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quant-ph9907046.txt |@word consider:1 rev:13 issues:1 technique:1 γt:2 environment:1 quasi:1 present:1 under:2 fax:1 reconstructions:1 bringing:1 condition:2 paz:1 vibrational:1 level:2 knight:3 proposals:1 solution:1 optica:1 puebla:1 markov:1 optics:2 lˆ:1 upper:1 slower:1 dutra:3 direct:2 pulse:1 approximation:2 zero:2 even:3 errors:1 sum:1 homodyning:1 above:1 international:1 method:3 coefficient:1 atoms:2 address:5 dissipated:1 strong:2 great:1 shift:1 losses:2 completely:1 usually:1 resonance:1 fourier:1 useful:1 although:1 consejo:1 2δn:1 wataghin:1 ıa:1 use:1 would:3 remains:1 therefore:1 ciencia:1 γn:2 started:2 initial:13 operators:1 phone:1 known:1 negativity:1 must:1 states:2 account:1 equation:1 work:1 evolved:2 making:1 mx:1 leonhardt:2 give:1 process:1 dependence:1 high:1 allowed:1 occur:1 information:3 endoscopy:1 how:2 cessa:3 may:1 after:5 applications:1 amparo:1 destructive:2 stress:1 short:1 light:2 sp:1 cascade:1 allow:2 subsequently:1 order:1 wigner:8 over:1 soon:1 paper:1 london:1 statistical:1 existence:1 its:5 paulo:1 decay:9 gleb:1 lt:1 permanent:1 superoperators:1 main:1 them:2 propose:1 they:1 now:1 wiley:1 easily:1 february:1 university:1 presented:1 γ2n:1 refresh:1 realistic:1 mode:4 2n:2 macchiavello:1 ifi:2 schemes:1 series:1 barnett:2 displacement:1 used:3 measurement:1 quantum:17 our:3 damped:1 eq:3 out:1 shown:1 matrix:5 driving:1 space:1 crucial:1 leidenuniv:1 cahill:1 induced:1 desenvolvimento:1 written:1 pue:1 ısica:1 diagonal:6 possibility:1 davidovich:1 approaches:1 york:1 driven:1 interaction:3 ion:1 determining:1 could:1 times:2 wallentowitz:1 already:1 probability:1 number:1 electronic:4 given:3 temperature:2 glauber:1 their:2 master:1 scheme:3 store:1 ictp:1 exactly:1 optical:1 injected:1 than:5 population:3 tomographic:1 annihilation:1 compensation:1 amplitude:1 need:1 any:2 note:1 instance:1 potential:1 take:1 new:1 centre:1 most:1 jul:1 phase:1 exico:1 δn2:3 cover:1 typeset:1 reflecting:1 exp:4 χm:1 normally:3 quantity:1 show:3 supported:1 tecnol:1 state:19 only:2 achieve:1 coherences:4 do:2 reconstruction:5 means:1 zurek:1 de:7 ones:1 words:1 despite:1 dv:1 reconstruct:3 processes:1 fields:1 arxiv:1 acknowledgments:1 qm:1 qn:1 withstand:1 thesis:1 up:1 habib:1 computer:1 injecting:1 result:1 techniques:1 brazil:3 preparation:1 wo:1 enough:4 barranco:1 importance:1 configuration:1 observable:1 cos:3 ıfico:1 region:1 cup:1 against:1 contribution:1 apdo:1 experimental:1 point:2 homodyne:1 sampling:1 schleich:1 aˆ:1 due:1 been:2 detuning:1 much:5 ph:2 pn:4 define:1 ariano:1 enable:1 corresponding:1 tecnolog:1 both:1 coherence:1 photon:1 instituto:1 coherent:3 determination:1 those:1 case:2 novel:2 moya:3 will:4 cancelled:1 procedure:1 vogel:3 mexico:1 different:1 italy:1 make:1 radiation:1 same:1 shorter:4 complex:1 quant:1 several:1 inaoe:1 literature:1 estadual:1 effect:2 campinas:2 possible:1 parametrized:1 action:3 robust:3 estado:1 identity:1 lower:1 off:1 expression:1 well:1 displacing:2 kiss:1 obtain:4 stored:1 thanks:1 immediately:1 ogico:1 density:5 nacional:2 valid:1 conacyt:1 lett:4 mod:1 transformation:1 generalized:1 reconstructing:1 louisell:1 inversion:3 using:2 postal:1 formal:1 loss:1 displaced:3 like:1 lost:2 herzog:1 signal:1 jˆ:4 unbalanced:1 reduces:1 therein:1 parity:1 methods:1 creation:1 tasche:1 born:1 choosing:1 specified:1 scale:3 amongst:1 cavity:11 electromagnetic:1 avoid:1 fapesp:1 comments:1 exit:1 τmax:1 welsch:1 conselho:1 trap:1 measuring:2 destroys:1 revtex:1 br:2 banaszek:1 properties:1 bz:1 about:3 basis:1 discussed:1 ρˆa:1 range:2 cambridge:1 presence:1 into:2 three:1 multiply:1 references:2 inverting:1 determine:1 operator:1 assumed:1 there:1 cient:1 stark:1 way:2 was:1 opens:1 function:9 but:1 atom:1 cnpq:1 funda:1 partially:1 made:1 inside:1 robustness:2 maximum:1 us:3 theoretical:1 below:1 pm:2 constant:2 computing:1 abstract:1 measure:1 ao:2 single:2 tomography:1 distributions:1 universidade:1 regime:1 nl:1 when:1 field:12 other:2 becomes:1 conclusion:1 picture:1 elements:7 phoenix:1 unicamp:2 pesquisa:1 nonclassical:2 prepared:2 generated:1 dissipation:8 transfers:1 implies:1 coupling:3 assume:1 physics:1 dτ:1 time:13 decoherence:1 having:2
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quant-ph9907047.txt |@word limited:1 consider:9 isotropically:1 results:4 leads:1 mni:1 helped:1 mnk:1 entropy:1 grateful:1 denotes:1 devoted:2 particles:3 depend:1 tr:13 a011:4 thapliyal:1 williamstown:1 monotonically:2 those:8 under:6 analogous:2 worth:1 resources:1 ta:3 belonging:1 supported:1 straightforward:1 returning:1 very:3 otteler:1 focus:3 manipulated:1 fall:1 σtl:1 difference:2 matrices:4 four:6 obvious:1 quantitatively:1 presented:1 did:1 positions:1 trc:1 indices:3 eigenvalues:8 mahler:1 configurations:2 consistent:2 murao:2 hillery:1 elegant:1 zero:7 further:2 even:1 established:1 what:6 abc:4 giving:1 sum:7 expressed:3 d3:4 above:2 shared:2 increasing:2 satisfy:2 simultaneously:1 ρac:5 ρab:26 applies:1 teleportation:1 here:3 desired:1 explore:1 objects:8 focused:1 governing:1 address:1 along:1 strong:1 equations:1 appears:1 interpret:1 extreme:1 obtained:1 institute:2 involved:1 study:1 studied:1 amount:4 resulting:2 published:1 action:2 hospitality:1 makes:1 involves:1 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quant-ph9907048.txt |@word limited:1 concept:1 partial:4 consider:1 interference:1 lack:1 results:5 illustrated:1 quadrature:17 entropy:4 overlap:1 broader:1 whose:1 amplification:1 producing:1 pˆj:1 squeezing:4 under:3 x02:2 analogous:1 applied:1 advantage:1 far:1 p0:1 wave:10 wishes:2 figs:1 mixing:1 matrices:1 condition:1 splitter:13 transmission:1 pacs:1 t2:3 t1:3 pˆ1:3 pˆ2:2 progress:1 science:2 indices:1 shows:2 optics:2 upper:1 work:1 deutsch:1 direct:1 second:1 displacement:3 what:1 sum:1 expressed:1 shared:6 increasing:1 method:1 full:1 simultaneously:1 degree:11 respectively:1 never:1 component:15 teleportation:18 here:1 diagonal:1 highly:1 plenio:1 represented:1 consideration:1 along:1 appears:1 change:1 extreme:1 box:1 sending:1 property:1 sender:2 institute:1 study:1 losses:1 suggests:1 base:1 resulting:4 schumacher:1 bob:5 plotted:3 transmittance:2 via:2 subtracts:1 reflectance:4 hermite:1 modifying:1 decrease:2 aimed:1 kurizki:1 apply:2 select:1 would:1 commun:1 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quant-ph9907049.txt |@word ibid:7 consider:2 amplifier:4 leads:1 quadrature:4 computation:1 follow:1 ρss:1 replacements:1 terms:1 auckland:2 faraday:1 nonlocal:1 kγ:1 finally:1 squeezing:1 γn:2 analogous:1 resources:1 p2:9 amplitudes:8 g0:5 very:2 frequencies:6 modes:7 seemingly:1 wave:5 electron:1 resonant:1 difference:1 condition:3 school:1 europhys:1 2κc:3 facilitate:1 vibrational:1 level:1 positions:2 tanh:1 mirror:3 solution:1 damped:1 large:3 discrete:4 science:3 small:1 darpa:1 optics:2 originally:2 configurations:2 smaller:2 broader:1 oscillation:2 foundation:1 direct:1 demonstrations:1 cosh:5 approximation:1 elegant:1 rate:6 timescales:1 further:4 dynamics:3 estimated:1 odd:1 hamper:1 theory:2 even:1 established:1 nonlinear:1 trapping:1 sum:1 axes:1 expressed:1 current:1 ˆb:3 experiment:4 goes:1 new:5 construction:1 acknowledgments:1 satisfy:1 edited:1 processing:1 led:1 degree:1 exchange:4 respectively:2 teleportation:5 here:3 atoms:20 canonically:2 les:1 operating:1 sinh:3 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quant-ph9907059.txt |@word represent:1 partial:1 consider:2 equalities:1 branches:1 leads:3 eds:1 generalize:1 nonuniqueness:1 c1:11 naudts:3 inverse:1 technique:3 tr:4 finally:1 program:1 dressing:1 analogous:1 case:3 straightforward:1 frequencies:1 summarized:1 zµ:1 exact:1 condition:7 level:3 turns:1 tanh:1 solution:20 integrated:1 deals:1 discrete:2 recall:1 eigenvalues:5 equation:4 degeneracy:1 bd:6 heinz:1 oscillation:1 foundation:1 sukhatme:1 pulse:2 cosh:2 past:1 fold:1 second:2 dynamics:3 theory:3 nonlinear:5 sum:1 reminiscent:1 bdt:8 3i:2 version:1 above:2 new:6 method:6 clausthal:2 eω0:1 simultaneously:3 exchange:2 spacing:1 here:4 asymmetry:1 consideration:1 quite:1 equations:7 great:1 spite:1 institute:1 allows:1 eberly:1 resulting:5 stressed:1 khare:1 appropriately:1 useful:2 family:4 highly:1 visible:1 redefining:1 linearly:1 plot:1 use:1 projector:1 prove:1 continuous:1 contains:2 generate:1 calculation:1 ψi:3 therefore:2 themselves:1 type:2 more:2 hahn:2 becomes:1 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quant-ph9907060.txt |@word represent:1 consider:2 caused:1 results:3 four:2 broader:1 causes:1 calculate:1 golshani:2 concerned:1 excluded:1 under:2 p2:10 g2:1 g1:1 very:1 choice:1 condition:3 leads:5 level:4 t2:14 t1:16 try:1 concluded:1 correct:1 consistent:2 past:1 zero:1 insertion:1 specker:2 linear:1 even:2 what:3 apparatus:3 incompatible:2 section:4 foregoing:1 experiment:13 tenable:1 above:1 new:2 order:1 consisting:1 iran:1 respectively:5 never:1 component:5 here:8 understanding:1 believed:1 separation:1 others:1 directions:4 path:1 along:10 box:1 institute:1 involved:2 vectors:1 reason:1 usually:1 makes:1 spatially:1 marginal:2 plenum:1 ipm:1 thought:10 stern:2 use:5 takes:1 would:1 probabilities:1 contains:1 predictions:3 taken:1 type:5 theoretical:1 more:1 separated:1 appendix:2 known:1 foundations:1 cases:1 hold:1 integrating:1 theories:4 values:12 following:11 example:2 point:1 stated:1 dependence:1 states:3 indicates:2 assumptions:1 sense:3 axis:1 influenced:1 means:4 negation:2 write:1 far:1 sate:1 significance:1 ordinary:1 parameter:1 sin:2 product:1 includes:1 information:2 earlier:3 collection:1 compatibility:1 physical:1 dynamical:5 light:1 correspond:1 so:1 make:2 over:2 interpreted:1 attitude:1 experiments:1 through:2 statistical:4 its:2 inquiries:1 derive:2 measuring:1 expectations:1 forms:1 systems:2 redhead:1 mail:2 hidden:10 might:1 factorizability:4 non:9 incompleteness:1 combination:2 press:2 similar:1 effects:2 oxford:1 now:6 hall:2 represents:1 february:1 hereafter:1 university:2 factorizable:5 applied:1 inequality:8 each:8 found:1 cliffs:2 2j:2 mean:2 independent:8 related:3 extended:1 obtains:1 combining:2 quantum:22 our:4 ultimately:1 space:3 since:3 rev:3 particles:12 integrated:3 math:2 shows:1 theory:8 possibility:5 standard:1 completely:3 base:1 york:2 e1:6 e2:8 definition:2 derivation:1 impose:2 times:1 counterpart:1 consequence:3 think:1 first:1 informations:1 probability:8 variables:7 clear:1 multiplying:1 open:2 similarly:6 introduction:1 system:7 relations:6 assumption:2 passed:1 postulate:5 gives:2 calculations:1 tehran:1 x1:6 representing:1 than:1 specify:1 kind:1 holland:1 preparation:9 determined:2 historical:1 epr:3 ann:1 seen:1 any:8 lie:1 conversion:1 angle:1 lim:4 take:3 resembling:1 gleason:2 singlet:1 involving:1 pair:2 assessed:1 measured:4 inconsistency:1 average:2 later:1 kl:1 braunstein:1 principle:2 mechanical:4 physics:1 notion:1 simultaneously:1 show:4 violation:9 dependences:1 x2:6 relation:4 gerlach:2 fine:1 synthese:1 postulates:2 parameters:1 ment:1 e12:13 should:4 only:2 version:5 sengupta:1 local:1 get:1 dependent:1 de:1 expectation:6 joint:4 cannot:2 conjunction:5 contextual:7 podolsky:1 arxiv:1 motion:1 paper:1 common:2 θaa:4 θab:10 kochen:2 view:1 set:1 exists:3 sep:1 violated:3 relative:1 see:3 individual:1 result:4 led:1 nonlocality:1 inequalities:2 shimony:1 justifies:1 state:15 between:5 incompatibility:2 prentice:2 caves:1 conditions:1 terms:1 extend:1 however:1 originates:1 both:3 cos:23 σb:2 taking:1 uncertainty:1 context:3 distinction:1 argue:1 whole:1 mechanics:8 bell:10 represented:1 ab:2 considering:2 pp:5 described:1 locally:2 due:2 been:5 describes:1 ph:1 define:4 obtained:6 direction:2 corresponding:1 quantities:1 c2:4 c1:8 spin:27 present:1 case:7 p3:13 p1:12 p4:8 expanded:1 value:5 property:1 σa:4 aa:1 orientation:1 almost:1 refs:1 ir:2 thus:5 them:1 xy:2 granted:1 same:4 quant:1 grand:1 units:1 gets:2 conflict:1 meets:1 used:2 comprehensive:1 nj:2 mech:2 nevertheless:1 locality:3 well:1 bohm:4 theses:1 components:6 consistency:1 proposed:1 being:4 generally:1 obtain:3 sources:1 contextuality:11 years:1 eigenstates:1 previous:2 density:1 conclude:1 character:1 sometimes:1 source:2 belongs:1 lett:2 θbb:7 possible:4 confined:1 using:5 outcomes:2 mod:1 englewood:2 necessary:1 like:4 particle:26 yields:1 either:1 arbitrary:2 probabilty:1 essential:2 logically:1 because:1 b1:21 b2:35 specified:2 home:1 happens:1 does:1 provides:1 assuming:2 inserting:2 equivalent:4 sixty:1 refers:1 emits:1 about:1 discussed:1 factors:3 o:1 compatible:3 remains:4 rosen:1 realism:1 introduced:2 other:6 cambridge:2 presence:1 into:3 lies:1 references:1 primarily:1 einstein:1 assumed:1 there:4 102a:1 way:4 was:1 function:3 form:11 but:4 failure:2 made:6 um:4 un:2 limit:2 ua:3 called:2 ub:3 originating:1 sort:1 ac:2 eprb:10 associated:1 defined:5 abstract:1 measurement:3 influence:1 dλ:3 commuting:1 defines:2 functions:2 no:3 when:3 valid:4 mathematics:1 prepared:1 a1:32 meaning:1 a2:22 variable:10 ballentine:1 correlated:2 assume:1 interval:3 original:1 time:9 observables:2 having:2 once:1
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quant-ph9907061.txt |@word consider:1 isotropically:1 consists:1 follow:1 remarkably:1 violate:1 departing:1 nonlocal:1 does:3 present:3 presentation:1 presently:1 orthogonal:1 very:3 difference:4 kaszlikowski:1 presented:4 leave:1 upper:1 second:1 incidentally:1 implemented:1 even:1 aim:2 what:2 contributed:1 overload:1 experiment:4 supplies:1 method:1 teleportation:3 here:2 directions:4 along:1 strong:3 obtained:1 remark:1 fwo:1 technical:1 changed:2 allows:3 amount:2 conveniently:1 makes:1 followed:2 aimed:1 apply:1 counts:1 total:1 proceed:1 would:2 massar:1 visit:1 predictions:1 program:1 taken:1 type:2 theoretical:1 more:1 visibility:1 tested:1 virtue:1 particular:1 known:1 cases:2 must:3 rotational:1 work:1 reproduce:1 values:4 following:1 stimulating:1 compare:1 pleinlaan:1 franson:9 sphere:4 performed:1 coincident:10 sense:3 station:1 occur:2 information:1 provide:1 discussion:1 feature:1 delay:2 how:1 instead:1 parameter:1 earlier:1 santos:1 symmetrisation:3 minimizes:1 gdansk:1 short:1 natural:1 effective:2 whenever:4 correspond:2 think:1 so:2 correlation:6 order:4 furnish:1 erasing:1 developed:3 saturates:1 still:1 before:2 perfect:2 superior:1 thank:1 dr:1 temporal:1 exhibits:2 mail:1 hidden:10 loophole:4 non:11 good:2 introduce:1 they:1 now:5 lies:1 fully:1 level:1 realistic:1 inequality:1 realism:1 constraints:2 financial:1 doing:1 static:1 reached:1 quantum:8 our:2 beyond:1 shown:2 interference:1 research:1 particles:1 reader:1 linear:7 possibility:1 standard:1 approaches:3 ask:1 pairs:1 could:3 times:2 counterpart:1 flanders:1 symmetrised:1 exhibited:1 first:7 already:3 symmetry:1 variables:3 number:1 directly:1 impossible:1 necessarily:1 exists:1 least:1 their:1 assumption:1 too:1 exactly:1 