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quant-ph9908090.txt |@word mechanics:1 mathematical:1 sep:1 am:1 paper:1 apologize:1 archive:1 erroneously:1 readers:1 cross:1 submit:1 should:1 re:1 quant:1 listing:1 print:1 ph:2 math:1 led:1 you:1 sorry:1 me:2 look:1 my:1 arxiv:1 will:1 terribly:1 hope:1 physics:1
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quant-ph9909005.txt |@word limited:3 measurements:3 partial:3 consider:6 represent:1 brownian:1 results:8 four:2 roy:2 commute:1 entropy:2 faster:2 compact:1 increase:3 iii:2 environment:11 finally:1 under:2 tegmark:2 td:1 p2:2 infinite:1 zhang:2 far:4 frequencies:2 conditions:2 maali:1 dispersions:1 2γt:2 experimentally:5 exact:13 2γr:2 entire:1 hamiltonian:9 positions:3 proposals:1 solution:2 solved:2 differential:1 small:2 optics:2 der:1 gerlach:3 upper:1 smaller:7 slower:1 deutsch:1 consistent:2 estimates:1 sign:1 approximation:1 zero:19 rigorous:1 further:4 dynamics:4 functioning:1 quite:1 theory:1 established:4 what:1 appear:2 apparatus:64 section:6 dr2:5 remain:1 current:1 experiment:4 goes:6 new:2 increasing:1 method:1 coefficient:1 ρss:2 full:2 whose:2 teleportation:1 here:7 understanding:3 behaviour:3 explore:1 ramsey:1 separation:10 relaxation:8 represented:1 sieve:3 equations:6 z1:2 z2:2 z3:2 obtained:3 involved:1 study:3 studied:6 experience:1 eberly:1 suggests:1 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quant-ph9909006.txt |@word represent:3 partial:1 consider:2 forbidden:1 amplifier:14 splitting:2 leads:1 quadrature:9 commute:1 per:1 go:1 amplified:2 poorly:3 whose:4 tr:6 send:5 γt:27 presents:1 finally:2 compensate:2 squeezing:9 under:2 stochastic:1 sent:19 supported:1 g2:10 straightforward:1 orthogonal:1 far:1 choice:5 electron:2 wishes:1 every:2 decide:1 condition:1 splitter:13 solves:1 presented:4 transmission:8 eve:23 travels:1 solved:1 differential:1 small:14 disturbs:2 optics:3 approximately:2 compensated:1 foundation:1 hillery:1 cosh:4 second:10 port:2 even:2 what:11 errors:4 rate:1 brackets:1 axes:2 agrees:2 above:4 new:3 boost:4 method:10 satisfy:1 edited:1 processing:1 chose:1 respectively:3 component:3 teleportation:1 here:3 understanding:1 ranges:1 desired:1 intercept:1 sinh:4 others:1 represented:2 along:1 appears:1 change:2 box:3 sending:1 involved:1 losses:11 allows:2 experience:1 suggests:2 accomplished:1 action:2 bob:42 fourier:1 makes:3 involves:1 examining:1 via:1 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quant-ph9909012.txt |@word secondly:2 folklore:1 limited:1 squared:12 dynamic:14 four:2 consists:7 sch:1 relationships:5 whose:15 aug:1 unanswered:1 γk:3 γi:2 under:16 reversibility:1 every:62 govern:1 affect:1 believed:1 school:1 solution:2 upa:4 admissible:9 convenience:7 vector:5 enhance:1 force:1 deutsch:6 approximation:9 second:6 valiant:5 10p:1 implemented:1 machines:11 even:2 supplied:1 φp:4 above:8 new:18 consisting:1 simultaneously:1 notions:7 mei:1 equals:23 here:1 represented:1 path:27 obtained:3 tapes:42 rests:1 study:9 changed:2 fourier:1 changes:1 elaborated:1 replace:2 brought:1 total:3 linearly:1 would:1 dni:1 negative:4 call:6 therefore:12 m2:4 25th:1 until:3 abusing:1 brings:2 reversible:6 separates:1 hold:2 must:4 mg:6 mf:6 word:10 work:3 mi:9 mh:8 grover:3 mr:19 root:1 example:8 wang:1 give:4 bennett:2 indicates:3 walsh:1 want:3 magnitudes:4 feasible:1 absolute:1 end:5 feature:2 machine:16 how:1 symposium:8 brassard:7 classifying:1 description:2 turing:12 coined:1 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quant-ph9909015.txt |@word secondly:1 consider:1 remarkable:3 rev:1 desirable:1 leads:1 ge:2 entropy:1 consists:1 ts:1 eβ:1 chennai:1 straightforward:1 song:2 very:2 corollary:1 traced:1 difference:1 hamiltonian:3 did:2 turns:1 tanh:6 indices:1 eigenvalues:4 employing:1 occurrence:1 exten:1 consistent:1 cosh:12 zero:6 value:5 odd:3 even:4 established:1 what:1 sum:4 brief:1 expressed:1 version:2 method:1 contrast:1 satisfy:1 behavior:1 respectively:1 here:2 understanding:1 desired:1 sinh:2 others:2 quite:5 z0:2 appears:1 interpret:1 halsted:1 institute:1 allows:1 stressed:1 hospitality:1 jagannathan:1 scaled:1 narayana:3 conventional:1 takes:1 would:2 commun:1 contains:2 next:2 therefore:2 historically:1 more:2 introducing:2 becomes:1 operators:5 ellinas:1 particular:1 known:3 cases:1 eγ:1 must:3 high:5 chaichian:2 deformed:18 recall:2 work:3 oscillator:2 reproduce:1 fock:3 values:4 my:1 qdeformed:1 allowed:1 states:5 numbers:6 sense:4 torino:2 feature:1 maps:1 fourth:1 instead:1 ordinary:8 parameter:1 l873:1 fq:5 algebra:6 may:7 oscillators:11 southern:1 applications:1 fh:1 kulish:2 su:2 so:2 allow:1 subsequently:1 birman:1 order:10 interpretation:1 indeed:2 pointed:1 course:1 already:1 statistical:6 before:1 derive:1 exclusion:21 ln:3 undeformed:7 boson:2 fruitful:1 differently:1 deformation:3 correspondence:1 non:3 return:1 pure:1 factorial:1 now:2 yu:1 nor:2 possess:2 represents:1 term:1 fully:1 university:1 drop:1 found:1 referred:1 rajasekaran:1 en:3 energy:15 hypergeometric:1 reduce:2 ex:1 quantum:5 our:1 eq:11 out:3 shown:2 jackson:1 restricted:2 furthermore:1 singular:1 crucial:1 contained:1 investigation:1 ref:6 correct:7 math:1 shows:1 henceforward:1 theory:25 circumstance:1 derived:1 free:1 standard:3 extraordinary:1 definition:2 could:1 βe:1 ltd:1 hence:3 repeats:1 first:7 ding:1 simplifies:1 