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quant-ph9903031.txt |@word partial:2 consider:5 alternatives:1 focus:1 proposition:1 go:1 certainly:1 inverse:1 depend:1 calculate:4 answered:1 finally:1 amplitudes:10 orthogonal:2 very:1 results:2 every:1 experimentally:1 did:1 cavendish:1 t2:2 solution:1 t1:2 leave:1 past:1 pass:1 dynamics:1 canonical:1 will:4 what:2 stands:1 new:2 contrast:1 here:3 address:1 represented:1 change:1 institute:1 allows:1 example:2 christchurch:1 proof:1 via:10 inference:1 madingley:1 namely:2 private:1 boolean:1 hindsight:1 apply:1 establish:1 use:1 proceed:1 sharper:1 entities:1 probabilities:4 comparing:1 therefore:2 totality:1 exhaustive:1 entails:1 initial:1 odinger:1 particular:2 known:1 cases:1 must:1 logarithm:1 equation:1 work:5 renders:1 my:1 caticha:7 history:1 give:1 process:12 states:4 slit:1 assumptions:4 conversely:1 discussion:1 how:1 stock:1 mar:1 algebra:2 our:5 earlier:2 demanding:1 multiplication:1 representations:1 law:4 parallel:6 departure:1 automatically:1 exclusive:1 paper:1 through:3 filters:5 satisfies:2 before:1 derive:3 thank:1 good:1 regarding:1 introduce:1 now:2 nor:1 february:1 equality:1 always:1 university:2 each:1 associative:2 referred:1 directly:1 series:4 combining:2 quantum:5 laboratory:1 transitions:3 eq:2 event:1 special:2 shown:4 opened:1 since:2 rev:2 denoted:1 compounding:1 ref:1 math:2 theory:1 put:1 could:1 transition:4 filter:1 introduction:1 canterbury:1 hence:1 assign:1 first:2 xi:5 probability:9 variables:1 number:3 restrict:1 done:2 another:1 reached:1 distributive:1 open:1 given:7 similarly:1 bears:1 needed:5 assumption:2 calculations:1 john:1 final:1 commutativity:2 geoff:1 determined:1 amplitude:11 need:1 their:2 contents:1 take:1 subject:1 shall:1 most:2 zealand:1 typeset:1 mechanical:3 physics:2 laws:1 futhermore:1 bring:1 carefully:1 find:4 resemblance:1 written:1 should:1 analytic:2 only:3 achieve:1 dependent:2 between:1 cannot:1 processes:11 arxiv:1 summary:1 bag:1 racah:1 set:1 achieved:2 0he:1 see:2 result:1 close:1 concern:1 satisfying:1 probable:1 ways:1 review:1 artificial:1 enough:2 simplest:1 neither:1 reading:1 approach:2 terms:2 attention:1 article:1 both:3 commenting:1 cox:4 taking:1 baltimore:1 ariel:1 comment:1 among:1 point:1 ca:1 pr:7 addition:1 been:1 int:2 much:1 combined:1 interest:2 basic:1 ph:1 corresponding:2 linearity:1 c2:7 c1:7 present:3 multi:1 look:1 pacs:1 amend:1 aim:1 applies:1 situation:1 property:1 dubious:1 helped:1 examined:1 hebrew:1 different:1 verified:1 author:2 things:1 make:1 same:3 complex:3 quant:1 arguments:2 independent:1 assigns:1 uses:1 changing:1 recent:1 task:1 schr:1 acknowledgement:1 without:1 consistency:6 drawing:1 realised:1 obtain:5 rest:1 yes:1 seems:1 combine:2 transformation:2 demands:2 rules:3 possible:3 press:1 using:2 execution:1 like:1 particle:2 follows:1 unnecessary:1 either:1 arbitrary:1 setups:1 works:1 classical:1 certain:1 born:1 recognition:1 does:1 minimal:2 obey:1 revtex:1 bz:1 would:1 hopkins:1 mutually:1 introduced:1 road:2 cambridge:1 markovian:1 references:1 jerusalem:1 assumed:1 there:3 fully:1 way:3 was:3 function:3 a57:2 form:5 but:1 made:1 us:2 agree:1 mechanics:1 ai:6 stedman:1 abstract:1 am:1 general:5 formulation:1 functions:4 no:2 department:1 mathematics:1 theor:2 briefly:1 kinds:1 calculating:1 cb3:1 astronomy:1 sides:1 assume:1 together:1 time:6 starting:1 indirectly:1
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quant-ph9903033.txt |@word represent:1 logarithms:1 epeau:1 consider:2 maximum:2 rev:6 results:1 four:2 eds:2 entropy:2 computation:1 research:1 issues:1 equiprobable:3 whose:1 maximally:2 depend:2 tr:2 send:2 excluded:1 under:3 tr1:1 tr2:1 workshops:1 advantage:1 orthogonal:11 far:1 dell:1 choice:5 ui:1 matrices:2 generalised:1 transmission:3 turns:1 vector:2 eigenvalues:2 mahler:2 upper:1 sin2:5 archirafi:1 imply:1 mason:1 theory:3 even:1 index:1 stands:1 ak1:1 decoding:1 above:3 consisting:1 full:1 notions:1 degree:5 respectively:1 never:1 teleportation:1 here:2 plenio:1 cos2:5 address:1 along:2 observing:1 scienze:1 vectors:1 allows:1 amount:1 akn:1 schumacher:1 action:5 composed:1 via:3 useful:2 explained:1 plenum:1 duca:1 unit:2 use:2 takes:1 would:3 codewords:1 probabilities:3 ministero:1 therefore:4 taken:2 scope:1 means:1 noisy:3 more:3 bennett:6 outputs:1 operators:3 maximise:2 berlin:1 particular:4 foundations:1 