:1 realized:5 joint:1 register:3 deutsche:1 so:1 enter:1 βk:5 order:3 operations:1 moussa:1 move:1 satisfied:1 produced:3 timing:1 paper:1 through:1 jaynes:2 roots:5 before:2 derive:1 rapidly:1 energies:1 ll:1 lm:2 lk:1 detected:1 offers:2 fig:2 photodiodes:1 eventually:1 non:2 propose:2 outlined:1 pegg:2 they:1 now:1 always:1 routines:1 alternately:1 possibilities:1 l2:1 mode:22 each:1 universit:1 2k:1 schemes:2 clausen:1 generation:5 barnett:2 displacement:13 challenges:1 jena:2 entering:1 measurement:6 quantum:12 laboratory:1 approximated:1 eq:13 event:1 shown:3 evy:1 crucial:1 mattle:1 shows:1 numerical:2 possibility:1 standard:1 approaches:1 ask:1 detecting:1 definition:1 pairs:1 interaction:1 times:1 place:1 hence:1 βn:6 5th:1 first:4 already:1 probability:11 laguerre:1 rydberg:1 pn2:1 number:1 channels:3 done:1 array:2 illustrate:1 given:7 rewritten:1 their:1 eqs:7 relations:1 indicate:1 calculations:1 realization:1 scheme:4 loudon:1 gives:1 collapse:2 forschungsgemeinschaft:1 tapster:1 optical:1 july:1 see:3 rarity:1 preparation:3 determined:2 kth:2 were:1 result:1 ann:1 substantial:1 seen:1 weinfurter:1 any:5 conversion:1 efficient:1 latter:1 note:3 phillips:1 generalized:1 detector:3 channel:1 accuracy:1 towards:1 αl2:1 αl1:2 most:1 germany:1 jul:1 phase:6 acknowledgements:1 kj:2 calculated:4 detectors:2 kn:3 tpi:1 proceedings:1 principle:1 exp:2 show:1 supported:1 bring:1 relation:2 superimposed:2 substituting:1 d2:2 find:3 ground:3 based:2 parameters:4 implementation:3 only:1 local:1 pk2:3 do:1 dk:1 ko:1 beam:17 preparing:3 international:1 opatrn:1 platz:1 carmichael:1 fields:5 arxiv:1 summary:1 experiments:1 photodetectors:1 ban:1 qo:1 shapiro:1 requirement:1 set:1 alsing:1 reference:1 achieved:1 depends:1 injecting:1 truncating:1 optimum:1 subject:1 interacting:1 resonantly:1 subsequent:1 state:44 various:1 αk:9 αj:2 conditions:1 αl:3 αn:3 emitted:1 article:2 both:1 last:1 uncertainty:1 according:1 mixings:1 chosen:5 experimental:4 splitters:4 point:1 simple:1 corresponds:1 nˆ:14 simply:1 polynomial:6 table:2 cp:1 schleich:1 conference:1 second:1 basis:1 wien:1 been:5 interest:1 basic:1 pk:1 ph:2 abstract:1 controlled:1 sergienko:1 bmk:2 photon:17 zeilinger:1 coherent:12 external:1 former:1 case:3 reciprocal:1 theoretisch:1 solid:1 value:2 applies:1 squeezed:1 procedure:2 reflectance:2 unitary:2 vogel:1 coupled:1 equal:1 im:1 il:2 yˆ:13 agarwal:1 different:1 radiation:2 same:2 unity:1 complex:1 quant:2 finite:3 used:6 schiller:1 i1:5 i2:2 uses:1 kim:1 modes:6 well:2 obviously:3 model:1 parametric:1 researchers:1 proposed:3 being:3 obtain:2 bi1:1 adding:6 enters:1 han:1 application:2 photons:6 alternate:3 improvement:1 friedrich:1 lett:7 excited:1 identical:1 bim:1 increases:1 vacuum:6 using:8 mod:1 displaced:2 follows:1 signal:2 performing:2 specific:3 yields:2 arbitrary:5 output:7 reduced:1 right:1 classical:1 truncated:6 conditional:4 oll:3 added:3 choosing:1 cavity:15 measurements:3 does:2 assuming:1 welsch:3 measuring:3 l1:2 expansion:1 step:3 binomial:1 become:1 exciting:1 repeating:1 stage:2 column:1 aˆ:2 recalling:1 mixed:1 introduced:1 sensitively:1 cummings:2 beamsplitter:1 into:3 within:1 attains:1 down:1 square:1 references:1 operator:4 institut:1 additional:1 assumed:2 question:1 mandel:1 way:1 was:1 synthesis:2 function:1 creation:1 form:2 some:2 registered:2 regard:3 but:1 repeated:1 atom:3 line:2 highest:1 collapses:1 made:1 characteristic:4 maximum:1 us:3 physikalisches:1 distribution:1 similar:1 shih:1 associated:1 ln:1 defined:2 certain:1 ak:2 combining:2 single:11 our:1 physical:1 compared:1 dotted:1 no:1 tara:1 when:3 field:16 other:3 leblond:1 ured:1 elements:1 superposition:5 symbol:1 nonclassical:1 prepared:10 generated:2 correlated:1 assume:1 starting:1 required:1 b1k:1 nasa:1 requires:1
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quant-ph9807091.txt |@word concept:3 partial:1 consider:23 rev:21 both:3 reversibility:2 results:9 illustrated:3 proposition:4 generalize:1 comments:1 prop:1 causes:1 equivalences:1 devoted:1 increase:3 certainly:3 inverse:1 depend:5 calculate:2 iii:4 subjected:2 technique:4 tr:6 quasi:23 protocols:2 fidelity:71 analogous:2 bni:2 dramatically:1 sent:2 applied:6 supported:3 performs:1 orthogonal:1 far:3 activation:1 none:1 seemingly:1 focus:1 reordering:1 allowed:3 fall:1 experimentally:1 matrices:2 condition:6 common:1 dim:1 presented:2 transmission:5 supports:2 trb:3 t0:3 large:3 convenience:1 adjust:1 math:2 science:1 small:3 eigenvalues:1 strongly:2 work:2 says:2 bn2:3 haar:3 direct:2 outcomes:2 second:7 noise:1 invariant:8 implemented:1 even:7 will:39 what:2 lemmas:1 plays:1 reformulated:1 rate:1 deliberate:1 diag:4 section:14 analogously:1 uniform:2 pawel:2 version:1 transformed:1 above:12 deal:2 shared:2 increasing:13 bn:14 contrast:1 aua:1 full:3 notions:2 degree:1 exchange:1 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