features:1 probability:8 number:4 will:1 directly:1 xu:2 given:8 temperature:12 lavagno:1 system:1 fermions:17 zeroth:1 x2:1 than:1 albeit:1 kind:1 accordance:1 iteration:8 second:1 annihilation:5 determined:3 contrary:1 lowest:4 spectrum:4 manner:3 need:1 seen:1 any:4 heine:1 self:1 isolate:1 note:2 sciences:1 internal:8 generalized:13 play:1 unless:1 fundamental:1 shall:4 ramachandran:1 boltzmann:1 pair:1 lee:1 cause:1 δn1:2 δn0:1 prevails:2 later:1 βen:4 principle:28 kt:1 swamy:3 physics:1 review:1 fact:3 spaced:1 show:2 analogously:1 purely:1 relation:1 find:4 based:2 just:1 should:1 only:7 explicitly:2 developed:2 imsc:1 preliminaries:1 do:2 over:2 closed:1 notation:1 di:1 express:2 cannot:1 words:2 occupational:2 resolve:1 arxiv:1 summary:1 qa:1 investigate:1 qb:1 set:1 sep:1 depends:1 result:3 biedenharn:1 discussions:2 analog:6 subject:2 interacting:1 visiting:1 away:1 various:1 probablity:1 limit:26 subscript:1 macfarlane:1 importance:1 attention:1 weak:8 however:1 reproduces:1 distinguish:1 suppressed:1 problem:2 thank:1 suggested:1 both:1 limits:1 many:2 according:1 hω:20 expression:2 mechanics:6 point:5 harmonic:1 insist:1 cd:1 described:3 been:1 int:2 basic:4 expected:4 extends:1 ph:1 pn:13 choose:1 hayashi:2 observe:2 present:1 case:8 p0:3 p1:3 pacs:1 evaluated:1 employ:2 while:1 evaluating:1 investigating:1 property:2 a22:1 thus:7 il:1 fermion:21 different:5 italy:1 make:1 same:3 quant:1 pauli:13 finite:1 infer:1 literature:1 see:6 trivially:1 effect:2 hand:2 levels:1 ingredients:1 well:5 analysis:1 without:2 lim:5 firstly:1 drawing:1 ny:1 proposed:2 able:1 obtain:5 valuable:1 horwood:1 yet:1 viswanathan:3 preprint:2 conclusions:1 interested:1 transformed:1 lett:4 ought:2 sums:1 corresponds:1 press:1 mod:3 imposed:2 alternatively:1 reduces:8 yields:1 follows:2 essential:1 mathematical:1 because:2 methods:1 classical:12 creation:5 some:5 begin:1 specified:1 ellis:1 lead:2 does:4 demonstrated:2 obey:1 bb:4 arbitrary:1 use:1 although:2 properties:3 proceed:1 usa:1 extension:1 obeys:1 equally:1 inclusion:4 communication:1 into:1 thankful:2 references:2 operator:8 jing:2 hep:1 additional:1 approximate:2 thirdly:1 accordingly:2 bosons:3 low:7 was:1 function:11 form:4 but:4 politecnico:1 true:1 ut:3 maximum:1 us:3 fermi:1 parthasarathy:6 distribution:8 define:1 agree:2 expect:3 aa:3 partition:2 constant:1 defined:5 abstract:1 contribute:1 am:2 general:2 examine:3 constructed:4 again:1 functions:1 no:2 when:4 vanishes:3 illinois:1 acknowledgments:1 other:3 role:1 department:1 apparent:1 a2:2 implies:1 longer:1 n0:1 requires:1
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quant-ph9909016.txt |@word surrounded:1 partial:1 consider:3 rob:1 results:6 four:1 schatten:1 proposition:9 computation:2 edu:2 follow:3 landau:1 gk:2 restrictions:1 compact:3 whose:5 violate:12 tr:52 contained:7 nonlocal:2 finally:1 under:1 norm:22 applied:1 conjecture:3 g4:1 g3:1 g2:1 straightforward:2 outside:1 very:2 springer:3 isomorphism:2 every:1 convexity:3 dim:3 developing:1 large:3 vector:5 math:1 recall:2 noted:1 still:1 upper:1 rohrlich:1 neighborhood:10 lewenstein:1 direct:1 surrounding:3 imply:2 street:1 equal:1 further:1 linear:1 spectral:1 established:3 errors:1 advantageous:1 section:2 henceforth:1 version:1 gn:2 above:3 sup:2 entanglement:1 new:4 increasing:1 method:2 contrast:1 coefficient:1 respectively:1 never:1 component:6 here:3 ranges:1 b2n:2 selective:1 them:1 represented:1 path:1 quite:1 respect:1 contraction:1 leaves:1 vectors:2 extreme:1 p2:3 permutation:2 action:3 conveniently:1 history:1 offs:1 schack:2 useful:2 projection:7 zyczkowski:2 elaborated:1 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quant-ph9909017.txt |@word limited:2 integration:1 whose:1 depend:2 calculate:1 technique:1 tn:1 tl:3 tk:2 th:3 under:1 case:1 far:1 entries:1 exact:1 κq2:1 solution:1 t1:4 large:1 vector:1 arnimallee:1 second:1 theory:2 what:1 expressed:1 agrees:1 version:1 above:1 new:2 method:1 3d:4 q2k:4 condmat:1 here:1 desired:2 κt:2 shift:1 study:1 resulting:2 procedure:1 suitable:1 changes:1 appropriately:1 via:3 integrations:2 relabelings:1 tools:1 use:1 would:2 remains:1 type:1 diagrams:5 more:1 introducing:1 ti:2 berlin:8 det:5 theories:2 mp:1 following:1 example:3 f1:3 calculation:2 expanding:1 high:4 performed:2 tal:3 rescaling:1 end:1 recursive:1 how:1 nontrivial:1 simplicity:1 ta1:1 may:1 after:1 diagram:1 physik:4 data:1 efficiently:1 lines:3 so:1 first:1 order:3 terms:2 developed:2 over:2 murray:1 symbols:1 course:1 industrial:1 through:2 its:1 ld:2 derive:2 matrices:2 masses:2 freie:1 production:1 systems:1 non:1 they:1 easily:2 each:1 universit:2 side:1 24d:1 24a:1 generation:2 series:1 hypergeometric:2 ea:2 gaussian:1 loops:3 our:1 transitions:1 eq:2 special:1 out:2 ultimately:1 matrix:2 fu:4 rev:4 print:1 formula:2 wick:1 squares:1 ref:4 linear:2 8a:1 automatized:2 completely:1 hep:3 integrand:2 simplifies:1 variables:1 number:1 directly:1 open:1 perturbation:4 their:1 iad:3 theoretische:2 relations:1 needed:1 kleinert:8 dt1:4 exponents:5 exactly:1 differentiate:1 than:1 coefficients:1 dtn:1 dtl:3 zero:2 superfluid:1 treated:1 perturbative:2 collecting:1 rewrite:1 hagen:1 argument:1 orders:2 efficient:2 note:2 k1:2 internal:1 take:3 finding:1 accuracy:2 pelster:1 most:1 beta:1 germany:2 phase:1 ke:2 url:1 kj:2 calculated:3 feynman:10 exp:1 