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quant-ph9905073.txt |@word consider:2 both:7 results:5 four:1 quadrature:2 commute:1 entropy:3 expressions:1 whose:3 calculate:6 alamos:1 shanghai:3 finally:2 th:1 under:1 worth:1 case:1 amplitudes:1 g2:5 g1:4 zhang:1 rise:1 densitymatrix:1 umezawa:4 nieto:1 matrices:2 collett:1 hamiltonian:1 did:1 knight:2 t2:22 t1:14 convenience:1 eigenvalues:1 optics:2 fearn:1 eλx:1 consistent:3 eλp:1 direct:2 cosh:68 second:6 dynamics:7 canonical:1 appear:2 sum:2 acknowledgments:1 mp:1 coefficient:1 condensed:1 ibid:5 respectively:6 component:1 here:4 china:2 cos2:3 sinh:24 address:1 equations:1 z1:1 box:1 involved:3 mx:1 vogt:1 published:1 action:3 involves:3 2f2:1 via:1 f1:25 analyzing:1 unit:2 use:1 takes:1 sake:1 contains:3 next:1 almost:1 noting:1 call:3 widens:1 means:1 more:1 introducing:1 operators:13 berlin:1 correspondingly:1 known:1 cases:5 kumar:1 springer:1 science:1 equation:1 oscillator:5 iα2:2 ρp:4 values:3 temperatures:6 following:3 ρx:8 conformity:1 example:2 beijing:1 f2:10 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quant-ph9905074.txt |@word concept:1 consider:3 roa:1 magnetic:3 lack:1 dynamic:1 roy:1 grateful:1 gr:1 concerned:2 equivalence:1 arif:2 charge:5 under:4 case:1 fax:1 outside:1 very:1 mn2:4 iτ2:1 wave:1 exact:3 condition:3 school:1 ro:1 hamiltonian:2 turns:1 deals:1 vector:2 math:1 upper:1 lagrangian:1 force:3 zero:1 ǫm:3 further:1 established:2 trapping:1 cimmino:2 uniform:1 axial:1 sur:1 above:1 new:2 direcci:1 acknowledgments:1 κn:1 tonomura:1 respectively:1 component:2 here:5 possibility:2 sinh:2 directions:1 ratio:2 along:2 equations:4 obtained:2 rdr:2 shift:1 vectors:1 approaches:1 hospitality:1 examining:1 although:1 iet:1 neutrons:3 unit:2 would:2 covariant:1 positive:1 stated:1 next:1 nucl:2 therefore:1 relativistic:1 theoretical:1 ψe:5 peshkin:1 duality:1 becomes:1 mishchenko:1 br0:1 correspondingly:1 leadbeater:1 cases:1 must:3 springer:1 r2:5 rβ:3 equation:6 mn:3 modified:2 geometry:1 ρr:1 values:5 making:1 example:1 performed:1 f1:2 conf:1 figure:2 give:1 discussed:1 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quant-ph9905076.txt |@word 2gij:1 concept:4 gr:1 pointing:1 switched:1 rev:5 forbidden:1 results:2 vr:3 four:2 roy:1 scalar:2 muller:1 into:1 go:1 follow:2 expressions:1 denotes:1 consider:6 increase:2 γx:1 number:16 calculate:2 indices:1 attracted:1 concerned:1 ts:12 vef:1 γj:2 charge:18 those:4 th:1 under:2 slowest:2 circumstances:1 penetrating:1 overlaps:1 case:7 conjecture:1 jensen:2 straightforward:1 returning:1 very:9 rise:2 seemingly:4 wave:17 bjorken:1 electron:16 refractive:3 experimentally:3 difference:3 condition:3 leads:1 unlike:1 hamiltonian:2 transmission:18 turns:1 solution:3 correct:1 large:19 discrete:1 vector:1 phase:1 waxman:1 subscript:2 small:4 referred:2 noted:1 zh:1 specially:1 ten:1 anticommutation:2 sin2:4 prediction:1 sign:2 zero:14 pass:2 further:4 dynamics:3 odd:4 substitute:1 even:7 index:1 what:4 qp:10 