simulate:7 authors:2 than:4 relative:2 showed:2 accordance:1 rate:2 ingenious:1 locations:1 close:1 null:1 relatively:1 angle:4 efficient:2 latter:1 violates:1 note:1 instance:1 ideal:2 build:1 detector:2 accuracy:1 sure:1 shall:3 price:1 triangular:1 most:1 but:3 device:1 dichotomic:1 acknowledgements:1 measured:1 considered:1 detectors:14 fact:1 thomas:1 show:3 violation:1 consult:1 ratio:1 simulating:1 parameters:1 situations:2 distributed:2 only:3 candidates:1 essence:1 circle:1 local:9 interested:1 larsson:2 his:1 means:1 noncoplanar:1 ones:2 closely:2 during:3 procedures:1 settings:10 arxiv:1 summary:1 whether:1 bad:2 experiments:3 analytical:1 fixed:2 valid:1 requirement:1 modulo:1 reference:2 job:1 aerts:1 correlations:6 detection:7 see:3 result:1 discussions:1 recently:1 arm:2 best:2 concern:1 phases:2 inequalities:4 artificial:1 state:7 between:13 reading:1 approach:2 checks:1 available:1 terms:1 efficiency:7 reproduces:1 distinguish:1 modeling:1 come:2 both:7 essentially:2 last:1 always:1 equal:10 fulfilled:1 otherwise:1 comment:6 point:3 appeared:1 corresponds:2 dimensional:2 considers:2 erased:2 analogies:1 quickly:1 erases:1 ph:4 lett:2 cerf:1 direction:3 corresponding:1 sufficient:1 photon:1 great:1 fund:2 angles:1 vub:1 fellow:1 former:1 those:1 case:12 appearance:2 single:4 evaluated:1 trick:2 replaced:1 situation:9 property:1 procedure:6 vectors:1 them:2 surface:2 different:2 author:1 pay:1 same:2 shifts:1 unity:3 quant:4 gets:1 events:3 higher:1 used:1 invariance:1 brussels:1 interferometers:4 nevertheless:1 locality:1 well:1 without:1 model:19 realised:1 less:3 observed:2 thanks:2 predicts:1 using:1 polish:1 doctoral:1 candidate:1 similarities:2 photons:1 bell:7 coplanar:6 source:1 other:1 treatment:1 tests:2 possible:1 increases:1 zukowski:2 belgium:1 necessary:2 bit:1 advanced:2 helpful:1 modifications:1 imposed:1 like:9 systematically:1 exploiting:4 performing:1 detections:9 imposes:1 either:1 arbitrary:2 therein:1 because:1 classical:3 some:1 sight:2 provided:1 avoid:1 efficiencies:1 collaboration:1 refer:1 biased:1 scientific:2 slight:1 deleted:1 disappeared:1 post:1 singlet:7 comparison:1 extension:1 discussed:1 dependence:3 kwiat:1 slightly:1 bloch:1 flemish:1 bound:1 arms:2 down:1 phase:4 finely:1 references:4 proportional:1 realisation:1 statistics:7 assumed:1 support:1 question:1 long:1 unreliability:1 way:2 triplets:1 was:3 function:5 considerably:1 invite:1 delayed:3 jul:1 true:1 polariser:1 inside:1 us:2 converted:1 problem:1 gisin:4 detailed:1 ac:1 sketched:1 general:4 conserved:1 associating:1 simulations:1 flight:1 exist:1 durt:1 no:5 whereas:1 when:1 priori:1 details:2 clicks:4 models:7 june:1 variable:6 time:2 observables:1 starting:1
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quant-ph9907062.txt |@word sci:1 consider:3 rev:6 varying:1 results:1 eds:1 ge:2 winds:1 whose:1 depend:2 quasi:4 γn:5 stable:12 tb:3 ta:3 p2:5 lack:1 song:4 wave:24 denoted:1 sons:1 every:1 fac:1 hamiltonian:4 turns:1 solution:16 convenience:1 ited:1 anal:1 force:11 tem:1 periodicity:3 zero:2 mπ:7 residue:1 oscilla:2 ordi:1 giving:1 section:6 pandey:1 goes:3 new:2 lee:2 here:1 understanding:1 equations:1 change:10 obtained:1 ref:1 divisor:2 studied:2 periodic:22 makes:1 winkler:1 rτ:1 univ:1 linearly:15 use:1 additive:1 prove:1 remains:1 iαt:1 peri:1 next:1 linear:1 ψn:5 therefore:1 separates:1 verges:1 under:12 odinger:1 particular:5 known:3 cases:8 iii:2 must:2 tence:1 equation:19 work:1 oscillator:14 obvious:1 making:2 example:1 states:9 assumptions:1 sense:1 tions:4 portional:1 information:1 needs:1 nary:1 provide:1 acts:1 sin:1 may:2 oscillators:3 after:1 different:2 plane:2 representations:1 choice:2 constants:1 dynamical:4 explicit:1 so:4 representation:9 order:2 quasiperiodic:12 over:2 move:1 mainly:1 paper:1 through:1 mentioned:1 acknowledge:1 gen:2 ticular:2 might:1 dae:1 them:2 dan:1 they:2 nor:1 easily:2 february:1 2p:3 always:3 university:2 magnitude:1 2m:2 2n:3 side:1 homogeneous:14 differential:1 related:1 frequency:2 expect:1 combining:1 quantum:5 our:2 eq:7 out:1 shown:8 driving:7 rep:1 since:1 induces:1 research:1 increase:1 hill:9 dxdt:1 cause:2 math:4 attentions:1 wiley:1 mρ:3 theory:1 possibility:1 plex:1 york:1 sys:1 could:2 motion:9 introduction:1 origin:1 toulouse:1 xb:3 xa:3 xf:1 number:1 philadelphia:1 restrict:1 another:1 neighborhood:1 xp:8 george:1 aharonov:2 illustrate:1 wilczek:1 given:17 necessarily:1 tor:2 eqs:2 system:10 construct:2 assumption:1 dt2:1 siam:1 floquet:2 gives:2 exactly:1 park:2 part:5 x2:2 anandan:1 coefficients:1 oscillate:1 john:1 showed:1 cyclic:3 require:1 see:1 amplitude:1 were:1 tion:1 undriven:1 w2:11 pro:1 generalization:1 manner:1 need:1 seen:1 any:4 depending:6 lim:1 lin:1 converges:1 δnf:1 generalized:1 korean:1 multiple:1 tainty:1 price:1 pleasure:1 phase:32 αt:2 considered:7 χf:2 exp:2 χn:3 physics:2 naively:1 fact:2 quantity:1 show:3 lewis:1 supported:1 nτ:1 relation:1 solutions:21 d2:1 find:7 subtracting:1 based:1 parameters:1 should:3 only:1 oct:1 adiabaticity:1 equilibrium:1 do:1 di:1 dependent:4 overall:6 expectation:1 dz:2 during:1 dt:16 geometric:2 evolution:17 arxiv:1 summary:1 whether:1 common:3 contain:1 london:1 set:7 ser:1 national:2 depends:1 result:1 discussions:1 recently:1 subject:1 phases:2 satisfying:1 exponent:1 written:8 various:1 closed:1 subscript:1 αn:2 korea:1 terms:5 attention:1 however:1 w02:3 stants:1 solu:2 both:4 cos:1 last:2 taking:2 equal:1 agree:1 berry:23 com:1 x2p:1 ji:2 nonadiabatic:1 point:1 simple:1 ca:1 period:4 wider:2 dislocation:1 considering:1 described:2 yeon:1 trajectory:1 due:1 been:3 ph:2 ann:1 define:1 corresponding:2 fund:1 external:1 func:2 child:1 general:3 those:1 case:14 p1:2 will:14 while:1 behavior:1 carlson:1 refs:1 thus:3 iv:4 ii:1 im:1 par:2 author:1 pay:1 complex:1 quant:2 finite:2 independent:14 used:1 infinity:3 singapore:1 hand:1 v0:5 driven:14 kim:3 cycle:1 schr:1 magnus:1 without:6 position:2 model:4 being:2 world:1 letting:2 conclusions:1 except:2 lett:3 theorem:5 real:7 aspects:1 khandekar:1 term:1 harmonic:15 early:1 confined:1 integer:1 helpful:1 reduces:1 adiabatic:1 specific:1 unstable:7 either:1 multiplicative:1 become:1 mathematical:1 right:1 classical:12 coddington:1 back:1 examples:1 nonzero:1 δn:3 does:1 unit:3 tends:1 prof:1 proc:1 restoring:1 scientific:1 equivalent:1 evolutions:1 bp:1 imaginary:2 periodically:1 bz:1 integers:2 o:1 positive:4 considerations:1 soc:2 soh:1 into:2 integral:1 additional:1 uncer:1 there:5 u0:5 long:1 u2:1 start:1 function:4 complete:3 shapere:1 but:1 failure:1 hn:1 2πi:1 uv:1 up:4 um:1 limit:3 called:1 diverges:7 constant:3 moore:1 defined:12 denote:1 ap:1 exist:3 functions:22 no:2 when:1 detail:1 other:1 department:1 mathematics:1 tic:1 a2:1 bounded:1 lution:1 auxiliary:1 curve:2 mass:9 time:10 original:1