show:1 multiplicities:1 trivial:1 find:2 ground:1 q1:2 q3:1 q2:1 q4:1 parameters:1 should:1 only:2 experiment:1 oct:1 boris:2 dd:12 de:3 watermelon:1 combinations:2 arxiv:1 expansions:11 yield:1 4πa:1 contain:1 qk:4 view:1 set:2 unpublished:1 computer:3 close:1 nissen:1 exponent:1 symmetric:1 state:1 routing:2 simplest:1 invariant:1 email:2 comparable:1 recently:1 ji:2 σl:1 powers:6 barely:1 equal:2 multiloop:3 bachmann:1 kastening:1 expression:1 experimental:1 ck:1 point:1 simple:1 respect:1 pt:2 been:2 basic:1 pk:2 ph:1 pi:4 pl:5 graphical:2 nickel:1 sufficient:1 chui:1 external:4 c1:2 present:1 p2:5 p3:5 multi:1 p1:10 5a:1 resummation:1 will:1 behavior:1 loop:9 seven:1 coupled:1 thus:1 reads:1 cond:2 helium:1 different:2 recursion:1 any:3 unity:1 quant:1 thphys:1 extended:1 http:1 hand:1 purpose:1 uni:1 expand:1 without:2 parametric:1 dimension:2 proposed:2 obtain:3 identify:2 momenta:13 preprint:4 except:1 source:1 lett:1 solvable:1 heidelberg:3 generalized:2 fluctuating:1 9d:3 swanson:1 vacuum:1 using:1 appearing:1 like:1 reduces:1 performing:1 specific:1 integrals:10 become:1 reduced:1 lipa:1 www:1 right:1 methods:1 some:1 describing:1 dimensions:1 lead:1 2c1:1 critical:6 run:1 confluent:2 expansion:8 although:1 carried:2 extension:1 extending:1 numerator:1 o:5 addendum:1 into:1 integral:6 appropriate:1 institut:2 pochhammer:1 way:2 was:1 propagator:1 function:5 eak:1 complete:1 form:3 phenomena:1 heat:1 construction:1 line:3 mat:2 up:1 ur:2 those:2 strongly:1 taylor:1 ak:8 determinant:1 general:2 quantum:1 single:1 schwinger:1 rewriting:1 field:3 philosophenweg:1 calculating:1 symbol:1 polynomials:1 a1:10 a3:5 a2:5 a4:13 algorithm:2 perturbatively:4 together:2 satellite:1 time:1 having:1
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quant-ph9909018.txt |@word rev:13 gy:1 lewenstein:2 consists:1 research:1 gk:5 inverse:7 calculate:1 concerned:1 finally:2 under:4 applied:2 amplitudes:1 far:2 wave:1 print:1 frequencydependent:1 resonant:3 experimentally:1 difference:1 hamiltonian:1 transmission:2 knight:6 solution:2 damped:1 large:1 solid:3 vector:2 small:2 markov:1 optics:2 upper:1 pulse:1 approximation:1 dalton:2 second:1 displays:1 chen:2 further:3 dynamics:1 implemented:1 situated:1 substitute:1 theory:1 trapping:1 section:1 near:4 expressed:1 current:1 poles:1 above:1 new:1 acknowledgments:1 respectively:2 angelakis:2 modify:1 here:3 behaviour:6 consideration:2 obtained:1 study:2 larger:1 through:1 products:1 microcavities:1 resonance:1 studies:1 via:2 visible:1 electromagnetically:2 unit:2 plot:1 use:2 waveguides:1 positive:2 lasing:2 dωρ:1 therefore:2 taken:1 type:7 more:2 becomes:3 odinger:1 transient:10 known:1 topic:1 account:1 equation:4 work:2 modified:12 erf:2 values:3 thin:2 transparency:9 root:5 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quant-ph9909019.txt |@word magnetic:1 decays:1 results:11 four:1 generalize:1 comments:1 broader:1 gn:1 hole:2 localized:1 calculate:8 eˆ:1 γk:1 finally:2 th:2 under:1 stochastic:1 analogous:1 include:1 γf:3 applied:1 orthogonal:1 very:7 frequencies:8 wave:1 resonant:7 affect:1 exact:1 level:14 positions:3 vector:7 small:6 optics:3 population:1 smaller:3 ten:3 approximation:2 located:1 second:17 pass:3 qualitatively:1 canonical:3 dr1:1 sum:5 dr2:1 ˆa:2 causes:1 ˆf:2 ˆi:3 ˆj:2 ˆm:2 ˆn:5 satisfy:1 respectively:1 operˆ:1 groups:1 situation:1 strong:2 equations:4 obtained:7 incoming:2 institute:1 spontaneous:1 vectors:3 eberly:5 hωn:2 microcavities:1 resonance:18 fourier:5 studies:1 uniquely:3 buˇzek:2 via:1 spatially:2 explained:4 marked:1 total:2 use:3 additive:1 takes:1 would:1 probabilities:3 physics:1 next:4 type:3 start:1 more:4 incorporates:1 operators:6 odinger:1 everywhere:1 normalized:3 known:4 cases:3 detects:1 iii:3 must:1 account:1 valued:1 integrating:1 equation:4 friendly:1 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quant-ph9909021.txt |@word sci:1 switched:2 amplifier:2 results:2 illustrated:1 quadrature:1 computation:1 follow:1 issues:1 auckland:2 γv:2 finally:2 squeezing:3 under:1 γb:2 γa:4 include:1 ingredient:1 interacting:1 g0:3 far:1 wave:5 mixing:1 difference:1 rotating:2 impressive:1 level:1 knight:1 tanh:2 culminating:1 large:1 small:1 optics:2 equation:1 oscillation:1 cosh:1 approximation:1 rate:2 timescales:1 further:2 dynamics:2 victor:15 aim:1 trapping:2 brief:1 ˆb:2 experiment:2 shared:2 satisfy:1 simultaneously:1 ibid:2 respectively:2 teleportation:17 transferred:1 atoms:11 desired:2 operating:1 free:1 consideration:1 along:4 strong:3 excitations:1 sending:1 sender:1 institute:2 involved:1 inspired:1 allows:1 suggests:1 accomplished:1 resulting:1 california:1 bob:20 suitable:2 king:1 via:5 projection:1 apply:1 total:1 linearly:1 use:1 would:3 distinct:1 tightly:1 next:2 depicted:3 ψi:3 criteria:1 taken:2 associated:1 until:2 milliseconds:1 separated:2 kˆ:1 outputs:1 operators:1 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quant-ph9909022.txt |@word called:3 footing:1 proposed:1 eaires:1 perelman:2 funtions:1 known:1 shape:2 already:1 through:1 nf:1 integer:1 possibilities:1 gaeta:1 briefly:1 eigenstates:3 localized:1 previous:1 devoted:1 initial:2 depend:1 application:1 exact:1 radcliffe:1 intensive:1 only:3 spread:2 squeezing:3 systems:1 rich:1 factor:1 mail:2 lz:5 averbukh:2 momentum:4 ly:2 real:6 cic:1 them:1 dm:1 ym:1 rev:3 richness:1 