entangle:1 kraus:1 springer:1 ρi:10 science:1 equation:2 work:2 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quant-ph9903037.txt |@word represent:3 concept:1 forget:2 comparatively:1 concern:1 results:6 four:1 eδ:1 consists:1 exceptional:1 reasoning:1 consider:2 whose:2 certainly:1 inverse:3 depend:2 referring:1 eα:10 concerned:7 equivalence:2 acting:1 environment:40 finally:3 analogous:1 worth:1 case:1 straightforward:1 outside:6 very:2 rise:1 choice:4 corollary:1 putting:3 summarized:1 mixing:1 emphasized:2 condition:15 leads:1 hamiltonian:26 ref:5 pˆ2:2 subscript:1 eigenvalues:1 occurrence:5 consistent:2 go:1 imply:3 rigorous:1 further:5 linear:4 spectral:1 tually:1 what:6 ˆs:6 appear:2 apparatus:1 incompatible:1 giving:3 section:12 analogously:2 expressed:1 subspaces:1 3b:1 3a:1 method:2 told:2 satisfy:1 8a:5 simultaneously:6 notions:2 exchange:1 respectively:3 here:6 desired:1 meet:2 along:1 appears:4 change:2 rigorously:1 mations:1 involved:1 changed:1 allows:2 contradiction:2 simultaneous:1 usually:2 vcoul:3 uniquely:2 ψm:1 via:2 elaborated:3 assertion:2 analyzing:2 redefining:4 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quant-ph9903038.txt |@word consider:2 forbidden:1 results:3 ψ1i:1 go:1 remarkably:1 cases:4 issues:1 whose:1 aug:1 deterministic:5 under:2 analogous:1 equalities:1 case:7 string:1 orthogonal:20 very:1 choice:1 novel:18 exact:2 condition:3 knight:1 guo:7 bangor:2 small:1 enhance:1 says:2 deutsch:1 consistent:2 hillery:3 past:1 zero:16 street:1 pass:1 further:3 machines:6 linear:20 abc:4 diag:3 sum:2 expressed:3 find:3 above:6 international:1 method:1 satisfy:2 bruß:2 simultaneously:1 chose:1 respectively:1 component:1 teleportation:1 here:4 desired:1 plenio:1 separation:2 others:4 pati:4 along:1 obtained:1 vectors:2 allows:3 suggests:1 amount:1 schumacher:1 suitable:1 useful:3 imagine:1 put:1 earlier:1 total:3 linearly:16 takes:1 would:7 prove:8 probabilities:4 positive:14 contains:1 negative:1 ψj:29 classically:1 ψi:57 call:1 therefore:4 ψl:8 means:1 type:1 theoretical:1 more:3 composite:6 india:1 particular:1 known:2 foundations:1 hole:1 producing:5 must:1 kumar:1 postselection:1 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quant-ph9903040.txt |@word represent:1 schwendimann:1 consider:1 pointing:1 desirable:1 results:1 sonderforschungsbereich:1 leads:4 consists:1 follow:1 causes:1 whose:1 inverse:1 const:2 calculate:1 producing:1 tr:2 environment:9 finally:1 petersburg:2 under:1 norm:3 amplitudes:1 presently:2 evolves:1 very:2 rise:2 unfamiliar:1 maali:1 anonymous:1 resonant:2 experimentally:2 difference:1 exact:1 four:1 level:3 evaluation:1 solution:1 damped:2 large:2 vector:2 laser:1 eigenvalues:2 upper:2 sin2:4 prediction:1 pulse:2 rate:5 theo:1 dynamics:4 haake:8 even:3 detuned:2 sum:1 selected:2 dephasing:1 d3:1 experiment:1 above:4 obvious:1 ever:1 never:2 component:1 atoms:14 met:1 cos4:2 cos2:2 separation:1 represented:1 based:2 stamatescu:1 strong:1 equations:1 differential:1 obtained:1 ref:1 rigorously:1 institute:1 involved:1 studied:1 reports:1 usually:1 resonance:1 changes:1 involves:1 composed:2 matos:1 via:1 scales:1 prefer:1 courtens:1 poyatos:1 linearly:1 superpositions:5 prove:1 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quant-ph9903041.txt |@word schwendimann:1 consider:2 pointing:1 lls:1 hint:1 results:4 leads:7 scalar:1 go:1 gl:2 whose:1 inverse:1 const:2 calculate:1 tr:1 containing:1 environment:10 γi:2 compensate:1 petersburg:2 stable:2 norm:3 straightforward:1 very:1 springer:1 maali:1 worst:1 resonant:4 experimentally:6 exact:8 encounter:1 four:1 hamiltonian:2 evaluation:1 solution:2 damped:1 large:6 bonifacio:1 vector:4 math:1 section:1 small:2 markov:1 degeneracy:3 upper:1 ρm:3 consistent:1 sin2:2 prediction:2 dimensional:1 approximation:1 located:1 rate:2 qmn:1 further:2 ρn:5 canonical:1 even:5 detuned:1 brackets:1 sum:2 remain:1 lengthy:1 experiment:1 poles:1 new:1 contributes:1 method:6 coefficient:2 evolving:1 simultaneously:1 diagonal:4 exchange:1 never:1 here:2 understanding:1 desired:1 separation:1 directions:1 sine:2 obtained:3 great:1 institute:1 involved:1 study:3 studied:1 allows:1 reports:1 suggests:1 usually:1 symmetrical:1 conveniently:1 suitable:2 reckoned:2 via:1 projection:1 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quant-ph9903042.txt |@word represent:1 logarithms:1 concept:1 consider:16 