stands:1 rate:2 giving:1 section:3 near:1 find:3 current:17 en:2 above:2 flowing:1 new:5 increasing:1 filled:2 paradoxical:2 satisfy:2 barton:1 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quant-ph9905077.txt |@word homomorphism:1 lagrangian:4 four:1 entropy:1 consists:7 whose:7 isometric:13 calculate:4 ohya:1 segments:1 theodore:1 γk:80 γj:9 patched:1 γh:10 under:5 lord:2 bφ:1 replaces:1 every:19 summarized:1 logarithmically:1 convexity:6 basics:1 specify:2 scholar:1 induction:1 solution:1 convenience:2 vector:28 red:1 indices:1 degeneracy:3 miller:1 consistent:6 direct:6 pulse:2 approximation:1 surrounding:1 second:11 rigorous:1 eigenspaces:1 even:21 established:3 fubini:1 blum:3 specification:1 interactions:3 near:3 above:20 new:35 net:2 consisting:4 coefficient:1 evolving:3 simultaneously:4 evaluating:1 never:4 equals:2 here:31 atoms:6 represented:11 path:1 interpret:3 obtained:6 derivable:2 property:26 study:4 changed:1 approaches:5 controversy:1 characterizing:1 stressed:2 complicated:4 suitable:1 changes:6 numerical:1 golden:1 orthonormality:2 projection:28 classification:3 elaborated:1 spooky:1 plenum:1 highly:2 remnant:1 moral:1 stern:3 total:18 schilling:1 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quant-ph9905078.txt |@word ny:1 2m0:3 axes:1 consider:2 being:1 delta:1 find:1 rest:5 scalar:1 relation:4 c2:11 involved:1 d3:7 whose:1 now:3 group:1 density:1 interesting:1 relativity:1 coresponding:1 here:1 simplicity:1 spread:2 hd:2 mail:1 through:1 transformation:2 momentum:5 correspondence:2 case:1 fax:1 supported:1 means:1 rules:1 familiar:1 de:2 term:1 wave:14 helicity:1 they:3 confined:1 progresses:2 matrices:1 becomes:1 represents:1 february:1 dirac:4 like:1 particle:9 level:2 follows:1 university:1 arxiv:1 t2:3 solution:1 t0:1 im0:2 vector:1 eigenvalues:2 movement:1 equation:1 mean:1 benjamin:1 because:1 reference:3 inevitably:1 ed:17 energy:7 some:1 gaussian:1 packet:9 up:1 relative:4 operator:1 see:1 frequency:2 result:1 measurement:1 quantum:8 laboratory:2 udec:1 eigenstates:1 out:2 nonzero:1 will:1 dimensions:1 space:3 furthermore:1 since:1 its:1 particles:1 may:2 does:1 hill:1 between:2 formula:1 direcci:1 deformation:2 shows:1 observer:1 considering:1 notice:1 doppler:2 theory:1 easily:1 respectively:1 correspondingly:1 hamiltonian:1 however:2 free:3 standard:1 velocity:4 galilean:1 separation:1 mcgraw:1 distinguish:1 article:1 cα:4 properties:1 bz:1 box:1 both:1 outcome:1 instant:1 shift:1 region:1 m20:2 dependence:1 attributed:1 important:1 universidad:1 consequence:1 expression:1 appropriately:1 note:2 although:1 probability:2 cl:1 spreading:1 dimensional:1 2a2:1 leighton:1 frames:3 proportional:1 ipx:2 throughout:1 considers:1 dispersive:1 given:2 checked:1 classical:1 sake:1 assumed:1 px:2 system:2 construct:1 dispersion:3 accordingly:1 assumption:1 therefore:4 interest:1 relativistic:3 ph:1 was:1 frame:4 m0:15 function:8 concentrated:1 modern:1 corresponding:2 relationship:1 quantities:1 ht:3 principles:1 