iα:2 components:1 assuming:2 possible:1 iη:1 wave:3 ones:2 effects:1 they:2 remarks:1 using:2 rotation:2 now:1 grenoble:1 gen:2 coth:1 oxy:1 evolution:3 like:1 variable:2 hamiltonian:2 intelligent:6 university:1 arxiv:1 lett:1 shapes:2 into:1 in2p3:1 l2:2 l3:3 arbitrary:1 analytical:1 found:2 2n:2 l149:1 valid:1 upper:1 sketch:1 des:1 ei:1 constructing:1 classical:1 sep:1 energy:1 between:1 aragone:3 fr:1 packet:1 crescents:1 internal:1 depends:4 frequency:1 cloning:2 respect:1 quantum:3 l2x:2 l2y:2 odd:1 even:1 edex:1 shown:2 extend:1 take:2 since:1 interference:1 expressed:1 review:1 state:1 does:1 fractional:7 denoted:1 international:1 increasing:1 ref:2 demonstrated:1 body:3 subdivided:1 terms:1 parent:1 modify:1 use:2 here:1 sh:1 following:1 concentrate:2 cos2:1 sinh:1 address:2 analyzed:1 imaginary:1 properties:1 change:1 deduced:1 obtained:1 rely:1 cos:1 dl:1 napoli:1 column:2 many:1 uncertainty:2 allows:1 times:2 math:4 bluhm:1 place:1 isn:1 contribution:1 studies:1 exhibited:1 ily:1 degree:1 relevant:1 family:3 simple:1 variables:1 wp:14 number:1 three:1 visible:1 exhaust:1 en:1 references:1 operator:2 tilted:1 ring:1 infinite:1 angular:8 illustrate:1 conference:1 uncertainties:1 given:1 rows:1 institut:1 discussed:2 revival:3 basis:1 umcs:1 trajectory:1 there:2 quasi:3 relations:1 france:1 their:1 nucl:2 therefore:1 extends:1 ph:1 topology:1 was:1 pl:2 fig:6 enable:1 molecules:1 form:2 square:1 becomes:1 differences:1 but:1 coherent:4 construction:1 lublin:2 studied:1 atom:1 clones:3 presented:1 spin:4 case:1 made:1 da:1 exponential:1 developing:1 work:4 up:1 value:1 will:2 while:1 dynamics:1 values:2 lx:3 freedom:2 squeezed:2 exp:2 other:1 similar:1 average:2 trev:5 mechanics:1 changes:1 transition:1 figure:1 defined:2 well:2 abstract:1 am:1 spectrum:2 general:2 states:16 sphere:3 minimum:1 right:2 our:3 seen:1 exist:2 hydrogen:1 clearly:2 constructed:1 rotor:1 different:3 us:1 zero:1 convenient:1 latter:1 when:1 expanded:1 mechanism:2 note:1 sciences:1 complex:2 quant:1 details:1 papers:1 instead:1 more:3 mutants:3 parameter:5 sin:2 evolve:1 sklodowska:1 investigated:1 description:1 algebra:2 may:1 molecule:1 functions:1 stroud:2 dimensions:1 plane:1 a4:1 significant:1 waves:1 revivals:1 changing:2 marie:1 cr:2 numerous:1 normalization:1 recent:1 lower:2 scenario:1 fully:2 6th:1 poland:1 rotational:1 packets:2 rashid:1 su:2 obviously:2 curie:1 part:2 diatomic:1 time:4 very:1 rigid:7 nuclei:1 make:1 choice:2 left:2
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quant-ph9909023.txt |@word ito:1 ui:1 particularly:1 phenomenon:3 show:1 september:1 eaires:1 pointed:1 results:1 years:2 ge:1 paper:2 turek:1 thanks:1 committee:1 polish:1 research:1 jaynes:1 λn:1 localized:1 effect:1 probability:1 density:1 energies:1 representing:1 zˆ:2 lj:3 enough:1 wps:2 other:1 ls:1 under:2 oscillate:1 eigenstate:3 momentum:2 do:4 non:3 cimento:3 pure:2 rev:2 dependent:1 evolution:7 kbn:1 wave:5 cho:1 example:1 entangled:1 cook:1 during:1 grenoble:1 discuss:1 moshinsky:1 name:1 loss:1 inversion:1 theor:1 dirac:9 particle:3 fizyki:1 presented:2 conditions:2 arxiv:1 pol:1 large:1 theory:1 moreno:1 predicted:1 zitterbewegung:2 arbitrary:1 small:2 found:2 shows:1 uniwersytet:1 foldy:2 school:1 periodicity:2 sep:1 b27:1 mori:1 energy:3 some:1 gaussian:1 packet:4 toyama:2 matrices:1 proportional:1 oscillations:1 our:1 out:1 shown:2 dimensions:1 nuclear:1 nuovo:3 washed:1 classical:1 mc2:2 state:4 zo:2 decomposition:1 subspaces:1 refreshed:1 prog:1 limit:2 approach:3 3d:2 notice:1 recently:2 linear:6 extend:1 initially:2 mω:1 component:1 lakes:1 following:2 cylindrical:1 references:1 wp:10 described:1 along:1 prepared:1 z0:1 periodically:1 change:1 thank:1 both:3 σi:2 enables:1 r0:3 σn:3 extension:2 many:1 study:1 studied:1 discussed:1 dependence:1 called:1 motion:5 turn:1 plane:1 period:1 oz:2 published:1 introduced:1 takeda:1 initial:7 projection:1 pendulum:3 nonrelativistic:1 within:1 harmonic:2 due:1 first:1 clear:1 symmetry:1 en:1 done:1 another:1 szczepaniak:1 respect:2 a22:2 b29:1 angular:1 given:1 institut:1 interesting:2 coherent:1 a50:1 introduction:1 positive:2 support:1 there:2 negative:2 been:2 france:1 a51:1 few:1 nucl:1 wouthuysen:2 scope:1 ph:1 p03b:1 was:1 pl:1 xxvi:1 function:1 a32:1 direction:6 only:1 corresponding:3 elsewhere:1 form:2 comparison:1 centered:1 exactly:1 jmj:1 reminds:1 cedex:1 lublin:1 ho:2 focusing:2 cases:2 spin:19 collapses:2 present:2 population:1 case:5 again:1 p0:6 pacs:1 equation:1 des:1 oscillator:5 maximum:1 value:1 aim:1 values:3 behavior:2 center:1 hdo:1 more:1 averages:2 poland:2 launched:1 fig:4 transition:2 century:1 almost:1 relativistic:10 a23:1 spectrum:1 states:3 a30:1 numbers:2 close:1 seen:1 coutinho:1 fermion:1 possible:1 axis:2 creates:1 grant:1 whereas:1 defined:2 same:1 sciences:1 potential:1 quant:1 forces:1 spatial:1 acta:1 gets:1 parameter:1 circular:2 deviation:1 investigated:1 exp:1 opposite:1 trajectories:2 expectation:2 average:2 important:1 instytut:1 cummings:1 entanglement:1 representations:2 parallel:2 ago:2 coupling:3 restores:2 sq:1 well:3 orbit:7 nogami:2 curie:2 scientific:1 so:1 components:2 time:7 moreover:1 representation:5 model:3 physics:3 lett:1 usual:1