crucial:1 edn:8 results:1 gy:1 leads:2 postponing:1 gt:3 gc:6 computation:10 edu:2 consists:1 gm:8 gj:8 c0:17 depend:1 mπ1:4 graph:4 concerned:1 technique:3 γt:1 γj:2 finally:2 program:1 squeezing:4 manifolds:1 nodes:2 case:14 g4:3 g3:4 string:4 straightforward:2 orthogonal:4 far:4 connects:1 seemingly:2 print:1 every:5 entries:1 ma:1 exact:2 condition:2 dim:1 indicate:1 roy:2 solution:1 discrete:2 vector:7 math:1 warren:3 upper:2 zj:1 deutsch:4 sℓ:2 consistent:3 sign:5 further:1 substitute:1 linear:2 even:2 index:1 essence:1 sj2:1 section:2 sj1:1 find:1 version:1 above:6 values:4 method:8 beals:1 leeuwen:1 margolus:1 degree:2 aπ:3 respectively:1 modify:1 here:1 simon:1 represented:3 path:15 along:1 strong:3 z1:2 z2:1 box:1 search:1 distinctness:3 study:1 vectors:8 resulting:1 permutation:1 usually:1 postponed:6 uniquely:1 formulated:1 divide:1 family:1 boolean:34 limn:1 apply:2 unit:5 use:3 superpositions:1 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quant-ph9903043.txt |@word caused:1 lack:1 results:2 leads:1 roy:1 scalar:2 woody:2 causes:1 whose:1 hold:1 calculate:1 paris:1 nonlocal:1 absorbing:2 th:2 under:7 must:1 cm2:1 very:1 rise:1 springer:1 wave:2 corollary:1 difference:4 condition:7 entire:1 vibrational:1 level:3 turns:1 anisotropy:5 large:4 science:1 small:2 relation:2 noted:1 enjoy:1 upper:1 fµν:1 ten:1 ze:1 za:1 second:6 dynamics:1 correspond:1 linear:3 spectral:1 3z:1 what:1 appear:4 giving:1 section:1 interactions:1 uniform:3 indian:1 above:6 new:3 cmbr:6 filled:1 coefficient:3 full:1 exchange:1 spacing:3 water:1 desired:1 address:1 directions:2 based:1 along:2 appears:1 obtained:1 noticeable:1 shift:7 allows:1 reason:1 amount:1 plotted:2 blackbody:12 scales:1 scaled:1 planck:7 use:1 figure:2 would:11 remains:4 nine:1 cultivation:1 therefore:2 type:3 today:1 distinct:1 becomes:1 apparent:7 line:3 mather:1 particular:1 mounted:1 iii:3 circumstances:3 high:5 account:1 rotational:1 recall:1 work:3 paragraph:1 values:1 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quant-ph9903045.txt |@word represent:1 partial:1 consider:2 spiridonov:2 expressions:4 zhedanov:1 naukova:1 row:1 ρss:12 whose:4 inverse:21 γs:11 technique:3 nonlocal:2 recurrence:1 neighbours:1 those:1 under:1 nodes:1 advantage:1 orthogonal:8 springer:4 wave:2 every:4 tridiagonal:4 difference:12 matrices:4 condition:6 immediately:2 presented:3 bn:1 turns:1 permits:1 solution:5 integrated:1 large:1 discrete:22 vector:10 indices:1 eigenvalues:2 anal:1 noted:1 direct:1 zero:2 nonhomogeneous:1 qualitatively:1 dynamics:1 substitute:1 linear:1 spectral:18 established:3 what:1 nonlinear:2 sum:3 analogously:1 expressed:1 version:3 above:3 new:6 net:1 method:2 satisfy:2 relationships:3 degree:9 here:1 desired:1 objects:1 represented:2 consideration:2 equations:7 appears:1 change:1 obtained:7 search:1 institute:3 study:1 vectors:7 allows:1 orthogonalization:7 minsk:1 action:2 formulated:1 family:1 elaborated:1 austria:1 summation:2 use:1 would:2 ψs:2 next:1 noting:1 therefore:2 ψm:4 taken:4 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quant-ph9903046.txt |@word replacing:1 logarithms:1 sci:3 consider:1 wd:1 results:3 proposition:7 overlap:1 computation:8 edu:1 consists:1 expressions:1 layers:2 inverse:1 pointing:1 factoring:3 languages:3 finally:5 does:1 bqp:1 qacc:3 include:3 conjecture:1 supported:1 splitting:1 fan:8 decide:1 little:1 matrices:1 conjugating:3 ajtai:1 notes:2 occurs:1 leave:1 discrete:2 commute:1 recall:1 small:1 focs:2 zero:2 hyde:1 further:1 implemented:2 odd:1 linear:1 even:2 intimately:1 xor:1 appear:2 sum:1 negates:2 19th:1 version:1 above:3 negated:4 acknowledgments:1 relationships:1 margolus:1 simultaneously:4 respectively:2 applies:2 here:6 diagonal:5 desired:1 mckenzie:1 address:1 change:1 digits:1 convert:2 provably:1 wesley:1 institute:1 shift:4 study:2 larger:1 allows:3 derandomization:1 usually:1 proof:2 makes:1 offs:1 useful:2 family:1 boolean:5 razborov:1 apply:6 total:2 use:8 would:2 prove:4 remains:1 stated:1 toffoli:6 classically:2 automata:3 call:2 therefore:2 theoretical:3 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quant-ph9903047.txt |@word consider:2 caused:1 results:5 illustrated:2 follow:3 calculate:1 tx:1 wavepacket:1 young:2 supported:1 superficially:1 tj:16 detec:1 under:2 breach:1 maryland:1 circumstances:1 tb:1 sent:2 ta:2 applied:1 labels:1 amplitudes:3 straightforward:2 