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quant-ph9907063.txt |@word sufficed:1 sci:1 caused:1 magnetic:4 brownian:1 splitting:1 four:3 executing:1 scalar:5 computation:1 reson:1 query:1 saved:1 leung:2 knill:2 under:2 case:1 probe:1 advantage:3 maas:1 choice:1 englert:1 sons:1 experimentally:1 magic:1 dij:1 hamiltonian:2 anisotropy:1 t2:5 solution:7 t1:4 large:4 small:1 lloyd:1 compensated:1 miller:1 prediction:1 pulse:4 likely:1 enhancement:1 implemented:1 auspices:1 spectral:1 clock:7 new:2 satisfy:1 degree:2 respectively:1 component:1 experimentalist:1 magnetism:1 selective:1 inversion:1 relaxation:6 solute:4 coupling:15 appears:1 wait:1 obtained:1 convert:1 hansen:1 shift:1 larger:1 preferentially:1 resulting:1 permit:2 advantages:2 narrow:1 spatially:1 family:1 requiring:1 manipulate:1 use:4 indicated:1 would:2 laflamme:2 physics:2 cory:2 classically:1 abragam:1 more:4 separated:1 successful:2 becomes:3 operators:1 emission:1 varying:1 must:1 states:2 ibm:3 permits:2 science:3 work:1 grover:7 meet:1 dec:1 control:1 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quant-ph9907064.txt |@word represent:1 concept:1 elongation:1 consider:4 gq:31 maximum:1 magnetic:17 varying:1 results:7 leads:4 commute:1 follow:2 expressions:3 contributions:3 localized:4 devoted:1 whose:6 eiα1:1 const:3 catastrophe:3 acts:1 acting:1 passage:4 recurrence:1 v12:1 charge:10 monotonically:1 device:1 midpoint:1 excluded:2 under:4 tg:1 equalities:1 divergent:1 kσ:2 eiq:1 supported:1 advantage:1 orthogonal:1 very:2 assuming:3 2rc:1 conditions:1 dokl:1 wave:13 electron:28 ultraviolet:7 2πc2:1 approximate:1 difference:4 exact:4 qv1:10 qv2:9 entire:3 obvious:1 mc:2 solves:2 hamiltonian:4 did:1 cosine:1 anisotropy:1 t2:144 solution:11 t0:9 t1:135 large:7 discrete:1 vector:16 d3:1 εki:5 subscript:1 small:13 gauge:1 drop:1 coinsides:1 noted:1 tenths:1 strongly:2 approximately:3 zh:5 coordinate:1 ten:1 iα2:1 iα1:1 consistent:1 builds:1 sin2:1 direct:4 understanding:1 sign:1 approximation:3 zero:5 ivanenko:1 evaluated:2 pass:2 further:3 airy:1 estimated:3 odd:1 linear:7 even:4 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quant-ph9907068.txt |@word proposition:1 concept:2 partial:2 consider:1 results:4 scalar:1 commute:1 computation:1 edu:1 denotes:1 rov:1 gh:4 compact:2 whose:3 calculate:1 iii:2 equivalence:1 environment:1 quasi:2 squeezing:1 under:2 case:15 advantage:1 orthogonal:3 nipne:1 experimentally:1 matrices:5 condition:1 transmission:2 solution:1 leave:1 vector:2 optics:1 equation:2 upper:1 ρj:1 direct:1 second:1 cfv:1 further:1 peredachi:1 linear:3 even:1 plays:1 section:3 analogously:1 decoding:1 above:3 new:2 method:1 nakamura:1 satisfy:3 devoted:1 answers:1 focused:1 consideration:1 equations:1 balian:1 cf0:1 obtained:8 great:1 institute:2 vectors:2 amount:1 scutaru:12 tu:1 family:2 vii:1 apply:1 unit:1 use:2 usa:1 prove:2 positive:2 finally:1 properties:4 few:1 ψi:1 type:1 until:1 initial:1 operators:20 jai:1 cannonical:1 interaction:1 particular:4 known:4 cases:2 effort:1 must:1 dominicis:1 states:26 mg:2 ρi:1 mo:1 work:2 det:18 remain:1 ρu:1 following:4 trans:2 root:2 def:1 proof:2 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quant-ph9907073.txt |@word limited:2 code:2 consider:8 forbidden:1 varying:2 splitting:3 leads:2 quadrature:24 edu:1 follow:1 increase:2 amplification:2 re:1 arthurs:1 send:3 squeezing:5 present:2 under:1 analogous:1 must:4 sent:4 fax:1 amplitudes:1 string:4 advantage:1 orthogonal:1 very:2 frequencies:1 results:4 wishes:1 mixing:2 difference:2 swapping:1 modulator:2 level:2 transmission:4 eve:27 discrete:1 unrelated:1 small:6 relation:1 noted:1 force:1 pulse:2 rate:5 pass:1 further:2 spectral:1 what:3 errors:2 appear:1 apparatus:1 indicated:2 giving:1 sum:1 above:1 shared:3 public:1 revealing:1 measurements:11 respectively:2 applies:1 here:3 protection:2 them:4 excess:1 consideration:1 strong:1 observing:1 obtained:4 sender:1 receive:1 shift:3 studied:1 tolerance:1 amount:2 simultaneous:12 resulting:1 pick:2 action:1 bob:26 fourier:1 makes:1 digitally:1 secure:1 bs:5 technologies:1 vc:2 total:1 predicted:1 use:5 additive:1 stream:1 working:1 prove:1 subtract:1 chooses:1 depicted:1 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quant-ph9907074.txt |@word secondly:2 since:1 partial:1 consider:3 maximum:1 equalities:1 global:1 results:6 leads:2 entropy:12 computation:4 research:1 causes:1 whose:1 calculate:5 eα:2 technique:2 tr:3 acting:1 preprint:1 environment:5 compensate:1 swap:10 under:2 include:1 case:3 supported:1 preserved:1 very:1 frequencies:1 rise:1 electron:10 difference:3 exact:5 condition:1 paz:1 four:1 hamiltonian:8 transmission:1 evaluation:1 trb:26 t2:1 solution:8 leave:1 integro:1 science:4 eigenvalues:2 deutsch:1 unpolarized:1 past:1 second:6 value:7 further:1 dynamics:6 chem:1 substitute:1 theory:5 spectral:2 rate:1 section:2 decoding:1 consistently:1 above:1 values:2 un:1 increasing:1 method:2 satisfy:1 wavefunctions:1 dahn:1 here:7 understanding:1 kimm:1 relaxation:1 represented:1 strong:1 equations:2 imperfections:2 change:1 obtained:6 ref:2 iπ:1 institute:1 study:6 studied:1 implementation:1 schumacher:4 action:1 opinion:1 changes:1 involves:3 plotted:3 composed:2 convolution:3 ls:4 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quant-ph9907075.txt |@word beckers:1 sector:3 lakshmanan:1 consider:3 funct:2 results:3 four:1 commute:1 higher:1 follow:1 zhedanov:1 compact:5 whose:1 amplification:1 th:1 anharmonic:1 multilinear:1 mehta:1 cm0:2 chennai:1 string:1 straightforward:1 very:1 zachos:1 brihaye:1 entire:1 school:1 hussin:1 hamiltonian:6 irreducible:1 sklyanin:3 large:1 differential:1 anal:2 optics:7 degeneracy:1 2k0:2 literature:2 sign:2 dynamics:1 cat:1 canonical:6 nonlinear:2 invertible:1 section:2 current:1 above:3 ground:1 method:7 satisfy:5 edited:1 respectively:3 realizations:1 κa:1 here:6 atoms:1 behaviour:1 inverse:3 ansatz:1 obtained:1 institute:1 study:4 larger:1 allows:1 leaving:1 fernandez:1 published:1 action:4 suitable:1 useful:1 panjab:1 substitution:1 highly:1 brought:1 unitary:1 rσ:1 use:2 chd:1 would:1 positive:2 negative:1 next:1 linear:8 m0:16 type:1 more:1 becomes:2 operators:6 curvature:2 berlin:1 particular:4 known:7 cases:5 iii:1 analogous:3 eβ:1 kumar:1 springer:1 junker:1 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quant-ph9907076.txt |@word represent:2 measurements:8 consider:3 remarkable:1 limited:1 keep:1 lack:1 brownian:1 results:2 gy:3 month:1 leads:2 roy:2 ginzburg:1 circuitry:1 per:3 broader:1 hanging:3 perturbations:1 expressions:1 adjustment:1 ǫi:2 issues:1 layers:1 depend:2 alamos:4 technique:11 binnig:1 gerber:1 finally:2 present:1 under:1 cm2:1 third:1 division:1 iǫ:1 transducers:2 cantilever:3 very:4 frequencies:14 translations:1 myself:2 distort:1 geometrical:2 electron:3 every:1 overbeek:3 sensitivity:7 blokland:3 80th:2 experimentally:2 difference:1 minute:1 entire:1 level:2 did:5 cause:1 cavendish:1 integrating:2 applicable:1 damped:3 large:4 barash:2 vector:3 dealt:1 small:4 relation:1 optics:1 noted:1 20th:1 possibility:2 upper:2 milton:1 smaller:1 force:45 2k1:1 ten:1 direct:1 equation:4 d6:1 zero:5 cost:1 equal:1 growing:2 further:1 chem:1 rough:1 quite:1 aspheric:1 even:1 index:1 expanded:1 errors:1 wavenumbers:1 apparatus:11 trivial:1 section:1 unwieldy:1 brief:1 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quant-ph9907077.txt |@word homomorphism:4 dynamic:1 extends:2 four:1 obstruction:1 entropy:59 consists:1 nwn:1 forget:1 whose:5 isometric:1 calculate:1 ohya:7 γu:2 under:11 teaching:1 cm2:1 cm1:1 conjecture:7 connects:1 unitaries:1 every:36 convexity:3 school:1 achievability:2 induction:3 convenience:1 vector:1 guiding:1 indices:1 markov:2 consistent:1 estimates:8 direct:10 kodai:1 approximation:2 elegant:1 second:14 7th:1 estimated:3 even:18 neg:2 decoding:6 nachr:1 above:27 new:16 satifies:2 contributes:1 1997b:3 1997a:2 j2c:3 notions:4 never:4 equals:3 here:14 atoms:1 reported:1 protection:1 represented:1 interpret:1 violate:1 obtained:1 study:4 stipulates:1 ignoring:1 credit:2 symmetrical:2 suitable:1 criticism:2 diameter:1 