volume:1 effect:1 observe:1 related:1 chile:1 particular:1 known:2 foundations:1 x0:3 considerable:1 those:1 must:3 p2:1 evolves:2 compute:1 pacs:1 2πi:1 inertial:2 work:1 say:1 us:2 theories:1 inversely:1 while:1 future:1 values:1 concepts:1 distribution:1 velocities:1 example:1 mechanics:3 references:1 associated:1 objects:1 gottfried:1 vol:1 well:2 abstract:1 vk:1 thus:1 non:5 concepci:1 ik:3 lorentz:1 vt:5 o:1 vx:2 limit:1 moves:2 any:1 constructed:1 different:1 grant:2 make:2 get:1 same:1 write:2 how:1 other:1 quant:1 build:2 spatial:1 department:1 green:2 evolve:1 product:1 exp:14 calculating:1 bruce:1 investigaci:1 miscellaneous:1 v2:4 a2:5 waves:3 fondecyt:1 parallel:1 ip2:1 assume:4 packets:1 without:2 mass:2 asserts:1 time:3 quadratic:1 dispersed:1 physics:2 usual:1
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quant-ph9905079.txt |@word lagrangian:9 comparatively:1 four:4 entropy:1 consists:2 localized:7 whose:2 calculate:4 aug:1 under:5 connects:1 every:2 summarized:5 vast:1 receiving:1 solution:8 vector:5 indices:1 cmu:1 cmt:5 force:12 excited:7 10b:1 10a:1 estimates:3 direct:1 approximation:9 elegant:1 second:8 estimated:1 even:19 established:2 interatomic:1 incompatible:1 above:19 new:9 increasing:4 consisting:3 pioneering:1 κn:2 simultaneously:2 notions:2 here:11 atoms:18 represented:2 path:3 ωa2:11 obtained:3 suitably:4 study:1 changed:2 approaches:1 ignoring:1 characterizing:2 stressed:1 california:2 suitable:4 changes:1 projection:2 explained:1 plenum:2 highly:4 total:4 linearly:2 plot:3 would:12 call:2 therefore:13 fractions:1 nkb:2 relax:1 odinger:1 hold:6 must:17 md:6 ma:1 permits:1 mm:1 work:2 mt:56 example:7 indicated:2 give:2 times:10 absolute:5 end:4 hoc:1 very:14 symposium:1 iiic:2 iiib:1 description:2 transforming:2 oscillators:2 after:2 lay:1 summarize:1 parallel:1 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quant-ph9905080.txt |@word logarithms:1 concept:1 sci:1 consider:3 rev:14 dynamic:1 results:9 commute:1 computation:6 edu:1 consists:1 follow:1 sch:2 extra:1 alamos:1 concerned:1 deterministic:2 languages:1 include:1 sorkin:1 conjecture:2 random:1 presently:1 advantage:1 orthogonal:1 very:2 springer:1 choice:1 every:1 lecture:1 experimentally:3 emphasized:1 difference:1 matrices:2 gov:1 wetensch:1 presented:1 positions:1 notes:1 michael:1 discrete:1 vector:9 small:1 optics:1 noted:1 concluded:1 neighborhood:4 consistent:1 measurable:1 imply:1 greenberger:1 specker:20 odd:7 machines:1 even:3 erd:1 what:1 specification:1 axes:1 kent:5 access:1 birkhoff:2 ˆb:8 experiment:4 subspaces:1 sixth:1 new:3 contrast:2 satisfy:2 philippe:1 simultaneously:2 component:4 teleportation:5 here:3 q2:1 separation:2 address:1 alone:2 along:2 simulating:1 arena:1 remark:2 colored:8 institute:1 study:1 vectors:22 contradiction:1 prior:1 triad:7 rafael:1 involves:1 via:2 useful:1 divide:1 classification:2 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quant-ph9905083.txt |@word represent:1 chinese:1 caused:1 