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quant-ph9909024.txt |@word consider:14 pointing:1 extremes:1 melts:1 pairing:1 magnetic:14 desirable:1 splitting:2 interpret:1 eds:1 ginzburg:1 generalize:1 rebbi:1 computation:3 consists:3 gl:5 hole:3 localized:5 whose:4 γx:6 depend:2 calculate:1 equivalence:2 nonlocal:2 finally:2 does:7 device:10 preserved:2 th:1 stable:3 analogous:2 include:2 xe:3 ingredient:1 p2:1 supported:1 amplitudes:1 straightforward:1 outside:1 far:2 frequencies:1 conditions:4 results:4 electron:2 wishes:1 2γx:1 noncontractible:2 experimentally:2 difference:6 condition:7 entire:5 gross:1 unlike:1 hamiltonian:4 ref:10 rectangle:1 solution:1 magnet:1 discrete:2 vector:2 science:1 small:6 equation:4 degeneracy:2 upper:1 smaller:2 force:3 core:5 d3:7 concentrations:1 pulse:1 sign:1 fold:1 rate:48 equipartition:1 enhancement:5 go:1 correlator:6 l2y:3 precession:1 estimated:1 odd:2 substitute:1 theory:8 even:8 what:6 plays:2 appear:1 fine:1 section:7 interactions:1 while:4 thickness:3 current:6 experiment:1 toric:1 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quant-ph9909032.txt |@word neighbors:4 limited:1 code:2 sci:1 consider:7 chain:31 caused:1 magnetic:12 results:6 known:2 computation:5 fig1:1 expressions:2 whose:3 alamos:2 present:1 th:17 under:3 vrijen:1 include:2 third:2 division:1 supported:1 amplitudes:1 frequencies:2 wave:5 electron:1 figs:10 polytechnic:1 resonant:27 difference:3 condition:10 hamiltonian:4 solution:5 t0:9 large:10 solved:1 small:9 chuang:1 upper:9 zk:2 sin2:1 pulse:21 sign:3 approximation:1 second:4 design:2 rigorous:1 dynamics:4 odd:1 10t:1 scientific:1 even:2 index:1 errors:1 sub:5 section:1 uniform:2 3n:1 new:2 method:3 bdz:3 satisfy:2 awschalom:1 respectively:1 applies:1 component:3 here:1 desired:2 explore:1 selective:1 cos2:1 groups:1 directions:1 consideration:3 along:3 equations:7 change:3 obtained:1 shift:1 study:3 studied:1 allows:1 action:3 unwanted:35 implement:1 makes:1 king:1 control:6 highly:2 decrease:1 apply:2 total:10 rkj:2 conventional:1 usa:1 probabilities:9 mexico:1 next:6 distortions:2 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quant-ph9909033.txt |@word measurements:3 sci:1 consider:6 chain:24 caused:1 magnetic:56 splitting:3 produce:1 computation:14 expressions:1 targeted:1 causes:1 whose:2 certainly:3 inverse:2 leung:1 alamos:4 technique:1 magnetostatic:3 created:1 finally:2 behave:1 γn:11 th:1 under:4 γb:5 anharmonic:1 tc:5 γe:9 division:1 supported:1 cantilever:43 far:1 frequencies:7 induce:1 electron:61 putting:1 sensitivity:2 polytechnic:1 resonant:18 experimentally:1 difference:4 exact:1 condition:3 level:2 did:1 ref:1 fhf:7 large:3 f1m:1 vector:1 succession:1 small:4 chuang:4 upper:1 smaller:1 force:11 estimates:1 direct:1 pulse:18 zc:4 past:1 second:3 design:2 initialized:1 dynamics:1 implemented:3 targets:1 10t:3 even:2 5ns:1 sun:1 sum:1 selected:5 near:2 uniform:5 experiment:2 3n:2 new:1 method:6 bdz:16 bi:1 fe0:6 respectively:1 kendrick:1 component:8 equals:2 here:6 atoms:17 selective:2 possibility:1 relaxation:1 directions:2 ratio:3 along:3 standard:5 appears:1 change:4 wait:1 100khz:1 shift:4 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quant-ph9909034.txt |@word gang:1 edu:1 kinetic:3 find:1 q1:3 villars:1 q2:3 calculate:1 density:1 ier:1 should:1 parts:1 other:3 mail:1 distributes:2 momentum:7 real:2 amplitudes:1 means:1 de:2 wave:1 know:1 vacuum:1 dt:1 february:1 particle:13 university:1 arxiv:1 indisputable:1 reasonable:2 mathematical:1 classical:2 sep:1 energy:16 some:3 idea:1 broglie:2 quantum:1 led:1 out:3 describing:2 space:3 electromagnetic:4 since:2 integration:1 assuming:1 contributes:1 movement:3 body:1 terms:1 respectively:2 lu:1 china:1 e1:3 e2:4 interaction:1 la:1 according:1 hψ:1 hence:2 whole:2 cn:1 maxwell:1 references:1 described:1 equations:1 there:1 assumption:1 too:1 way:1 taken:2 ph:1 telle:1 quantities:3 explanation:1 odinger:3 but:3 volume:1 heat:1 filed:1 natural:1 easiest:1 distance:1 equation:11 assume:3 zhao:1 quantique:1 mechanics:1 crazy:1 abstract:1 modern:1 accept:1 itself:2 exist:3 nankai:2 qiu:1 moves:1 any:1 physical:3 make:1 physique:1 admit:1 note:1 field:14 potential:6 quant:1 spatial:1 department:1 used:1 electric:1 most:1 zhen:1 schr:3 coulomb:1 charges:2 dτ:3 element:1 so:1 physics:3 fact:1
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quant-ph9909035.txt |@word neighbors:4 externally:1 sci:1 consider:3 maximum:1 rev:8 focus:1 four:1 generalize:1 consists:2 perturbations:1 expressions:1 depend:2 calculate:1 alamos:2 technique:1 environment:1 charge:2 under:1 stochastic:2 include:1 division:1 breathing:5 amplitudes:3 string:23 orthogonal:3 very:5 frequencies:21 modes:69 results:3 ωz2:1 figs:3 sidebands:1 affect:2 exact:1 cool:3 treating:1 ladders:1 positions:6 anisotropy:2 standards:1 large:6 science:1 small:11 eigenvalues:2 refer:1 linearizing:1 configurations:3 prevent:1 zn:1 smaller:2 force:2 zi:5 zj:2 det:3 guidelines:1 approximation:1 second:2 surface:1 dynamics:2 implemented:1 odd:6 schiffer:1 canonical:1 even:10 ǫs:14 errors:1 appear:1 rate:8 section:1 axes:1 remain:3 expressed:3 uniform:8 current:1 axial:30 3n:2 above:2 fractional:1 expresses:1 increasing:3 method:1 body:1 pose:1 respectively:2 applies:1 component:1 here:2 operating:1 address:1 alone:1 along:12 strong:2 equations:1 z1:1 generalizing:1 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quant-ph9909036.txt |@word consider:3 leads:1 depend:1 technique:3 