projection:1 arbitary:2 advisor:1 highly:3 brought:1 rπ:1 achievable:13 total:4 unit:6 would:12 codewords:8 negative:1 noting:1 call:11 therefore:2 m2:20 type:27 until:2 separated:1 successful:1 brings:1 hereby:1 aware:1 berlin:6 hold:2 must:6 me:4 kraus:3 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quant-ph9907081.txt |@word homomorphism:1 consider:1 results:1 disc:1 entropy:4 inverse:1 ohya:1 tr:48 γi:3 monotonically:1 th:1 ti:2 conjecture:1 jensen:2 very:1 corollary:6 every:1 decide:1 fakult:1 convexity:2 dim:1 riemann:1 t2:10 t1:7 large:1 discrete:1 vector:1 bxa:1 eigenvalues:2 bxb:1 upper:3 zero:1 rigorous:1 peredachi:1 theory:7 spectral:1 plays:1 appear:1 invertible:1 section:6 version:1 above:1 new:1 increasing:1 acknowledgments:1 respectively:1 never:2 here:5 strong:1 equations:1 contraction:2 great:1 trans:1 vectors:1 pick:10 usually:1 t22:7 via:1 followed:1 vii:1 texts:1 unit:1 use:3 andreas:1 projector:1 prove:2 positive:16 negative:1 properties:3 vol:7 call:2 therefore:2 taken:1 theoretical:1 more:1 operators:6 berlin:2 hold:1 iii:1 springer:2 orner:1 modified:1 obvious:1 following:1 fulfill:2 hansen:1 root:2 example:8 proof:13 claim:1 give:1 preserving:2 states:10 axis:1 information:9 lemma:4 sit:1 fortunately:1 s2:7 s1:5 holds:7 write:1 maps:8 obius:1 map:16 product:1 algebra:4 may:3 max:1 wiley:1 davis:1 abuse:1 ff:2 data:9 winter:2 realized:1 advan:1 element:1 inform:2 si:4 so:1 representation:4 order:1 wigner:2 closely:1 developed:1 soon:1 interpreted:1 london:2 ieee:1 its:9 derive:1 monotonicity:8 thank:1 chosen:1 fruitful:1 onb:1 concavity:2 systems:13 mail:1 dyson:2 non:2 introduce:2 half:1 now:2 eigenvalue:1 probl:2 equality:1 concave:4 inequality:12 transmitted:1 universit:1 differential:1 reduce:1 elementary:1 ex:2 measure:2 quantum:29 our:2 special:2 matrix:2 space:6 furthermore:2 holevo:5 denotes:6 increase:2 reader:1 denoted:1 math:4 shows:1 linear:6 monotone:12 divergence:3 quite:1 completely:5 york:1 monographs:1 definition:9 could:1 ati:6 consequence:1 rudolf:1 support:1 first:1 xi:5 xn:2 probability:1 xb:1 xa:9 coding:2 channels:3 done:1 owner:1 open:2 xu:2 given:3 1v:1 introduction:1 adjoint:1 system:2 too:6 final:1 tool:1 continuous:3 part:3 authors:1 x2:2 x1:3 uhlmann:7 kind:1 accordance:1 sections:1 imply:1 supposed:1 ann:1 generalization:1 need:1 clearly:1 viewed:1 lin:1 csisz:1 pederson:1 channel:3 play:1 converse:1 trace:2 but:2 xµ:2 considered:1 sometimes:1 cover:1 physics:2 notion:3 fact:2 laws:1 thomas:1 show:1 spaces:3 state:11 should:1 analytic:2 only:2 postfach:1 indeed:1 notation:4 get:1 de:2 joint:1 dx:2 dy:1 arxiv:1 whether:2 processed:1 analytical:1 set:1 bounds:1 relative:2 see:5 sec:2 result:1 discussions:1 dµ:2 ways:1 αx:1 αz:3 enough:1 closed:1 between:2 petz:1 notice:1 jr:1 key:1 topology:1 received:2 essentially:1 cor:2 last:1 limits:1 etc:1 uni:2 otherwise:1 ci:2 point:1 donoghue:1 cf:5 dimensional:5 assertions:1 moreover:1 selfadjoint:1 pp:8 commutative:1 basis:3 cauchy:2 ph:1 deduced:1 pn:9 define:4 corresponding:3 both:1 remark:8 denote:2 case:2 will:3 s2µ:3 iy:2 engl:1 memoryless:1 vi:1 von:1 av:1 iv:2 ii:1 itself:1 im:1 cone:4 ready:1 unity:1 complex:2 quant:1 s2t:3 finite:16 subalgebra:1 interpolation:1 independent:1 interscience:1 mutual:4 t21:5 uses:1 identity:1 eigenvectors:2 academic:2 self:1 just:1 detail:1 transforms:1 using:1 useful:1 easy:1 theorem:19 input:2 transformation:1 real:6 around:1 measurement:1 spanned:1 harmonic:1 press:2 immediately:1 unique:1 like:4 remind:1 schwarz:2 δi:3 output:4 pointwise:1 continuation:1 ahlswede:2 because:3 often:1 classical:1 conditional:1 some:3 s1t:3 examples:1 convex:5 peter:1 decomposition:1 t11:4 t12:1 proc:1 bf:2 equivalent:1 processing:10 ober:1 hilbert:5 about:1 central:1 theorems:1 introduces:2 o:1 important:1 consequently:1 op:2 lieb:3 considerations:2 soc:1 communication:3 into:4 bound:3 latter:2 appropriate:1 bielefeld:4 references:1 operator:20 next:4 neumann:1 log:3 transfer:1 strictly:1 there:2 question:2 start:1 borel:2 inner:1 was:2 function:16 yanase:2 complete:1 form:1 sequel:2 jul:1 so2:1 convergence:1 true:1 commun:1 algebras:1 supp:4 up:1 ur:1 limit:1 distribution:1 called:5 aa:1 ai:21 abstract:1 describe:1 am:1 general:1 transl:1 transm:1 ar:1 promised:1 aw:2 formulation:2 inf:1 physical:25 again:1 functions:13 proofs:2 no:4 mathematik:3 whereas:1 stinespring:3 role:1 shannon:1 nice:1 elements:1 a1:21 a3:2 a2:15 implies:4 interval:3 ti2:1 equivalently:1 quantity:1 starting:1
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quant-ph9907082.txt |@word consider:6 results:31 illustrated:2 generalize:1 r1n:1 expressions:9 involved:2 row:1 devoted:1 whose:6 certainly:1 referring:1 advantage:1 assigning:1 former:1 presents:1 finally:5 those:4 exposition:2 analogous:1 characterised:4 necessary:3 case:31 belonging:1 amplitudes:100 r13:9 straightforward:2 r11:6 very:4 connects:3 wave:6 sons:1 putting:1 orientations:2 promise:1 rm:2 difference:1 exact:1 condition:5 treating:1 four:6 obvious:1 presented:2 turns:1 solution:1 reminding:1 discrete:2 vector:23 dealt:1 indices:1 eigenvalues:12 sin4:8 sin2:133 consists:1 zero:6 j22:1 j21:1 further:2 columns:1 approached:1 even:1 index:3 what:4 section:27 expressed:2 debate:1 above:2 s12:1 new:21 method:10 contrast:1 satisfy:1 respectively:9 component:1 here:20 behaviour:1 cos4:8 cos2:130 others:1 represented:1 along:29 equations:1 appears:1 interpret:1 deduced:3 obtained:12 great:1 technical:1 shift:1 study:2 vectors:17 completely:1 suggests:2 simultaneous:3 resulting:5 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quant-ph9907083.txt |@word consider:5 rev:4 particular:1 amplifier:3 intracavity:3 leads:1 go:1 amplified:4 amplification:10 finally:1 compensate:1 squeezing:1 td:10 dell:1 wave:3 resonant:1 condition:3 entire:1 gatti:2 ref:1 noiseless:9 solved:2 vector:3 small:1 dip:2 round:1 smaller:1 sin2:2 approximation:1 rate:1 odd:2 substitute:1 spectral:2 section:1 reconstruction:1 ibid:1 respectively:1 component:1 here:2 inverse:1 cos2:2 separation:1 situation:2 ratio:3 change:1 scienze:1 resonance:1 fourier:2 spatio:1 via:2 extra:1 modulated:1 use:2 takes:2 would:1 faint:2 quasi:1 therefore:1 taken:1 means:2 introducing:1 degeneracies:1 becomes:2 operators:1 mismatch:2 impulse:1 varying:1 known:1 equation:4 oscillator:1 following:2 arrive:1 compare:1 figure:4 photocurrent:1 preserving:1 neglected:2 high:1 assumptions:1 degenerate:1 sense:1 axis:1 celoria:1 e2r:2 s2:5 get:2 photoelectrons:1 write:1 located:1 instead:1 parameter:1 fp:2 product:1 may:1 containing:1 plane:14 snr:1 coming:1 multiplication:1 response:1 sp:3 so:2 enter:1 order:1 sd:5 indeed:1 amplifying:1 satisfied:1 captions:1 its:1 no2:1 denker:1 perfect:1 decay:1 temporal:1 window:1 fig:5 bout:2 pixel:3 uniformely:2 introduce:1 they:1 half:1 now:5 easily:1 cavities:2 2r:2 characterizes:1 mode:1 each:2 universit:2 mean:2 domain:3 ei:1 frequency:4 into:1 our:1 eq:1 out:2 large:1 shown:1 space:1 furthermore:2 since:1 interference:2 projected:2 denotes:1 ro:2 evaluation:1 ri:2 lugiato:3 fisica:1 possibility:5 milburn:1 lucini:1 definition:1 interaction:1 geometry:1 confocal:4 length:4 hence:3 neglect:2 first:1 laguerre:1 number:4 least:1 another:1 ring:2 size:1 πc:1 given:2 introduction:1 eqs:5 system:3 unspecified:1 amplifiers:3 realization:2 scheme:6 free:1 centered:1 transverse:4 optical:7 2ap:1 yurke:1 than:1 coefficients:2 see:1 submitted:1 amplitude:2 motivation:1 seen:1 kolobov:1 