magnetic:3 results:10 computation:1 compose:1 knill:1 factoring:1 pte:1 p2:1 advantage:1 matrices:1 ibm:1 hamiltonian:1 did:1 proc:1 list:1 discrete:9 b24:1 b23:1 pulse:5 second:1 implemented:1 errors:3 plays:1 section:1 version:1 above:2 berman:1 3b:1 3a:1 method:1 chose:1 respectively:2 wuhan:2 china:1 separation:1 deduced:1 obtained:1 institute:1 shift:2 accomplished:1 resonance:2 implement:1 fourier:11 composed:1 useful:1 tools:1 unit:2 alamitos:1 use:3 taken:1 theoretical:4 becomes:1 operators:4 apparent:1 foundations:1 states:1 none:1 room:1 science:2 labeled:1 hansen:1 example:1 computers:1 figure:5 give:2 sample:1 walsh:1 performed:1 axis:2 information:1 acts:2 chemical:1 how:1 pure:1 instead:1 fu:1 may:1 after:7 minimized:1 spectrometer:4 b12:1 data:1 realized:1 third:2 register:1 explicit:2 correspond:2 complexity:1 so:5 ultimate:1 inhomogeneity:1 representation:3 operate:1 order:4 operations:4 insight:1 produced:1 paper:2 pulses:8 ieee:1 before:1 chosen:1 temporal:1 li:1 choose:1 annual:1 might:1 integral:2 introduce:1 igure:2 they:1 symposium:1 rotation:4 realize:4 applied:1 magnitude:3 each:2 2l:1 2j:6 2k:3 schemes:1 ei:2 transform:2 doing:3 density:4 society:1 expect:1 measurement:2 quantum:22 laboratory:2 approximated:1 shown:3 matrix:6 since:1 crucial:1 research:2 got:3 squares:1 evaluation:1 gate:1 theory:3 b34:1 wanted:1 definition:1 interaction:4 transition:1 tolerant:1 thing:1 ltd:1 first:2 initial:2 lond:1 probability:1 number:3 approximate:1 fast:1 illustrate:2 temperature:1 introduction:2 dft:22 system:3 least:1 realization:1 1k:6 molecular:1 mainieri:1 gives:1 imperfect:1 academy:1 relative:3 environmental:1 simulate:1 observed:1 1j:9 effective:1 doubly:1 were:3 tion:2 need:1 any:3 efficient:1 sciences:1 fitting:1 algorithms:2 opposite:1 measures:1 sequence:1 most:1 phase:5 measured:1 considered:1 proceedings:1 principle:2 exp:4 mechanical:3 ky:2 kx:3 physics:4 shor:7 shot:1 rotating:1 chuang:3 keywords:1 agrees:1 based:1 spite:1 implementation:2 θjk:1 should:6 only:1 experiment:7 do:1 ϕy:1 ϕx:1 means:3 watson:1 report:2 reconstruct:1 areas:1 prime:2 arxiv:1 factorization:1 luo:1 arx:1 undergoes:1 frame:1 yorktown:1 achieves:1 computer:10 result:4 operated:2 techniques:1 nuclear:1 state:15 between:2 discovery:1 jx:3 jy:2 nature:1 qubits:1 implementing:2 wr:1 suggested:1 last:1 reverse:3 fault:1 kji:1 0j:9 0k:4 qubit:15 experimental:9 co:1 ca:1 sequences:4 polynomial:2 actually:2 considering:1 described:1 publishing:1 capable:1 px:2 py:7 three:4 expected:1 ph:4 abstract:1 corresponding:3 radiofrequency:4 tranform:1 finished:1 spin:9 those:1 case:1 p1:1 classifications:1 exponential:1 pacs:1 bruker:1 evaluated:1 b01:1 b03:1 b02:1 b04:1 35th:1 procedure:1 unitary:2 averaging:1 xiao:1 reads:1 henv:1 perform:7 realizing:2 same:1 quant:4 used:3 doolen:1 center:1 well:1 analysis:1 components:1 simulated:1 dimension:1 ny:1 magnetization:1 obtain:2 rest:1 atomic:1 world:1 rotates:1 speed:1 josa:1 field:1 regarded:1 had:2 