orthogonal:1 very:1 frequencies:2 wave:7 electron:2 wishes:1 figs:2 emphasized:1 difference:1 condition:1 four:3 disturb:1 o4:1 presented:1 transmission:2 t4:1 t2:8 t3:1 t0:25 t1:7 large:2 small:2 optics:2 noted:1 upper:1 consistent:1 sin2:2 prediction:1 pulse:3 sign:2 approximation:1 rate:8 further:1 even:2 index:2 what:1 nonlinear:4 apparatus:1 sum:1 find:2 experiment:12 above:1 new:2 learned:1 edited:1 simultaneously:1 respectively:9 never:1 atoms:4 reported:1 cos2:2 address:1 path:26 along:6 observing:2 transformation:1 obtained:1 naval:1 extraordinary:1 shift:5 study:1 reports:2 fourier:1 makes:1 delays:1 klyshko:2 appropriately:1 via:3 explained:1 marked:2 outcomes:1 county:1 herzog:1 unitary:1 motor:2 welch:1 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quant-ph9903048.txt |@word sergei:1 consider:3 represent:1 rev:9 alternatives:3 results:1 illustrated:1 scalar:1 comments:1 consists:2 tt:1 ti:2 breach:1 maryland:2 include:1 amplitudes:18 orthogonal:2 rod:7 wave:1 orientations:1 experimentally:1 difference:2 condition:3 propagating:1 pbs:2 purely:1 did:2 t2:6 solution:1 t1:7 coincidences:1 optics:1 smaller:2 sin2:2 pulse:40 second:7 further:2 spectral:1 nonlinear:2 plays:1 stands:1 clock:2 thickness:1 experiment:12 new:1 90m:1 satisfy:1 supporting:1 respectively:3 gathered:1 never:2 here:3 met:1 address:1 path:3 change:2 obtained:1 naval:1 involved:1 vectors:2 accomplished:1 resulting:1 usually:2 narrow:1 klyshko:1 apr:1 explained:2 polarizers:1 brought:1 1st:1 counts:5 univ:2 unit:2 fed:1 eω:3 would:2 positive:1 visit:1 classically:1 therefore:3 type:3 theoretical:1 diagrams:5 more:1 separated:9 introducing:2 envelope:1 visibility:15 train:1 normalized:1 varying:1 must:2 md:1 science:1 setup:4 work:1 following:1 spontaneous:1 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quant-ph9903049.txt |@word represent:1 concept:2 allowed:2 consider:5 secondly:1 rev:6 forbidden:1 global:1 results:4 existing:1 leads:7 roy:1 code:2 entropy:71 ts:1 computation:2 go:1 follow:2 reasoning:3 soc:1 minω:3 certainly:1 violate:1 knill:5 tr:11 acting:2 nonlocal:1 environment:16 company:1 finally:3 efficiencies:1 those:1 under:4 exposition:1 analogous:2 swap:2 started:1 p2:1 conjecture:1 infinite:1 returned:1 orthogonal:14 very:5 than:9 mβ:1 me:2 ωsi:2 manipulated:1 additional:4 surprise:1 fab:2 difference:3 appropriately:1 condition:1 ibm:1 treating:1 believed:1 swapping:1 presented:3 did:2 applicable:1 occurs:2 large:5 dealt:1 gc:8 markov:1 deleting:2 noted:1 upper:10 smaller:3 says:1 occurrence:1 dealing:1 direct:1 sign:1 jump:1 consists:2 second:12 perspective:1 further:2 dynamics:1 ρn:2 even:1 aim:2 what:8 errors:11 plays:1 appear:1 apparatus:70 section:12 analogously:1 expressed:1 version:1 goes:1 deal:1 new:4 net:1 increasing:5 preserved:2 satisfy:1 edited:1 bi:2 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quant-ph9903050.txt |@word limited:1 partial:1 switched:1 gz:1 ladders:1 generalize:1 follow:3 expressions:1 nwo:1 hole:3 whose:1 rmki:1 dα1:1 aug:1 tail:1 th:1 under:1 summarizes:1 straightforward:2 zhang:1 very:1 multi:2 choice:1 putting:1 summarized:1 nieto:1 matrices:1 hamiltonian:1 t0:2 correct:1 large:15 solved:2 minimal:2 small:2 dαn:1 referred:1 optics:2 2πmt:1 work:1 approximation:1 elegant:1 zero:1 street:1 canonical:1 even:1 index:2 what:3 sum:1 annals:1 above:4 new:5 increasing:2 method:3 satisfy:1 condensed:4 full:1 never:1 component:1 here:3 hundreds:2 behaviour:2 pratt:1 free:2 equations:2 appears:1 change:1 obtained:1 studied:1 suggests:1 amount:3 poisson:1 permutation:1 action:1 hospitality:1 suitable:1 highly:1 aph:1 matthews:1 condensates:3 counts:1 total:2 dnf:1 would:1 emiai:2 lasing:1 contains:2 classically:1 nucl:1 call:2 attribute:1 taken:2 zim:2 today:1 more:2 formally:1 becomes:1 operators:4 odinger:3 ip0:1 appendix:1 normalized:5 particular:1 known:2 ασi:1 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quant-ph9903052.txt |@word consider:3 chinese:2 caused:1 magnetic:1 particular:1 results:7 leads:1 broader:1 follow:1 remarkably:1 reynaud:1 calculate:3 c0n:1 tr:2 quasi:1 stable:1 conjecture:1 supported:1 amplitudes:5 straightforward:1 very:2 frequencies:6 rise:1 wave:1 electron:1 breit:1 resonant:5 difference:3 condition:1 level:11 solution:4 solved:1 differential:1 math:4 small:6 lines:3 smaller:3 force:1 shatin:1 oscillation:7 sin2:1 direct:1 sign:1 approximation:8 