finally:5 worth:1 sent:1 g3:11 g2:5 g1:6 evolves:1 frequencies:1 wave:1 experimentally:1 difference:1 four:2 vibrational:17 hamiltonian:3 proposals:1 discrete:1 adjust:1 work:3 pulse:4 dynamics:1 cesar:1 stands:1 current:2 increasing:1 acknowledgments:1 transportation:1 respectively:1 teleportation:13 reported:2 olica:1 pub:1 separation:1 luis:1 instituto:1 popescu:1 bob:10 makes:1 matos:2 deterministic:2 private:1 modifying:2 2φb:8 composes:1 apply:2 lima:1 use:1 proceed:1 jozsa:1 peru:1 taken:1 theoretical:1 milliseconds:1 lowering:1 successful:1 eiθ:6 operators:1 basically:1 known:4 producing:1 must:1 states:12 account:1 science:1 challenge:1 accomplishment:1 cat:1 del:1 following:4 ions:11 boschi:1 process:10 bennett:5 haroche:1 high:1 axis:1 lamb:2 teleport:1 needs:2 end:1 means:5 how:1 parameter:1 e2i:6 brassard:1 map:1 product:1 may:1 after:6 mapping:13 readout:1 stress:1 caixa:1 effective:5 sp:1 so:1 villas:2 fundamental:1 order:7 typical:2 developed:2 moussa:2 move:1 through:4 lasers:3 still:1 its:5 teleporting:4 thank:1 wineland:3 degrees:5 rabi:1 mail:1 janeiro:2 disentangled:1 outlined:1 bˆ:1 mention:1 rotation:1 now:4 easily:1 level:1 possibilities:1 mode:1 each:2 references:1 polzik:1 carlos:2 ei:8 doing:1 measurement:6 quantum:2 operation:1 eq:4 shown:1 accomplish:1 epeau:1 rev:8 research:1 acting:1 investigation:1 mattle:1 gov:1 ref:6 rj:1 ısica:3 departamento:2 davidovich:1 e1:7 e3:11 e2:5 pairs:4 brasil:1 recovering:1 could:1 universidad:1 ionic:5 first:3 reversing:1 already:1 probability:1 variables:2 number:4 done:2 another:3 electronic:7 given:2 publication:1 leading:1 achieved:2 their:2 cooling:1 station:2 scheme:1 trapped:2 continuous:1 manipulation:1 reverses:1 secci:1 king:2 polarized:1 submitted:1 project:1 matter:1 were:2 e2iφ:1 function:1 epr:3 need:1 weinfurter:1 depending:1 note:1 ideal:1 internal:18 channel:3 exactly:1 iφ0:1 pair:5 considered:1 km:1 martini:1 braunstein:1 points:1 fact:1 show:1 ground:1 just:1 dehmelt:1 enough:1 only:2 eibl:1 he:1 achieve:1 equilibrium:1 do:2 his:1 handle:1 get:5 beams:1 de:9 joint:1 nearly:1 despite:2 dv:1 during:2 adiabatically:1 evolution:5 arxiv:1 mapped:1 pulses:2 communicated:1 nist:3 approaching:1 available:1 set:1 sep:1 detection:1 result:5 brazil:2 preparation:1 phases:2 interacting:2 federal:2 motional:3 state:39 between:2 affecting:1 brune:1 knowing:1 recently:2 nature:1 however:1 efficiency:1 group:1 jc:5 both:4 reverse:5 taking:1 equal:1 itano:2 sensitive:2 raimond:1 receiver:2 experimental:2 bell:1 wootters:1 zubairy:1 anti:4 associated:3 described:2 cavities:1 basis:1 due:2 been:3 detuning:1 maia:1 ph:3 lett:5 sorensen:1 photon:1 remark:1 zeilinger:1 external:2 maximally:1 present:3 case:1 handling:1 laser:7 pacs:1 reliable:3 kimble:1 accumulator:1 reliably:1 unitary:3 expenses:1 rio:2 reads:1 examined:1 technology:1 monroe:2 make:1 proceeds:1 φa:7 φb:8 html:1 quant:3 pan:1 φo:1 eiφ0:1 http:1 filho:2 ion:26 recent:1 traps:1 zagury:3 well:2 know:1 without:3 entangled:1 protocol:3 proposed:3 being:2 via:1 distant:2 atomic:2 point:1 dicke:2 attractive:1 5d:1 guarantees:1 5a:1 excited:1 5c:1 5b:1 around:1 ciencias:1 using:2 postal:1 necessary:2 success:1 hardy:1 alice:8 specific:1 steps:1 arbitrary:6 evolutions:1 cooled:1 pontificia:1 classical:2 sequence:1 phenomena:1 cr:1 transport:1 cavity:2 electromagnetic:1 measurements:1 fapesp:1 per:1 does:2 assuming:1 demonstrated:1 trap:9 eiϕ:1 power:1 br:1 proceeded:1 bz:1 freedom:5 carrier:1 furusawa:1 efforts:1 almeida:1 previously:2 communication:2 into:3 washington:1 phase:6 accounts:1 operator:1 her:2 support:1 there:1 generation:2 way:1 raman:8 dispersively:1 some:1 but:1 cnpq:1 raising:1 auxiliary:1 applying:1 wish:1 inside:1 us:3 ωo:1 minutes:1 detailed:1 required:4 constant:1 defined:1 abstract:1 ao:2 peres:1 single:3 lifetime:2 apartado:1 universidade:2 regime:1 bouwmeester:1 meekhof:2 field:4 branca:1 solano:3 superposition:3 prepared:4 generated:3 sandberg:1 coupling:1 fluorescence:1 interval:2 together:3 original:4 leibfried:1 teleported:7 time:4 requires:1 having:1
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quant-ph9909037.txt |@word concept:1 partial:1 consider:4 illustrates:1 duplicates:3 induces:2 results:2 quadrature:2 computation:4 expressions:1 denotes:2 localized:3 devoted:1 whose:1 inverse:1 depend:1 calculate:1 supported:1 finally:1 program:1 squeezing:1 under:1 tr1:2 pˆx:1 analogous:2 tr2:1 worth:1 p2:4 conjecture:1 eigenstate:1 amplitudes:1 straightforward:1 very:2 rise:1 wave:7 denoted:1 solution:1 pˆ1:1 discrete:3 pˆ3:1 pˆ2:1 pˆ4:2 small:1 optics:2 lloyd:1 grateful:1 direct:1 hillery:2 second:5 manipulating:1 implemented:1 machines:2 ba:1 even:1 what:2 errors:4 appear:1 section:1 expressed:3 ˆb:1 above:1 ˆk:1 contrast:1 satisfy:2 respectively:4 error:19 teleportation:1 here:2 desired:1 plenio:1 win:1 cerf:2 remark:1 institute:1 shift:9 study:1 suggests:1 resulting:1 fourier:5 makes:1 useful:2 projection:1 ipe:1 marginal:1 apply:1 ipx:2 manipulate:1 use:1 projector:5 would:1 massar:1 remains:1 noting:1 therefore:1 taken:1 jonathan:1 more:6 ecole:1 outputs:4 operators:3 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quant-ph9909038.txt |@word limited:2 saturating:1 switched:1 magnetic:7 comparatively:1 results:1 computation:2 consists:1 fmrx:2 calculate:1 technique:2 vs:1 acting:1 environment:2 