improvement:1 signals:1 transformed:1 lett:1 role:1 transformation:11 gave:1 real:1 rev:3 couple:1 five:1 press:1 using:14 bit:2 mod:1 like:1 follows:1 performing:5 steps:1 arbitrary:1 become:1 preskill:1 classical:2 people:1 successfully:1 some:1 b4:1 b1:4 b2:3 b3:2 ijk:1 affects:1 o3:1 demonstrated:1 nmr:17 scientific:1 bk:1 eiπ:1 step:2 hadamard:1 cycling:1 imaginary:1 about:2 basis:1 simulation:4 important:3 introduced:4 soc:1 computational:1 h2:1 into:1 within:1 bjk:10 due:1 references:1 primarily:1 operator:6 coppersmith:2 area:1 simulator:6 jzb:3 jza:2 los:1 was:3 conditional:1 form:2 jun:1 versatile:1 up:1 demonstrate:1 problem:2 agree:2 aa:1 ab:1 defined:1 ak:1 aj:9 zeng:1 denote:1 single:1 our:2 tomography:2 ax:1 operation:4 constructed:1 mosca:1 compared:2 calibration:1 ekert:1 composing:1 application:2 b14:1 other:1 republic:1 b13:1 mathematics:1 conclusion:1 deviation:1 elements:1 time:3 a1:1 a0:1 a3:1 a2:1 nucleus:1 peak:1 network:5 jones:1 coupling:1 algorithm:6 4j:1 eiθ:1
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quant-ph9905084.txt |@word partial:1 consider:3 pointing:1 results:10 illustrated:1 c3:3 tripartite:1 grateful:1 sci:1 increase:1 theorist:2 violate:2 disposal:1 finally:1 case:2 orthogonal:1 very:1 choice:5 untenable:1 experimentally:6 four:1 level:2 list:2 fewer:1 try:1 coincidences:2 manifestly:2 der:1 upper:1 β2k:1 occurrence:1 prediction:3 located:1 rate:1 uncomfortable:1 greenberger:5 theories:3 depression:2 even:1 will:2 what:2 abc:4 appear:1 apparatus:1 giving:2 experiment:2 fortschritte:1 above:1 new:3 acknowledgments:1 satisfy:4 bruß:1 component:1 here:3 agreement:1 b2k:2 address:1 directions:3 ratio:1 along:4 strong:1 implicit:1 change:1 institute:1 prior:1 products:2 published:2 usually:1 opinion:1 involves:1 york:2 invalidate:3 formulated:1 projection:2 hardy:7 confidence:4 would:3 probabilities:8 give:5 predictions:4 explicitly:2 call:1 therefore:2 type:2 theoretical:1 today:1 more:3 yes:8 clever:1 successful:1 acceptable:1 holt:2 validity:2 labelled:2 particular:1 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quant-ph9905085.txt |@word concept:1 consider:3 rˆ:4 2r2:1 devoted:1 paris:1 tr:1 finally:2 squeezing:1 those:1 yˆ2:2 under:2 analogous:1 worth:1 overlaps:2 r10:1 conditions:1 bratislava:1 manipulated:1 figs:1 mixing:4 condition:1 splitter:11 presented:2 yˆn:3 yˆk:7 large:1 coincidences:1 small:1 optics:1 setup:1 lˆ:2 direct:1 pulse:3 zero:5 traveling:5 further:1 port:3 what:1 ˆy:1 section:5 expressed:1 above:1 increasing:3 outgoing:4 simultaneously:1 respectively:2 here:1 desired:2 address:1 concluding:1 strong:2 obtained:2 incoming:1 institute:1 studied:1 allows:1 yˆ:18 products:1 transmittance:3 appropriately:1 highly:3 decrease:1 fed:1 superpositions:2 commun:2 probabilities:1 noting:1 ψn:4 therefore:1 type:1 yˆ1:3 ψout:2 operators:4 odinger:5 particular:2 known:1 none:1 equation:2 work:1 modified:1 cat:7 fock:10 example:4 f2:1 give:1 implementations:1 states:42 performed:3 