limǫ:1 second:3 further:3 dynamics:2 ode:1 even:8 will:3 what:1 appear:2 giving:1 while:1 new:6 method:1 hasenfratz:1 never:1 equals:1 here:1 behaviour:5 cos2:1 along:1 strong:1 equations:1 change:2 box:1 great:1 leung:1 involved:2 study:7 studied:3 allows:2 vibrating:2 periodic:2 resulting:1 suggestion:1 usually:1 resonance:10 narrow:1 changes:3 plotted:3 emerge:1 via:1 regardless:1 nikonov:2 vij:1 wij:2 highly:1 scaled:3 linearly:1 plot:1 use:2 remains:1 jaekel:1 next:1 few:1 chu:2 more:4 flat:1 eiθ:1 acceptable:1 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quant-ph9903053.txt |@word secondly:1 gt:3 rev:2 results:4 four:1 scalar:2 tenuous:3 go:1 woody:4 expressions:2 depend:2 cobe:2 paris:1 father:1 acting:1 nonlocal:5 spirit:1 finally:1 those:1 th:1 under:7 must:4 delhi:1 g0:3 very:5 rise:1 wave:1 electron:3 every:1 experimentally:2 difference:2 condition:9 generalised:1 entire:4 level:3 notes:1 viable:1 large:1 science:2 relation:3 shows:2 dip:1 upper:1 ψi:1 consistent:1 direct:1 past:3 astrophys:1 second:4 further:2 dynamics:1 theory:5 spectral:1 established:2 what:1 appear:2 giving:2 exactly:1 indian:1 above:3 new:4 cmbr:9 satisfy:1 here:1 atoms:1 address:3 directions:1 obtained:2 substance:1 shift:1 larger:1 allows:1 reason:1 suitable:1 settled:1 blackbody:3 via:2 useful:1 fand:1 spooky:1 replace:1 visible:1 should:2 planck:5 bra:1 proceed:1 would:2 recalling:1 negative:1 few:1 cultivation:1 call:1 therefore:3 type:2 until:1 today:1 distinct:3 started:1 becomes:2 operators:2 apparent:3 clue:1 appendix:5 mather:1 particular:1 known:1 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quant-ph9903054.txt |@word consider:4 rev:7 reversibility:1 results:4 leads:1 entropy:3 follow:1 whose:1 inverse:1 concerned:1 deterministic:3 presents:1 γi:6 vee:1 protocols:3 under:2 applied:2 provides:3 very:2 blj:1 ηij:3 choice:3 sons:1 condition:2 generalised:1 presented:2 die:1 trb:1 solution:7 solved:2 small:1 upper:2 work:3 zk:2 exten:1 consistent:1 zero:1 rigorous:1 qualitatively:1 theory:7 guarantees:1 what:2 appear:1 advantageous:1 expressed:1 above:3 shared:3 appeal:1 method:5 seeks:1 satisfy:1 exchange:1 never:1 teleportation:1 here:1 understanding:1 plenio:4 obtained:5 studied:1 p2:1 amount:5 simultaneous:1 procedure:3 stressed:1 complicated:1 bob:14 suitable:1 βik:3 uniquely:1 showing:1 merely:1 convexity:1 hardy:3 achievable:1 apply:5 manipulate:1 readily:1 use:4 asymptotic:3 would:2 prove:2 probabilities:1 positive:2 therefore:4 criteria:1 taken:1 jonathan:2 type:1 until:2 more:4 optimizing:1 bennett:6 formally:1 composite:2 distillation:1 operators:2 constructs:1 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quant-ph9903055.txt |@word 1st:1 represent:2 consider:6 edh:1 results:8 four:2 scalar:2 commute:4 computation:1 foundations:1 consists:2 expressions:2 issues:1 particles:1 inverse:1 calculate:1 knill:1 technique:6 ts:2 tp:2 γk:1 finally:2 those:1 under:1 tg:2 analogous:1 b212:3 tc:3 applied:6 r14:3 supported:1 r13:3 very:2 choice:1 entries:1 difference:1 matrices:1 arrange:1 entire:3 num:1 hamiltonian:14 turns:1 list:1 applicable:2 t0:2 z11:1 large:9 solved:5 vector:5 succession:2 small:11 anal:1 noted:1 3x5:1 mn:1 force:1 deutsch:1 b25:1 b24:2 b23:3 b22:4 initializes:1 sign:2 approximation:7 go:1 second:8 cost:1 equal:2 further:1 odd:5 canonical:1 residue:1 index:1 what:3 errors:5 developed:2 sub:2 iterating:2 brackets:1 giving:4 section:5 selected:2 above:8 method:89 body:1 tasso:1 focuses:1 led:1 b2x:3 respectively:1 error:21 residual:1 here:5 b2p:2 iσz:1 iσy:1 iσx:1 focused:1 ansatz:3 separate:1 represented:2 equations:21 αip:3 change:1 box:1 search:10 suitably:1 involved:1 study:2 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quant-ph9903056.txt |@word concept:1 consider:2 rev:14 results:3 roy:1 cooperative:2 edu:1 bergmann:1 expressions:1 devoted:1 pax:1 clarification:1 reuven:1 graph:1 suits:1 th:1 under:1 analogous:1 charles:1 far:1 frequencies:3 wave:1 resonant:2 vibrational:1 level:12 knight:2 notes:1 solution:4 ox:1 large:1 vector:1 small:3 3b:1 optics:2 caltech:2 upper:3 computation:1 deutsch:3 pulse:8 sign:1 approximation:1 zero:6 qualitatively:1 dynamics:2 casual:1 even:3 aim:1 interatomic:4 sub:1 richard:2 section:1 goes:5 ˆi:3 3a:1 exchange:2 burnett:1 component:1 teleportation:1 here:4 atoms:22 plenio:2 relaxation:1 directions:1 along:5 strong:1 violate:1 