angle:1 built:1 depending:1 efficient:1 self:2 take:1 even:4 shall:3 object:6 but:1 phase:2 observation:1 considered:1 calculated:1 milano:2 part:5 electrons:1 exp:1 ky:1 typical:1 physics:1 quantity:2 show:1 relation:1 based:2 state:1 only:2 factor:2 local:1 over:2 above:1 di:3 dependent:1 express:1 db:1 dt:3 areas:1 arxiv:1 fixes:1 investigate:1 scanning:1 operates:1 detection:1 depends:1 arg:3 optimum:1 subject:1 pump:1 smallest:1 between:2 caves:1 preserve:1 terms:3 however:2 efficiency:1 como:1 configuration:1 observable:1 repeating:1 many:1 region:2 infinitely:1 equal:2 sensitive:1 variance:3 whole:2 lenses:4 relevant:1 groups:1 point:1 moreover:2 considering:2 described:1 transformations:3 geometries:1 basis:1 due:1 laplacian:1 detuning:3 much:1 slowly:1 interest:2 ph:1 wants:1 quantities:2 photon:1 coherent:1 case:5 expanded:1 value:1 while:3 behavior:1 aid:2 2k:1 bin:4 planar:2 orientation:1 non:1 surface:1 reads:1 ni2:4 aspects:1 ic:1 different:1 italy:2 author:1 same:3 quant:1 split:1 finite:1 a2p:4 again:1 effect:1 possible:3 focal:2 gauss:1 modes:6 well:1 analysis:1 severe:1 position:2 parametric:7 latter:2 obtain:1 bandwidth:1 λf:11 previous:1 mirrors:1 density:1 scales:1 guaranteed:1 exclusively:1 input:2 real:1 sim1:1 insensitive:1 around:1 iδ:6 insubria:1 using:1 necessary:1 signal:5 specific:1 benefit:1 steps:1 δi:2 output:2 classical:1 creation:1 some:2 images:1 scale:1 cavity:14 investigations:1 langevin:2 integration:1 refer:1 limitations:1 noise:15 power:1 equivalent:1 bp:1 properties:2 simpler:1 carried:1 o:1 range:1 introduced:1 ηg:4 presence:2 image:19 photodetection:1 integral:1 references:1 been:1 operator:1 proportional:1 area:3 there:1 transform:1 long:1 function:4 form:1 offer:1 registered:2 analyse:1 jul:1 gain:3 true:1 infm:2 places:1 characteristic:1 inside:1 up:1 us:3 constant:1 abstract:1 dξ:2 ap:6 trip:1 ni:6 functions:1 compared:1 no:2 dashed:3 whereas:1 when:1 field:9 spatial:5 presenting:1 symbol:1 lens:2 kx:1 longer:1 assume:1 required:1 dρ:7 mancini:2 pupil:4 time:3 resolution:1 having:1 once:2
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quant-ph9907084.txt |@word represent:1 consider:3 magnetic:1 particular:1 results:2 leads:2 eds:2 grateful:1 whose:1 technique:1 finally:2 under:1 stochastic:2 case:6 straightforward:1 very:1 springer:1 focus:1 difference:1 treating:1 level:2 solution:4 damped:1 large:1 small:5 markov:1 challenge:1 lewenstein:1 milano:2 approximation:8 elegant:1 rate:1 dynamics:5 ba:1 aim:1 what:1 nonlinear:3 sun:1 expressed:1 above:3 replaced:1 method:2 body:1 condensed:1 component:1 here:2 atoms:14 andrews:1 along:1 institute:1 study:3 studied:1 resulting:1 usually:2 fourier:1 via:1 private:1 total:7 unit:1 plot:1 use:2 takes:1 would:2 next:1 predict:1 linear:1 taken:1 survive:1 means:3 hulet:1 more:1 introducing:1 becomes:2 operators:9 everywhere:1 virtue:1 γb:2 known:2 must:1 high:1 account:2 valued:1 vladimir:1 deformed:7 science:1 equation:5 oscillator:2 modified:1 values:2 following:4 csorgo:1 figure:1 calculation:1 neglected:1 states:2 numbers:1 sense:1 celoria:1 end:1 rather:1 get:1 zaccaria:1 instead:1 parameter:1 l873:1 description:2 algebra:4 may:6 thermodynamic:1 ladder:1 after:1 derived:1 stefano:1 fd:1 date:1 fi:1 response:1 man:6 kurn:1 natural:1 effective:1 light:10 so:1 correlation:1 sackett:1 typical:1 developed:1 eqs:1 soon:3 course:1 experiments:1 through:1 statistical:1 captions:1 linewidth:1 group:1 interesting:1 presence:1 decreases:1 systems:1 deformation:2 investigated:1 walls:1 effects:2 they:1 now:4 yu:1 term:2 finite:4 hamiltonian:8 javanainen:1 trap:2 2b:1 each:1 universit:1 heavy:2 differential:2 generation:1 energy:1 related:1 constitute:1 elementary:1 frequency:3 measurement:1 quantum:6 our:3 beyond:1 eq:9 ketterle:1 shown:2 tombesi:1 driving:1 furthermore:1 since:2 rev:8 research:1 particles:4 collisions:1 eprint:3 shows:1 achievements:1 foundation:1 theory:3 gardiner:3 fisica:1 possibility:1 quark:1 completely:1 besides:1 matthews:1 interaction:1 could:1 transition:1 signature:1 hence:3 retain:1 condensate:6 already:1 symmetry:2 variables:1 number:22 ensher:1 precisely:1 a610:1 given:5 rewritten:1 introduction:1 dipartimento:1 system:1 relations:1 1c:1 assumption:1 realization:1 oversimplified:1 violated:1 gives:2 trapped:1 moscow:2 braun:1 iωt:1 unfortunately:1 bec:8 approximations:1 second:1 limiting:1 project:1 matter:3 future:1 amplitude:1 russia:1 biedenharn:1 mind:1 spectrum:11 manner:1 seen:2 cumbersome:1 forced:1 zero:1 efficient:1 pursued:1 latter:2 note:1 internal:1 bogolubov:5 davies:1 coincide:1 heisenberg:1 scripta:3 shall:1 decreasing:1 satisfy:1 simplify:1 jul:1 acknowledgements:1 commutation:3 nonlinearity:1 considered:1 ko:6 physica:3 proceedings:2 exp:1 physics:1 tollett:1 fact:2 quantity:2 signatures:1 lebedev:1 probe:1 scattered:6 rotating:1 relation:2 ground:2 parameters:2 should:2 only:1 summarizing:1 di:2 dependent:1 pions:1 beam:1 remedy:1 arxiv:1 investigate:1 mewes:1 valid:1 view:1 coefficient:2 frame:1 correlations:1 see:1 result:1 eliminating:1 arg:2 macfarlane:1 subject:1 invoked:1 interacting:2 marmo:1 state:8 approach:3 preserve:1 triplet:1 terms:2 initially:1 attention:1 weak:1 bose:6 come:1 suggested:2 observable:1 essentially:1 last:1 many:1 taking:1 equal:1 experimental:1 otherwise:1 ck:7 druten:1 mollow:2 harmonic:1 semiclassical:1 cs:1 moreover:1 ct:1 conference:2 due:1 been:3 devise:1 describes:2 damping:1 interest:1 basic:1 tino:1 ph:4 fig:7 gas:3 gao:1 general:1 those:1 applied:1 laser:4 pacs:1 single:1 value:1 heidelberg:1 will:2 suppose:1 promising:1 property:1 coupled:1 reads:2 conserve:1 ig:4 different:2 italy:1 radiation:3 lett:5 same:1 beside:1 stimulated:1 quant:1 physical:2 used:2 trivially:1 sudarshan:1 hand:2 ion:2 infinite:1 zimanyi:1 recent:1 weakly:1 modes:2 well:3 roughly:1 obviously:1 thought:1 solve:1 model:3 usual:2 being:1 obtain:1 shape:2 atomic:7 renewed:1 cornell:1 character:2 iω:2 belongs:1 treatment:1 excited:1 bin:10 possible:2 increases:1 vacuum:1 confined:1 gη:1 particle:10 prospekt:1 reduces:1 δb:9 imprints:1 pertaining:1 because:1 methods:1 deal:2 creation:3 back:1 shortcoming:1 describing:1 lead:1 hep:2 refer:1 bf:1 noise:2 obey:2 bc:1 broken:1 substituted:1 central:1 munzinger:1 algebraic:2 dependence:1 o:1 introduced:1 plan:1 final:1 strangeness:1 undeformed:1 communication:1 into:2 numerically:1 bath:4 references:1 determine:1 einstein:4 operator:6 anderson:1 bosonic:3 van:1 classical:3 few:2 initial:2 question:1 nucl:1 long:1 hadronic:1 hef:1 conservation:4 bosons:1 was:1 function:4 form:1 but:1 heat:2 atom:2 line:1 longer:1 bradley:1 infm:1 durfee:1 default:1 characteristic:1 us:1 ωk:4 limit:3 fluctuations:2 problem:2 ab:1 defined:1 steady:4 abstract:1 describe:1 mode:2 conserved:3 graham:1 regime:1 no:2 nc:8 vanishes:1 field:8 other:3 you:2 deviation:1 picture:1 denote:1 excitation:1 photon:1 peak:1 cooper:1 structure:1 condensation:2 coupling:3 dω:1 mancini:5 phonon:3 time:4 requires:1