sought:1 r20:1 how:2 need:1 opt:3 acta:1 absolute:1 parameter:1 displacements:1 ψin:3 product:3 may:5 max:1 derived:1 βl:5 designed:1 waves:1 engineering:5 realized:4 occurence:1 joint:2 6th:1 register:1 deutsche:1 so:1 fundamental:1 order:2 pointed:1 pulses:1 fidelity:2 rapidly:1 chosen:5 interesting:1 decreases:1 offers:3 fig:10 mail:1 maximal:1 non:4 combination:3 outlined:4 pegg:1 subtraction:1 they:2 now:1 discuss:1 sin:1 possibilities:1 sufficiently:1 mode:9 each:4 2l:2 universit:1 2i:1 schemes:3 clausen:8 generation:12 barnett:1 displacement:5 jena:3 frequency:2 measurement:15 quantum:26 event:1 special:1 out:2 shown:2 since:2 rev:3 contained:1 aˆk:2 possibility:3 detecting:1 generate:3 ordering:2 exponentially:1 hence:1 βn:6 βk:4 fischer:1 probability:7 omitted:1 coming:1 number:2 simplified:2 array:6 passes:1 given:9 introduction:1 unknown:2 system:1 calculations:1 1i:1 scheme:5 forschungsgemeinschaft:1 optical:1 relative:2 see:1 discriminating:1 preparation:1 determined:3 fˆ:4 tion:1 result:2 sas:1 seen:1 strength:2 latter:1 click:3 note:3 phillips:1 coincide:1 channel:1 formulas:1 denominator:1 germany:1 successive:1 remarks:1 acknowledgements:1 measured:4 considered:3 clear:1 detectors:7 kn:9 tpi:1 principle:1 exp:2 physics:1 show:1 nπ:1 supported:1 registers:1 relation:1 solutions:1 d2:3 find:1 d1:8 parameters:1 state:43 should:2 transmitting:2 only:1 factor:1 dn:10 dl:1 dm:1 dk:10 means:1 ϕt:2 de:1 overall:1 ϕr:2 beam:21 reconstruct:1 platz:1 reveal:1 ˆk:3 fields:1 arxiv:1 summary:1 photodetectors:3 reveals:2 reference:12 achieved:2 detection:4 depends:1 individual:1 us:2 detect:1 written:1 αk:5 approach:3 αl:1 αn:3 available:2 terms:1 august:1 combining:1 both:1 cos:1 equal:3 april:2 uni:1 expression:1 regarded:1 arbitrarily:2 splitters:10 nˆ:4 represented:1 described:1 source:1 wien:1 been:1 workshop:1 combined:1 basic:1 ph:1 choose:1 generating:3 corresponding:1 received:1 offered:1 photon:20 coherent:16 denote:1 former:1 present:1 case:4 novel:1 theoretisch:1 single:1 value:1 excited:1 replaced:3 squeezed:2 property:1 procedure:1 reflectance:4 unitary:5 vol:1 them:2 ih:2 reads:2 leaving:1 perform:1 radiation:1 same:1 complex:1 quant:2 arguments:1 finite:1 european:1 used:1 schiller:1 hand:2 normalization:1 euro:1 task:1 schr:6 modes:10 nevertheless:1 well:2 obviously:1 without:1 ˆout:4 composed:1 teich:1 freyberger:1 being:3 assigned:1 underlying:1 adding:6 photons:6 alternate:4 friedrich:1 add:1 valid:1 lett:1 input:2 transformation:8 identical:1 possible:1 campos:1 entangled:1 vacuum:4 press:1 using:5 accepted:1 like:5 shaped:1 follows:1 signal:18 performing:1 specific:3 detections:1 arbitrary:8 output:7 reduced:1 truncated:2 czech:1 conditional:9 oll:9 b1:2 b2:1 ˆin:9 provided:2 measurements:5 overlap:15 welsch:9 measuring:8 bn:2 bk:2 subtract:1 2n:2 out1:1 out2:1 central:1 aˆ:1 discussed:1 mixed:3 considerations:1 into:1 within:1 references:1 operator:7 ei:2 statistics:1 institut:1 prepare:1 slovakia:1 way:1 was:1 some:2 regard:2 arrays:3 devices:2 physikalisches:1 problem:2 semiclass:1 calculated:1 mechanics:1 ordered:2 choosing:1 tβ:1 measure:2 general:1 inn:1 physica:1 saleh:1 formalism:1 ni:1 no:1 slovaca:1 whereas:1 when:2 field:5 other:4 republic:1 clicks:4 conclusion:1 in1:1 in2:1 prepared:4 generated:3 allowing:1 assume:1 required:2 4n:1 requires:2 once:1