obtained:2 antisymmetric:13 technical:1 allows:1 amount:2 resonance:3 implement:1 plotted:1 negligibility:1 via:1 spatially:1 transit:2 manage:1 logical:1 coinciding:1 addressed:1 apply:1 plot:1 use:3 hegerfeldt:1 proceed:1 working:2 remains:2 positive:2 few:1 therefore:1 ψa:6 ψg:2 more:1 possession:1 populations:6 operators:1 stable:2 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quant-ph9903057.txt |@word represent:1 sci:3 consider:1 pointing:1 interference:6 magnetic:2 dollar:2 shor:2 eds:3 computation:6 edu:1 cerf:1 query:1 issues:1 woodhouse:1 inverse:4 leung:2 reformulate:1 knill:1 factoring:1 presents:1 finally:2 behave:1 th:3 under:1 recycle:1 analogous:5 resources:8 division:1 supported:1 wave:10 worst:2 exact:1 fourth:1 splitter:7 hamiltonian:5 applicable:1 fewer:1 large:1 solved:2 science:8 ups:1 undoes:1 throught:1 deutsch:2 pulse:6 second:5 cost:5 pass:3 turning:1 chem:1 click:1 putting:2 what:3 minimize:1 contributed:1 version:11 above:5 new:3 net:1 increasing:1 method:5 contrast:1 processing:1 lange:1 teleportation:1 answers:1 atoms:1 desired:1 objects:2 alone:1 along:1 appears:1 box:29 sending:2 search:38 hansen:1 incoming:1 institute:1 involved:1 goldwasser:2 allows:1 suggests:1 accomplished:3 usually:1 composed:3 tasks:1 followed:1 requiring:1 private:1 neutrons:1 put:5 turchette:1 send:1 translational:1 apply:1 manipulate:1 alamitos:2 use:3 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quant-ph9903058.txt |@word teich:1 guang:1 chinese:1 show:2 joshi:1 when:1 over:2 atom:1 displayed:1 obtain:1 produce:1 thermal:1 through:1 expressed:1 statistical:3 erent:4 keywords:1 japan:1 expressions:1 excitations:1 find:2 define:1 northeast:1 barnett:1 remarkable:1 parameters:4 sciences:1 interesting:4 character:1 written:1 boson:1 quadratures:1 1dn:2 production:1 squeezing:13 fig:6 easy:1 vourdas:1 mail:1 pass:1 excited:20 momentum:1 real:3 dattoli:1 non:4 supported:1 expressing:1 easily:2 ya:1 evaluate:1 3aa:1 am:1 db:1 processes:2 introduce:3 beam:1 increases:5 conjugate:1 effects:3 they:3 vacuum:2 dv:1 using:1 now:1 new:1 gen:2 becomes:5 mod:1 splitter:1 february:1 finite:1 like:1 always:3 university:1 arxiv:1 quadrature:5 expectation:4 try:1 derive:1 component:6 math:3 dodonov:1 science:1 found:2 2n:1 fixed:2 reduced:6 mean:2 mathematical:1 engendered:1 classical:3 foundation:1 nbs:11 series:1 mechanism:1 creation:3 reduce:7 lett:3 understood:1 see:1 investigated:1 enhanced:2 measurement:1 chen:1 laboratory:1 odd:1 zs:1 even:1 a46:1 shown:1 nonlinear:1 sub:9 cavity:3 section:3 investigations:1 rev:6 ak:7 its:1 state:7 above:2 between:4 print:1 limit:2 welsch:2 occurs:2 demonstrated:1 shows:3 gives:1 terms:6 lee:3 degree:2 2m:2 initially:1 respectively:4 a41:1 combining:1 interpolate:2 atoms:1 ar:4 following:2 york:1 binomial:16 china:3 here:1 bs:8 a50:1 super:2 properties:8 calculate:1 obtained:2 both:7 interaction:1 srinivasan:1 limits:4 kn:2 institute:2 determining:1 study:2 conclusions:1 discussed:2 equal:3 recognized:1 jansky:1 etc:1 amount:2 base:1 products:1 poisson:1 expand:1 ecs:9 tables:1 introduced:2 first:1 aa:1 soc:2 via:1 useful:1 cn:5 f1:3 apr:1 poissonian:8 narrower:1 number:2 aphy:1 except:1 references:1 national:1 operator:7 ordered:1 conditional:1 gallardo:1 commun:2 plot:1 given:2 statistics:10 integrals:1 iphy:1 become:1 introduction:1 negative:8 been:2 a51:1 their:1 intermediate:4 constants:2 pj:1 torre:1 ph:2 was:1 theoretical:1 mandel:2 function:10 field:8 a31:1 hypergeometric:6 corresponding:1 form:2 integers:1 some:4 operators:2 exactly:3 photon:5 ryzhik:1 but:1 var:2 repeated:2 optical:1 normalized:3 particular:1 removed:1 present:1 case:1 wide:2 pacs:1 variances:1 equation:1 work:2 value:3 different:7 annihilation:1 theor:1 fock:17 fub:1 a43:1 were:1 squeezed:1 distribution:1 property:1 similar:1 called:1 procedure:1 stoler:1 exhibit:3 beijing:1 ac:1 matsuo:1 constant:3 b2:1 figure:4 give:2 defined:2 certain:1 abstract:1 vk:1 thus:2 xiao:1 ordering:1 states:56 quantum:6 examine:1 examined:1 numbers:1 saleh:1 sense:1 seen:1 ebs:32 bishop:1 viewed:1 physical:1 agarwal:3 variance:2 hong:1 provide:1 eq:7 tara:3 zhang:1 radiation:4 range:5 same:1 note:1 application:2 di:4 other:1 quant:2 sasaki:3 academy:1 opt:7 acta:1 several:1 parameter:8 conclusion:1 deviation:1 literature:1 fu:3 normal:2 kis:1 measures:1 functions:4 changchun:1 prepared:1 generated:1 a2:7 significant:2 gradshteyn:1 infinite:1 oll:2 normalization:5 man:2 jones:1 barranco:1 narrow:2 acknowledgement:1 values:10 semiclass:3 ko:2 coherent:11 academic:1 dn:8 part:1 adam:1 time:1 coordinate:1 fan:2 physics:3 sum:2 contrary:1 quantity:2