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quant-ph9907085.txt |@word consider:3 broaden:3 splitting:1 four:26 broader:4 causes:1 ρss:2 whose:1 inverse:3 calculate:4 tr:1 γt:8 presents:1 finally:2 program:1 present:1 γf:43 amplitudes:1 g2:1 returning:1 very:4 frequencies:1 2γf:2 springer:2 results:7 clemens:2 difference:1 castin:1 europhys:1 obvious:1 incoherent:10 level:71 schawlow:6 2κn:7 occurs:5 large:13 gρn:2 differential:1 microlaser:2 small:12 eigenvalues:1 refer:2 optics:2 der:1 upper:13 unexpected:1 oscillation:2 trend:1 consistent:1 past:1 rate:23 qualitatively:2 dynamics:2 even:5 index:1 what:1 appear:1 section:6 above:7 new:2 occupation:1 satisfy:1 edited:1 κn:1 here:8 atoms:2 explore:2 amplification:1 focused:1 equations:15 appears:1 change:1 obtained:3 turchette:1 increments:1 2aρ:3 involved:1 changed:1 periodic:1 resulting:1 usually:2 fourier:4 plotted:1 composed:4 examining:3 via:2 followed:1 lasts:1 scales:1 transit:1 explained:2 unitary:1 decrease:3 planck:1 linearly:1 readily:1 plot:18 use:1 haken:1 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quant-ph9907087.txt |@word logarithms:1 code:2 consider:2 remarkable:1 equalities:1 tamagawa:1 results:1 schatten:1 proposition:6 entropy:4 computation:2 equiprobable:1 calculate:3 ohya:1 technique:1 tr:40 finally:2 permanently:1 those:1 ti:2 presentation:1 indicating:1 inform:5 conjecture:1 supported:1 assuming:1 springer:1 print:4 corollary:2 putting:2 difference:1 matrices:2 convexity:1 implying:1 did:1 applicable:1 trf:1 noiseless:1 commute:1 small:1 trs:3 optics:1 upper:3 grateful:1 estimates:1 direct:1 rate:6 value:2 substitute:1 linear:1 spectral:1 established:2 what:1 giving:2 diag:1 section:1 sj1:1 nondegeneracy:1 version:2 above:1 sup:3 values:1 increasing:1 acknowledgments:1 westmoreland:1 satisfy:1 full:1 degree:1 here:2 reported:1 packing:2 represented:2 along:1 logarithmic:1 obtained:1 sending:2 remark:1 institute:4 sjn:1 schumacher:2 usually:1 hospitality:1 makes:1 via:1 useful:1 investigate:1 namely:2 apply:2 derivatives:1 use:6 takes:1 prove:3 probabilities:3 λαj:14 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quant-ph9907088.txt |@word secondly:1 code:1 schumaker:1 consider:2 amplifier:1 results:2 four:1 quadrature:1 concept:1 entropy:3 computation:1 edu:3 2r2:10 2r1:4 gh:1 amplification:1 calculate:2 tr:11 environment:1 finally:1 dz2:4 squeezing:5 under:1 analogous:1 applied:1 straightforward:3 very:1 plausibility:1 wave:1 vaccuum:1 mixing:1 experimentally:3 matrices:3 hausdorf:1 34a:1 34b:1 hamiltonian:1 transmission:1 knight:1 notes:3 noiseless:2 solved:1 convenience:1 recall:1 optics:2 oscillation:1 cosh:15 rate:1 rigorous:1 further:1 theory:5 plays:1 expressed:2 version:2 method:1 eω1:3 eω2:2 applies:1 plenio:1 groups:2 address:3 z4:4 appears:1 z2:6 z3:11 obtained:3 technical:1 studied:1 prior:2 twamley:3 schumacher:6 action:1 scutaru:3 suitable:1 apply:2 readily:1 proceed:1 next:2 calculation:3 chr:2 m1:14 therefore:1 m2:25 simpler:1 metric:1 more:4 appendix:3 known:1 a5a:1 a5b:1 science:3 equation:1 reproduce:1 following:3 arrive:1 example:1 proof:2 wang:2 give:1 process:1 bennett:3 states:21 occur:1 information:6 needs:1 quantph:1 s2:10 s1:14 get:2 rippin:1 sacchi:1 how:2 pure:1 optimal:1 parameter:3 ensemble:2 brassard:1 ζa:1 barnum:1 cz2:4 reps:1 faculty:1 transposed:2 realized:1 explicit:2 purification:1 so:4 sg:3 z2i:2 shield:1 sood:1 indeed:1 interpreted:3 thermal:11 paper:3 through:3 fidelity:22 its:1 before:2 write:1 rojo:1 actually:2 systems:1 mail:3 overcome:1 non:1 they:1 oxford:2 now:1 discuss:1 easily:3 term:1 gets:2 2r:2 establishment:1 university:1 sufficiently:2 transmitted:2 mode:1 2m:1 hausdorff:1 another:1 simplicity:1 barnett:1 displacement:3 related:1 obtains:1 measure:2 quantum:15 our:1 eq:11 shannon:4 out:1 large:2 shown:1 matrix:9 furthermore:1 since:3 rev:6 denotes:1 content:1 kent:1 formula:8 ref:2 math:3 shows:1 sinh2:5 sympletic:1 linear:2 standard:1 definition:2 r1:7 r2:7 a4a:1 xiang:1 already:1 probability:4 relate:1 coding:7 number:6 simplified:1 directly:2 message:5 given:1 πa:1 a4b:1 publication:1 similarly:1 eqs:1 their:1 calculations:1 bits:1 final:3 optical:2 representing:1 albeit:1 fuchs:1 treated:1 sees:2 7a:1 rewrite:2 correction:1 argument:3 need:4 clearly:1 bz1:4 convenient:1 note:8 k2:2 k1:2 modulus:1 smolin:2 channel:5 shall:3 measures:1 simplify:1 phase:1 class:1 observation:1 considered:2 calculated:1 sometimes:1 exp:28 quantifying:1 quantity:1 show:4 tenet:1 relation:3 d2:8 d0:7 d1:10 q1:3 ni:1 merlin:1 ratio:1 popescu:1 parameters:3 written:1 should:4 explicitly:4 factor:3 do:2 his:1 invoke:1 means:2 express:1 overall:1 degradation:1 methods:1 cannot:1 closely:1 compute:3 gen:3 shr:2 conditions:1 arxiv:1 investigate:1 national:1 nus:3 see:3 result:3 recently:3 alternative:1 state:4 difficulties:1 myriad:1 closed:3 approach:1 available:3 terms:1 qubits:4 however:3 key:1 article:2 uρ:2 essentially:1 always:1 σb:1 sensitive:1 whole:1 aa:1 sinh:26 reasons:1 others:2 simply:3 considering:1 most:1 described:2 generality:1 due:1 been:2 z1:7 faithfully:1 bures:13 pi:2 define:4 ariano:1 6a:1 6b:1 josza:1 coherent:1 maximally:1 protocols:1 case:2 extracted:1 replaces:1 exponential:1 while:1 suppose:1 error:1 squeezed:19 real:1 von:1 thus:1 ia:1 qecc:2 same:3 unity:1 complex:3 quant:4 several:1 difficult:2 singapore:3 hand:1 average:1 entanglement:6 recent:1 lower:1 expression:2 well:1 epp:2 firstly:1 parametric:1 possesses:1 protocol:1 cosh2:7 proposed:3 when:1 obtain:2 campbell:1 purified:1 eigenstates:1 density:5 ideal:1 signals:1 source:5 other:1 lett:2 theorem:4 republic:1 bin:1 σn2:3 evaluate:1 possible:1 entangled:1 vacuum:1 press:1 using:8 paraoanu:1 displaced:11 imposed:1 like:1 signal:11 wooters:2 yields:2 arbitrary:4 output:1 works:1 reduced:1 neumann:1 classical:1 some:3 b1:14 b2:30 nonzero:1 realistic:1 electromagnetic:1 garrett:1 per:2 does:1 provides:1 kwek:2 whitaker:1 noise:1 reduces:1 although:1 noisy:1 plug:1 central:1 oh:2 introduces:1 generated:1 carries:1 important:3 mixed:2 introduced:1 consequently:1 previously:1 communication:3 into:3 within:1 operator:7 quickly:1 often:1 a3:1 ridge:1 strictly:1 vedral:2 specifically:1 quadratic:1 az1:4 was:1 decoded:2 form:6 phenomena:1 collapsed:1 jul:1 idea:2 ph:5 he:1 applying:1 instructive:2 us:2 theoretical:1 ωi:2 limit:3 fluctuations:1 problem:2 clear:1 detailed:2 defined:2 am:4 general:1 single:1 proves:1 tedious:1 again:1 codes:1 generally:1 σb2:2 field:2 setting:1 role:1 department:1 elements:1 denote:2 generates:1 a1:1 commutator:1 reiφ:1 a2:3 needed:1 bch:4 physics:1 baker:2 n1:10 n2:5
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quant-ph9907090.txt |@word consider:1 remarkable:1 particular:1 results:1 illustrated:1 gi:2 optical:4 inverse:1 absorbing:2 compensate:1 squeezing:6 x03:8 x02:8 td:5 x00:4 worth:1 x04:8 far:1 ηij:5 ηii:5 figs:5 experimentally:1 condition:1 hamiltonian:1 lter:1 solution:4 t0:1 damped:2 solved:1 small:1 optics:2 smaller:1 vasilyev:1 pulse:2 sign:1 approximation:2 second:1 further:1 linear:2 spectral:3 nonlinear:2 sub:1 assisted:2 ˆb:3 new:1 solitonic:1 method:1 contrast:1 coefficient:7 full:1 degree:1 respectively:2 component:2 here:1 l21:1 objects:1 relaxation:1 strong:3 obtained:1 zones:1 studied:1 resulting:1 domains:2 fourier:2 changes:2 plotted:1 transmittance:1 explained:1 highly:1 dirk:1 achievable:2 aitchison:1 commun:1 negative:1 discrepancies:1 noting:1 associated:1 more:2 introducing:1 solitons:8 operators:1 odinger:1 berlin:1 varying:1 known:1 cases:1 x01:8 kumar:3 springer:1 onig:1 equation:4 work:1 mi:3 mj:1 f1:4 f2:3 f3:1 f4:3 f5:3 introduces:1 indicates:1 verlag:1 filter:2 rather:1 very:1 ordinary:1 cjj:2 lai:1 replacing:1 max:1 after:1 fi:1 realized:2 light:2 fibers:1 deutsche:1 fundamental:6 correlation:13 order:4 typical:2 dx:4 cumulant:2 over:1 soc:2 pulses:2 filters:2 mentioned:1 perfect:1 group:1 temporal:1 detected:2 fig:9 schmidt:2 