compensate:1 present:1 th:2 stable:1 broaden:1 indicating:1 alternating:1 p2:1 far:1 frequencies:5 modes:2 engineered:1 electron:2 manipulated:2 sidebands:3 resonant:2 cool:1 vibrational:11 level:12 expectation:1 large:1 vector:1 small:3 der:1 degeneracy:2 upper:2 smaller:1 oscillation:1 consistent:3 requirements:1 pulse:7 discriminated:1 rate:6 dynamics:3 blue:7 sub:2 axes:1 d3:2 axial:4 experiment:5 above:2 tips:1 occupation:9 method:1 contrast:3 3d:1 full:1 simultaneously:1 erb:2 respectively:2 here:1 pumping:5 behaviour:2 desired:1 focused:1 alone:1 along:1 deduced:1 dehmelt:1 rests:1 study:2 allows:2 prior:1 accomplished:1 resulting:2 narrow:1 engineer:1 diameter:1 via:4 stray:2 highly:1 austria:1 unitary:1 apply:2 manipulate:1 use:3 would:1 rohde:2 probabilities:1 pred:1 next:1 few:1 therefore:2 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quant-ph9909040.txt |@word logarithms:2 sci:2 consider:2 interference:1 proposition:1 generalize:2 computation:5 go:1 looking:1 amplification:2 calculate:1 tx:2 subjected:1 factoring:2 indicate:1 helps:1 case:4 random:1 straightforward:1 orthogonal:6 very:2 geometrical:2 unstructured:1 corollary:4 emphasized:1 logarithmically:1 høyer:5 entire:1 beginning:1 presented:1 notes:1 list:2 solution:2 large:5 item:1 vector:1 small:5 pretend:1 consistent:1 direct:2 hillery:1 sign:1 approximation:1 consists:1 second:2 compensates:1 evaluated:1 further:1 attributable:1 theory:2 even:1 appear:1 section:2 subspaces:1 new:2 learned:1 increasing:1 2iθ:1 acknowledgments:1 contrast:1 satisfy:1 full:1 lee:1 aij:2 here:3 desired:2 objects:5 inversion:1 represented:1 along:1 observing:1 transformation:4 logarithmic:1 box:1 search:27 institute:1 items:6 vectors:2 trial:3 permutation:1 action:2 studies:1 malley:1 york:2 projection:1 bounds:1 addressed:1 boolean:1 welch:1 planck:1 unit:1 use:4 takes:3 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quant-ph9909041.txt |@word monte:1 consider:18 chain:2 saying:1 global:4 results:2 entropy:5 consists:1 follow:1 issues:1 row:1 devoted:1 whose:2 calculate:5 graph:6 equivalence:1 tr:10 posteriori:5 monotonically:2 γm:7 under:4 nodes:26 eβ:1 henderson:1 applied:1 belonging:1 amplitudes:5 orthogonal:5 very:2 maximized:4 choice:1 replaces:1 entries:3 ρe:7 difference:1 matrices:8 vast:1 transmission:5 induction:4 tre:1 fewer:1 trf:2 try:1 trx:1 essays:1 indices:3 eigenvalues:5 markov:1 jλ1:2 jλ2:2 upper:3 smaller:5 says:2 maximization:1 sign:2 zero:11 perspective:2 further:1 implemented:2 carlo:1 append:1 linear:1 will:54 what:6 power:1 diag:2 section:14 brief:1 expressed:5 henceforth:3 3j:2 version:1 goes:2 new:4 net:46 increasing:2 multivariate:1 stρ:3 exchange:1 respectively:2 equals:7 here:5 following:11 explore:1 them:2 strong:3 z0:3 appears:1 z2:1 knowledge:1 box:1 trans:1 antisymmetric:5 sender:1 algebra:1 popescu:3 larger:4 completely:2 amount:1 resulting:2 schumacher:2 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quant-ph9909042.txt |@word αxi:4 schumaker:1 quadrature:2 research:1 violate:1 topic:1 analogous:1 norm:1 p2:21 amplitudes:1 rise:1 wave:12 experimentally:2 condition:1 positions:2 array:1 proposals:1 discrete:2 small:1 optics:1 employing:1 tex:1 zero:3 greenberger:3 even:2 employ:1 what:2 brackets:1 section:1 experiment:4 new:3 coefficient:1 edited:1 simultaneously:1 notions:1 degree:1 here:5 active:1 strong:1 obtained:1 ahead:1 rigorously:3 reports:2 amount:2 products:1 conveniently:1 fourier:2 pxx:3 followed:1 pxp:6 hardy:9 pβ1:1 ipx:2 univ:1 use:1 would:4 probabilities:5 positive:4 ψp:8 negative:6 therefore:1 type:8 tell:1 separated:1 holt:2 ascribe:1 ip1:1 normalized:1 known:2 must:2 high:1 keeping:1 equation:3 work:1 labeled:1 universe:1 following:3 making:2 trans:1 example:4 heart:1 give:1 predict:2 states:3 performed:3 provide:2 niemann:1 holds:1 entangled:1 regions:1 how:2 simplifies:1 sin:1 transforming:1 dx1:2 demonstrating:1 data:2 realized:2 ghz:2 βi:1 cannot:1 so:2 allow:2 representation:3 horne:5 breaking:1 wigner:1 eip2:1 satisfied:2 murray:1 years:1 course:1 experiments:6 through:3 argued:2 satisfies:2 ieee:1 its:1 2λe:1 derive:1 la:1 chosen:1 actually:1 peng:1 systems:1 pena:1 violating:7 contention:1 practice:2 hunter:1 effects:3 they:1 now:2 february:1 university:1 2x:1 sufficiently:1 inequality:2 each:2 found:1 side:4 realism:17 referred:2 domain:2 square:1 ei:3 series:1 obtains:3 measurement:4 quantum:10 eq:26 event:6 out:3 shown:2 rep:1 since:1 rev:13 denotes:3 particles:14 hill:1 denoted:3 occurs:1 shows:1 theory:4 york:3 members:1 could:1 messages:1 david:1 hence:2 exhibited:1 xi:1 probability:4 striking:1 possessing:1 kafatos:1 impossible:1 message:3 ψxx:7 city:2 given:7 similarly:1 eqs:2 achieved:1 system:2 their:1 ryzhik:2 continuous:2 park:1 speakable:1 optical:5 because:2 x2:24 yurke:4 x1:20 lucent:1 showed:1 instruction:2 rate:2 future:1 amplitude:2 were:4 enforced:1 epr:5 mind:1 spectrum:1 seen:1 conversion:1 mermin:1 depending:1 take:1 deuar:1 detector:7 formulas:1 though:1 most:1 propagate:1 drummond:1 gradshteyn:2 pair:3 measured:3 constructed:3 dordrecht:1 later:1 detectors:4 part:1 principle:2 mechanical:3 physics:1 fact:3 show:2 violation:2 substituting:4 analogue:2 dp2:2 dp1:1 bernard:1 only:4 factor:1 employed:3 local:17 over:2 hope:1 do:1 mixture:1 means:1 spurious:2 de:1 joint:4 made:1 dx:4 report:4 compute:1 dp:2 regarding:1 