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quant-ph9903059.txt |@word limited:1 consider:2 illustrates:1 rev:18 results:3 four:3 iim:5 p01:1 computation:1 consists:3 whose:1 certainly:1 terms:2 leung:1 knill:1 concerned:1 environment:1 summarised:1 does:1 protocols:2 under:2 kλ:5 maitre:1 analogous:4 applied:6 eigenstate:1 amplitudes:1 presently:1 advantage:2 orthogonal:1 very:7 frequencies:12 springer:3 subject:1 wave:15 manipulated:1 every:1 resonant:1 experimentally:3 difference:2 pumping:2 condition:4 cool:1 leads:1 gkλ:4 level:31 knight:5 notes:1 proposals:1 large:10 vector:4 phase:5 small:5 chuang:1 optics:3 possibility:1 upper:1 dilute:1 slower:1 cooperative:3 oscillation:4 deutsch:2 cond:1 sin2:1 pulse:14 l3:1 jump:3 likely:1 evaluated:1 dynamics:5 estimated:1 linear:1 even:3 will:16 what:2 rate:3 section:8 favour:1 networks:1 current:1 experiment:1 fifth:1 above:3 international:1 3a:2 method:1 coefficient:2 edited:1 full:2 erb:1 ibid:1 excludes:1 respectively:7 spacing:1 here:8 atoms:3 ei:2 plenio:4 cos2:3 separation:4 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quant-ph9903060.txt |@word four:1 obstruction:1 whose:6 isometric:2 const:1 presents:1 under:1 worth:1 rise:3 p0:24 summarized:1 affect:1 cause:1 solution:7 humps:1 degeneracy:5 specially:2 estimates:1 direct:3 approximation:6 second:6 implemented:1 even:6 lesser:2 selected:2 above:19 new:3 coefficient:2 here:13 met:1 possibility:1 represented:1 path:4 interpret:1 obtained:6 study:2 changed:1 controversy:1 suitable:2 txl:1 explained:1 unitary:6 counts:1 total:1 txs:15 txr:1 unit:3 seligman:1 would:16 negative:5 noting:1 call:1 therefore:1 skewness:1 successful:2 odinger:5 glass:1 berlin:1 excellent:1 hold:2 springer:1 leavens:2 work:7 macroscopically:1 mp:1 example:1 defer:1 indicated:2 give:11 relativistic:2 indicates:1 times:17 absolute:1 preferably:2 end:5 turn:2 verify:1 travel:1 feature:4 very:5 answer:3 ordinary:1 description:1 after:5 summarize:1 attempt:3 third:1 complexity:1 green:2 acknowledges:1 order:2 restriction:2 interpretation:2 over:1 satisfied:1 london:1 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quant-ph9903067.txt |@word leighton:1 consider:1 pointing:1 four:2 consists:1 inverse:2 tr:2 young:1 under:1 kλ:2 fermionic:2 p2:1 expressing:1 straightforward:2 orthogonal:1 harmonics:1 wave:1 print:1 entries:2 experimentally:2 matrices:7 condition:1 smithey:1 presented:2 irreducible:2 solution:1 standards:2 deals:1 convenience:1 vector:2 equation:2 leibfried:1 smaller:1 det:1 measurable:3 go:1 zero:2 linear:6 index:1 what:1 apparatus:7 axes:1 expressed:1 dunn:1 version:1 reconstruction:11 obvious:1 method:4 coefficient:1 degree:3 multipole:1 component:1 equals:2 answers:1 atoms:1 met:1 others:1 directions:11 along:4 constructive:1 equations:10 appears:1 obtained:3 wesley:1 shift:3 vectors:1 allows:1 vibrating:1 nationalfonds:1 fourier:3 uniquely:1 appropriately:2 shorthand:1 projection:1 extra:1 iph:1 weigert:5 stern:7 total:2 unit:1 projector:1 would:4 probabilities:6 positive:2 contains:2 sµ:3 therefore:3 taken:1 type:3 theoretical:1 more:2 becomes:2 operators:3 pairs:1 berlin:2 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quant-ph9903068.txt |@word represent:1 commutator:1 since:1 consider:1 show:1 indeed:1 vacuum:1 aside:1 course:1 iǫ:14 paper:6 frequency:3 klauder:1 consists:1 contributions:1 line:1 exchange:1 make:2 expansion:1 increase:1 q2:4 ratio:1 zamick:2 parameters:1 ny:1 iii:1 relevant:1 paran:2 start:1 values:1 analytic:2 only:2 internal:2 isica:1 choose:1 theorem:2 rabi:1 anharmonic:1 might:1 into:1 take:1 do:1 loss:1 depends:1 easily:1 factorial:1 de:4 increases:1 evolution:1 harmonic:14 self:1 process:1 iǫa:2 af:1 ǫq:5 new:1 using:5 now:1 exact:1 discuss:1 ǫf:2 expq:1 following:1 inversion:1 europhys:1 hamiltonian:10 altering:1 university:1 level:4 quadrature:1 occurs:1 separately:1 applied:1 vector:1 mode:3 recall:2 walls:1 2m:1 shows:1 elements:3 valid:2 reduces:1 coefficient:2 hausdorff:2 arxiv:1 classical:2 energy:8 creation:6 some:1 related:1 up:1 approximation:3 go:1 second:1 mar:1 ey:1 ex:2 quantum:3 our:10 transitions:1 eq:11 analog:10 er:1 