into:1 maximal:1 integral:1 disregarded:1 scaling:1 oxford:1 always:1 establishing:1 possibilities:1 inequality:3 each:1 instability:2 universit:1 mean:2 domain:24 defocusing:1 gaussian:2 related:2 jena:2 frequency:1 quantum:4 our:2 nonlinearities:1 special:1 shown:2 acknowledgment:1 space:1 rev:2 increase:3 may:2 fiber:3 turning:1 theory:1 formation:1 york:1 e5:3 e4:3 e1:3 e3:1 e2:2 motion:1 hence:1 there:1 features:1 variables:1 number:11 restrict:2 given:2 kodama:1 temperature:1 ordering:1 master:2 ordered:1 testing:1 explanation:1 forschungsgemeinschaft:1 transverse:1 part:1 focusing:2 x0:7 than:5 relative:1 require:1 see:6 contrary:1 fˆ:1 sech:1 sp:1 fluctuation:1 seen:2 note:1 emphasis:1 internal:3 even:1 play:1 normal:2 optimized:4 germany:1 phase:1 measured:2 stands:1 soliton:20 nonlinearity:2 considered:2 stronger:2 kn:2 points:1 velocity:1 left:1 normally:1 show:2 violation:2 supported:1 bright:1 hasegawa:2 parameters:2 should:1 only:1 factor:3 silberberg:1 hope:1 c2ij:1 means:1 beams:1 expectation:1 beam:2 cannot:1 closely:1 platz:1 reveal:1 evolution:2 continuum:1 fields:1 arxiv:1 predicted:1 undamped:2 including:1 kernel:1 achieved:2 violated:1 correlations:5 observed:5 intensity:3 gunnar:1 best:1 techniques:1 chirkin:1 fano:3 state:1 smallest:2 between:2 physikalisches:1 approach:1 x20:1 terms:1 amplitude:2 attention:2 analyzed:1 both:2 according:1 propagation:6 figures:1 otherwise:1 filtering:2 simple:1 poissonian:1 corresponds:1 dimensional:2 losses:1 moreover:1 broadening:1 oliver:1 described:1 transformations:1 aˆ:3 wien:1 due:1 cauchy:2 slowly:1 damping:1 ph:1 corresponding:1 formed:1 photon:11 coherent:1 those:1 case:2 multi:1 laser:1 theoretisch:1 variances:1 aip:1 value:2 alter:1 near:1 optimization:1 n2j:1 n2i:2 larger:1 vogel:1 almost:1 4db:1 ii:2 ij:2 leuchs:1 γtd:1 etc:1 lengths:1 media:2 unity:1 complex:1 quant:1 filtered:1 ludwig:1 higher:3 schiller:1 effect:4 haus:1 parametrized:1 entanglement:1 schr:1 well:1 analysis:1 obviously:1 patterns:1 without:1 components:2 coordinate:1 maxima:1 distances:1 intervals:2 scattering:1 absorption:2 smith:1 improvement:1 passive:1 friedrich:1 extends:1 lett:2 transformation:2 opt:5 nonoverlapping:1 depends:1 iγ:1 possible:1 press:1 using:3 qualitative:1 communications:1 either:1 output:2 weiner:1 classical:4 oll:2 strongest:2 provided:1 broadband:2 assuming:1 welsch:2 schwarz:2 noise:3 eduard:1 expansion:2 clarendon:1 plots:7 properties:2 central:1 vysloukh:1 anomalous:1 ρˆa:1 sensitively:1 discretization:1 markovian:1 presence:1 spreading:1 numerically:2 eiωx:1 variable:1 appropriate:1 square:1 operator:2 korolkova:1 bosonic:2 statistics:2 institut:1 compression:1 assumed:1 initial:2 dispersion:4 width:2 6db:1 low:1 way:1 was:1 function:2 offer:1 femtosecond:1 jul:1 line:2 considerable:1 cij:2 cii:2 ωi:1 converted:1 limit:1 fluctuations:1 semiclass:1 bandpass:1 detailed:1 constant:3 fokkerplanck:1 diffraction:2 am:2 general:1 substantially:1 dν:1 exist:1 relates:1 interferences:1 ni:6 nj:2 compared:1 dotted:1 eq:2 whereas:1 when:2 field:4 other:3 role:2 spatial:3 elements:1 nonclassical:7 a0:2 linearization:1 multimode:1 correlated:1 cauchyschwarz:1 interval:1 pseudo:1 governed:1 time:1 n2:1
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quant-ph9907091.txt |@word now:3 customary:1 consider:3 switched:1 amplifier:4 focus:1 four:8 eds:1 quadrature:2 repetition:1 technique:5 tr:1 efficiencies:2 kη:4 those:1 th:1 γl:1 divergent:1 advantage:3 orthogonal:2 keeping:1 results:7 sidebands:1 experimentally:1 splitter:2 randomness:1 smithey:1 pbs:3 presented:2 large:1 vector:2 small:1 eigenvalues:1 optics:3 vasilyev:2 direct:1 pulse:1 feasibility:2 second:2 cost:1 plenum:2 pass:1 eiϕ:1 estimated:1 carlo:2 linear:2 even:1 nonlinear:2 apparatus:3 selected:1 lengthy:1 homodyning:1 experiment:6 new:3 order:2 method:1 full:2 respectively:9 tomographically:1 here:2 diagonal:3 following:5 focused:1 directions:2 along:2 box:1 dividing:1 involved:1 vectors:1 allows:3 ignoring:1 usually:1 studi:1 narrow:1 caro:1 composed:1 via:1 spatially:1 bs:3 polarizers:1 unitary:2 decrease:1 counts:1 total:2 circumvent:1 unit:1 plot:2 use:2 sacchi:1 would:1 dalibard:1 probabilities:8 process:1 sample:1 ψi:1 shaded:2 taken:1 type:1 theoretical:4 more:4 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quant-ph9907092.txt |@word ibid:2 externally:1 concept:1 partial:1 consider:5 lagrangian:2 forbidden:22 trigonometric:5 leads:2 executing:1 proposition:1 generalize:1 go:3 recami:1 transits:2 objections:1 causes:1 indeterminism:1 whose:3 inverse:1 ver:1 zone:1 irrelevant:1 equivalence:22 canonical:1 edward:1 infinitesimally:3 those:1 th:6 include:1 incurs:1 very:2 semi:1 wave:9 electron:3 exact:2 school:7 level:5 suffices:1 solution:14 travels:1 solved:1 convenience:1 small:3 noted:4 inconsistent:1 louis:1 wronskian:2 force:2 findings:3 consistent:14 mantica:1 approximation:1 zero:11 premature:1 copenhagen:12 linear:9 even:14 established:1 what:2 nonlinear:3 barrier:8 giving:1 section:1 expressed:5 schwarzian:4 wxxx:4 infinitesimal:8 goes:4 renders:3 increasing:1 hamiltonjacobi:1 contrast:5 hˆopital:1 coefficient:2 degree:2 respectively:3 residual:21 here:4 bi:3 aid:1 alone:1 path:1 equations:3 change:1 knowledge:7 remark:1 numerator:2 cts:1 shift:5 study:2 changed:1 allows:1 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quant-ph9907093.txt |@word represent:1 consider:11 squared:7 results:8 ala:1 leads:4 quadrature:21 consists:1 contributions:1 ρss:8 whose:1 hold:1 overlapping:1 calculate:2 iii:1 tr:4 γt:2 finally:1 squeezing:43 under:4 stochastic:1 indicating:2 amplitudes:2 evolves:1 far:1 frequencies:3 rise:1 springer:1 induce:1 wave:2 resonant:7 clemens:2 difference:1 pumping:1 incoherent:27 level:10 transmission:3 applicable:1 md:1 leave:1 solved:1 small:7 smith:1 optics:3 noted:2 smaller:1 force:1 oscillation:1 consistent:1 sign:1 go:1 zero:7 enhancement:1 further:5 odd:1 shining:1 even:2 index:1 what:2 nonlinear:9 sub:2 rate:8 section:5 above:4 new:2 increasing:3 coefficient:1 unsure:1 d1:3 component:3 κa:1 here:16 atoms:1 highly:1 desired:1 focused:1 free:2 akin:1 represented:1 consideration:4 strong:2 equations:9 appears:4 change:1 obtained:2 splitting:1 root:1 leaves:1 larger:3 amount:4 simultaneous:1 resulting:3 usually:2 resonance:6 fourier:4 plotted:1 9i:1 9h:1 via:3 9a:1 9c:1 9b:1 9e:1 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quant-ph9907094.txt |@word managed:1 consider:2 remarkable:1 rev:6 lack:1 results:7 four:7 commute:1 maxima:1 whose:1 careful:1 depend:1 violate:1 tr:2 nonlocal:1 uniqueness:1 does:4 spain:1 under:1 applied:1 amplitudes:1 straightforward:2 choice:8 wishes:1 every:1 matrices:5 condition:9 switches:1 immediately:1 tra:2 turns:1 notes:1 trb:2 deals:1 vector:12 eigenvalues:2 noted:1 consistent:1 coefficient:3 direct:2 sign:4 located:1 zero:7 incidentally:1 further:3 established:1 what:1 incompatible:1 giving:1 sum:1 axes:1 analogously:1 expressed:3 version:2 above:8 del:1 pioneering:1 simultaneously:3 respectively:6 component:2 jointly:2 ranges:2 identifications:1 cos2:2 fulfill:1 directions:2 along:5 equations:2 19b:1 alto:1 remark:1 involved:2 vectors:3 allows:1 contradiction:13 resulting:1 pick:1 makes:1 involves:1 plotted:1 uniquely:1 golden:1 projection:1 requiring:2 explained:1 outcomes:2 hardy:22 sgn:3 total:1 readily:2 would:3 prove:1 remains:2 positive:1 give:1 interception:1 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