exhibiting:1 heaviside:1 podolsky:2 arxiv:1 reid:3 common:3 shapiro:1 set:2 sep:1 violated:1 correlations:1 detection:3 college:1 αp2:3 αp1:3 violates:1 satisfying:1 inequalities:1 shimony:3 definite:6 state:6 conditions:2 αpi:4 terms:1 gedanken:1 emitted:4 analogues:2 ascribed:1 however:2 both:3 cos:1 realizable:1 region:1 according:1 became:1 finds:1 among:1 bell:7 ψpp:5 homodyne:5 table:1 schleich:1 pp:1 described:2 capable:1 been:8 mark:1 ph:1 pi:1 generating:1 am:2 offered:1 photon:1 argument:1 zeilinger:3 spin:1 case:2 p1:25 pacs:1 appearance:1 kimble:1 evaluated:1 will:6 while:2 situation:2 stoler:5 opt:2 vogel:1 thus:3 ave:1 santos:1 perform:1 same:1 parts:1 quant:1 finite:2 events:2 emanating:1 development:1 numerical:1 hand:4 arrived:1 normalization:1 specialize:1 nevertheless:1 min:2 well:1 academic:2 gilchrist:1 components:3 sets:1 coordinate:2 position:20 laboratories:1 parametric:2 left:1 λp:1 proposed:3 generally:1 via:2 momenta:3 kluwer:1 ny:1 had:1 source:6 lett:15 theorem:1 violations:2 momentum:23 real:1 iλ:3 devised:3 possible:4 know:1 press:2 using:2 appearing:1 particle:8 follows:3 reduces:2 performing:1 specific:1 imposes:1 yields:5 either:1 integrals:1 pereira:1 page:1 right:3 classical:1 some:2 examples:1 nonzero:2 provided:1 describing:1 electromagnetic:4 measurements:6 integration:3 does:3 prog:1 demonstrated:1 measuring:6 yuen:2 imaginary:1 properties:1 bz:1 about:1 carried:1 constraint:2 island:1 certainty:3 αx2:3 remains:1 range:1 αx1:3 ou:1 mechanics:5 cambridge:2 presence:1 into:6 clifton:2 predictions:1 down:1 phase:2 appropriate:3 ppp:9 references:1 einstein:2 ppx:5 support:1 there:1 transform:2 long:1 was:4 synthesis:1 function:15 complete:4 form:1 regard:1 but:1 hoped:2 technologies:1 count:1 responding:1 applying:1 evident:1 whether:4 bounds:1 demonstrate:2 similar:1 strongly:1 computing:1 defined:1 measure:1 chan:1 clauser:3 single:1 exist:1 file:1 inf:1 physical:1 nj:1 2dp:2 variety:1 when:12 field:4 conceptions:1 other:2 inherently:1 prepared:1 generated:2 needed:1 correlated:2 odds:1 factorizes:2 carrying:1 rosen:2 incomplete:2 time:1 observables:3 having:1 unspeakable:1
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quant-ph9909043.txt |@word represent:1 consider:4 remarkable:1 switched:1 caused:1 magnetic:5 results:2 sh:1 segr:1 known:3 generalize:1 reinserting:1 consists:1 expressions:2 faster:1 contributions:4 scr:1 whose:7 inverse:8 depend:2 dp:1 contained:3 experimentally:3 finally:3 ny:1 those:4 th:2 under:6 kλ:34 γb:2 ev2:1 include:2 interacting:1 saying:1 straightforward:4 evolves:2 very:6 frequencies:3 a18:1 rise:3 keeping:1 dokl:2 wave:2 electron:3 every:1 summarized:1 resonant:6 affect:2 emphasized:3 matrices:1 condition:3 splits:1 riemann:12 level:38 schawlow:1 knight:4 notes:1 solution:2 damped:1 large:9 vector:3 red:1 quick:1 eigenvalues:1 optics:1 configurations:1 upper:2 smaller:2 zh:2 oscillation:1 zk:1 hindered:3 estimates:1 hillery:1 approximation:13 slowed:2 a41:1 qii:6 value:7 substituting:4 incidentally:3 spontaneously:1 situated:2 substitute:1 eqs:1 even:1 will:10 what:1 fℓ:5 const:2 stands:1 rate:11 chicago:5 tewari:1 d2:1 section:13 ak0:5 area:1 expressed:2 find:1 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quant-ph9909047.txt |@word concept:2 consider:2 similarity:1 interference:1 magnetic:2 focus:1 illustrated:3 antennas:1 kato:1 follow:1 row:3 passage:2 rise:1 results:2 resonant:1 experimentally:1 difference:1 four:3 riemann:2 level:23 did:1 turns:1 proposals:1 heiss:6 deals:1 contexts:1 eigenvalues:1 enforce:1 degeneracy:4 upper:1 smaller:1 findings:1 sign:2 imply:2 pass:2 further:2 situated:3 linear:1 even:1 lesser:1 what:1 nonlinear:1 plays:1 appear:1 giving:1 rotter:1 access:1 experiment:3 above:3 judicious:1 crossed:2 increasing:1 contrast:1 ek0:1 respectively:1 loose:1 here:2 behaviour:6 fluke:1 illustration:2 consideration:1 strong:2 appears:1 change:4 intersect:1 suitably:1 institute:1 involved:1 larger:1 domains:1 resonance:7 suitable:1 studies:1 useful:1 addresses:1 elaborated:1 app:1 africa:1 plenum:1 private:2 a23:1 achievable:1 viz:1 planck:1 use:1 figure:1 would:1 remains:1 coalesce:2 centre:1 means:1 type:4 theoretical:1 possible:2 more:4 formally:3 definition:1 brings:1 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quant-ph9909049.txt |@word limited:1 consider:7 represent:1 rev:6 results:7 illustrated:1 commute:14 entropy:1 assigned:4 edu:1 reasoning:5 issues:2 row:13 certainly:1 referring:1 assigning:2 concerned:1 editors:1 containing:1 finally:1 preserved:1 th:1 under:1 analogous:2 include:1 case:6 belonging:2 outside:2 very:2 rise:1 unfamiliar:2 every:12 entries:1 difference:3 treating:1 four:1 magic:5 forth:1 list:1 correct:2 hartle:2 assignments:1 proposition:5 science:1 eigenvalues:5 cmu:1 noted:4 employing:1 foundation:1 dealing:1 consistent:13 raised:1 fold:1 zero:4 perspective:1 specker:5 linear:1 even:2 employ:1 what:2 plays:1 incompatible:6 σxb:7 expressed:1 agrees:1 cell:3 birkhoff:3 version:2 above:4 basic:1 obvious:3 appeal:1 acknowledgments:1 exercise:2 satisfy:4 edited:1 simultaneously:4 ibid:2 respectively:1 never:1 here:4 understanding:2 refinement:5 explore:1 others:1 represented:2 quite:2 remark:1 algebra:23 remarks:1 involved:1 larger:1 wherever:2 contradiction:3 adopt:1 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