brazil:2 qa:1 what:1 sharma:4 stands:2 mentioned:1 space:1 shall:1 rev:1 motional:3 piscataway:1 may:2 state:6 determined:1 various:1 above:1 between:1 reply:2 increasing:1 ref:2 correct:2 trap:19 commute:2 commutation:2 notice:1 give:1 terms:2 written:1 ikx:1 points:1 diagonal:1 departamento:2 atica:1 travelling:1 here:9 put:1 article:4 diagonalised:1 refers:1 hilbert:1 obtained:1 both:1 interaction:5 clarify:1 freedom:2 vectors:4 discussed:1 vibrating:1 through:1 agree:1 motion:3 σz:2 amount:2 hω:4 due:1 act:1 distinction:1 eiǫ:1 ionic:1 adjoint:1 jersey:1 comment:2 a56:1 initial:1 term:4 conclude:1 effective:2 wave:1 number:3 system:4 down:1 en:2 been:1 another:1 operator:16 factor:1 diagonalising:1 bosonic:3 atom:1 given:7 described:1 rewritten:1 usa:1 basis:4 lett:1 5th:1 there:1 shelly:2 relations:2 next:1 their:1 detuning:1 quanta:4 dicke:1 way:1 certain:1 degrees:2 ph:1 perfectly:1 type:1 cited:1 define:1 function:2 p110:1 corresponding:2 typo:1 form:4 gives:1 benjamin:1 operators:15 hq:1 but:2 optics:1 larry:2 recoil:1 gain:1 particular:1 cases:1 presented:1 representing:1 analogous:2 dependent:2 population:1 case:3 so:1 kind:1 made:1 laser:4 processes:2 quantized:1 deformed:5 characteristic:1 approximations:1 expanded:1 oscillator:15 reads:1 value:1 final:1 annihilation:6 considered:1 while:2 rutgers:1 limit:2 ωl:2 eqs:1 ωa:2 sec:2 problem:1 2k:1 matrix:3 calculated:1 result:1 aa:3 claim:1 transition:1 associated:1 approximate:2 rewrite:1 defined:2 calculation:3 ak:5 thus:1 matem:1 equal:1 states:2 single:5 loosing:1 moves:1 universidade:2 examine:1 inc:1 lamb:1 again:3 containing:1 verified:1 no:1 amounts:1 things:1 whereas:2 detail:2 same:2 linked:2 write:1 field:5 potential:1 quant:1 special:1 analogy:1 department:1 destroy:1 coincide:1 parameter:3 recursively:1 gaining:1 fq:11 product:2 used:6 estadual:2 replacing:1 numerical:4 satisfy:1 αn:1 counterparts:1 ion:18 moment:1 paragraph:1 moving:1 comparing:1 entanglement:1 risken:1 astronomy:1 opportunity:1 contribution:1 types:1 interacting:4 implies:1 center:5 third:2 whenever:1 light:6 baker:2 well:1 correspond:1 having:1 fundamentals:1 implied:1 mass:5 calculations:2 exp:9 time:1 authors:1 position:1 model:3 physics:1 order:1 usual:2
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quant-ph9903069.txt |@word ibid:2 ungar:1 consider:4 caused:1 magnetic:1 results:1 month:1 leads:3 eds:1 scalar:1 commute:4 edu:1 go:1 follow:1 expressions:1 contributions:1 row:2 whose:2 γx:1 const:1 violate:4 young:1 environment:1 charge:1 those:2 th:1 under:4 maryland:5 fermionic:1 forbidden:1 norm:1 odinger:1 me:1 conjecture:1 amplitudes:2 presently:1 very:4 bilinear:3 exception:1 wave:1 electron:15 rotational:1 every:2 difficult:1 fall:2 associated:1 difference:1 exact:1 deformations:1 condition:9 4pp:1 four:1 kinematic:1 quartic:1 hamiltonian:11 stimulus:1 irreducible:1 nucl:1 michael:1 fewer:1 t1:2 large:1 annihilates:1 safko:1 small:13 gauge:1 shows:2 accumulation:1 prevent:1 zn:3 mn:1 neighborhood:1 zi:1 zj:2 det:1 consistent:2 derr:3 direct:5 sign:1 approximation:1 rate:2 invariant:3 estimated:1 odd:2 haag:5 scientific:1 blue:1 dial:1 adds:1 bb:2 deeply:1 section:1 contracted:1 d3:7 current:6 experiment:7 above:5 lond:1 new:4 net:2 method:1 filled:2 coefficient:1 chose:1 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quant-ph9903070.txt |@word secondly:1 logarithms:2 sci:1 rev:4 results:6 computation:6 particles:2 leung:1 deterministic:1 factoring:3 environment:1 finally:2 program:3 aut:1 under:2 norm:2 case:4 supported:1 amplitudes:3 worse:1 very:6 trough:2 entries:1 exact:2 believed:1 solves:1 turns:2 list:2 large:6 item:6 vector:1 small:5 eigenvalues:1 enforce:1 smaller:9 occurrence:2 sin2:1 approximation:1 zero:3 displays:1 equal:1 implemented:4 seth:1 linear:2 even:6 what:3 errors:8 appear:1 section:3 experiment:1 goes:1 new:2 increasing:1 acknowledgments:1 full:2 respectively:1 discrete:2 here:1 desired:2 generic:1 disastrous:1 represented:2 invented:2 equations:2 change:3 extreme:1 pleasant:1 instituto:1 study:4 studied:1 ignoring:1 amount:4 simultaneous:1 action:3 suitable:1 makes:1 evolve:1 appropriately:1 via:1 useful:2 scales:3 worthy:1 decrease:5 total:1 establish:2 linearly:1 plot:5 superpositions:1 would:2 distinct:1 uniformly:1 next:2 definiteness:1 disregarding:1 call:1 therefore:1 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