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quant-ph9905086.txt |@word ibid:1 limited:1 measurements:3 sci:1 consider:3 remarkable:1 represent:4 consolidated:2 both:2 desirable:1 results:5 four:5 commute:1 computation:8 consists:1 query:2 primes:1 calculate:1 alamos:2 technique:3 waveplate:4 factoring:1 answered:1 finally:2 critical:1 those:1 marks:3 indicating:2 division:1 lrc:1 lack:1 amplitudes:2 straightforward:1 shifters:2 frequencies:1 polarization:25 englert:1 affect:1 difference:1 condition:1 entire:1 exponential:1 pbs:9 presented:1 transmission:1 list:1 large:1 convenience:1 circuitry:3 optics:2 still:3 limitations:1 employing:1 direct:2 sign:2 second:10 design:1 enhancement:2 insertion:1 run:3 implemented:1 remarkably:1 addition:1 hwps:1 will:9 what:3 adds:1 appear:3 abh:4 assistance:1 thickness:1 cell:1 experiment:2 abv:4 mosca:2 new:1 net:2 ground:1 ever:2 equivalent:1 implementable:1 satisfy:2 edited:1 simultaneously:4 chose:1 degree:2 tapp:1 respectively:2 here:2 desired:3 focused:1 possibility:1 separation:1 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quant-ph9905088.txt |@word consider:4 results:3 leads:4 scalar:3 go:1 follow:4 shorthands:1 coleman:1 simon:1 calculate:2 tx:1 equivalence:7 tr:2 tn:2 finally:2 program:3 stable:6 cm0:2 case:5 orthogonal:1 very:5 translations:2 springer:1 wave:1 experimentally:1 exact:1 condition:2 presented:1 t2:7 solution:12 t0:5 t1:6 large:4 vector:1 small:4 shows:2 enforce:1 degeneracy:1 miller:1 estimates:1 measurable:1 approximation:29 zero:6 equal:2 rigorous:1 further:1 dynamics:1 goes:2 even:3 what:2 errors:2 appear:1 bϕ:9 section:2 while:1 liberty:1 localized:1 reconstruction:1 values:8 method:2 coefficient:1 ibid:2 jointly:1 understanding:1 desired:2 ratio:1 strong:1 equations:11 appears:1 change:7 deduced:1 obtained:1 study:1 changed:2 allows:1 completely:3 couplings:1 trial:1 aφ:11 changes:1 technique:1 b266:1 explained:1 welch:1 apply:5 univ:1 select:2 derivatives:1 use:3 asymptotic:1 prove:4 give:1 negative:1 next:2 nucl:1 call:1 m0:29 m2:47 taken:1 type:1 more:4 formally:1 brings:2 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quant-ph9905090.txt |@word gw:7 gv:13 consider:1 ali:1 rev:4 excellent:1 results:3 plenary:1 illustrated:1 eds:1 alt:2 sch:2 particles:16 etching:1 tv:5 tw:11 passage:1 those:2 sent:1 p2:12 amplitudes:4 presently:3 straightforward:2 g0:8 very:4 implicitly:1 rise:1 springer:1 induce:1 wave:11 should:1 experimentally:2 difference:1 exact:1 leads:1 incoherent:1 vibrational:1 hamiltonian:1 transmission:7 large:4 small:11 optics:9 equation:3 dimer:3 smaller:6 second:3 further:4 estimated:1 distance:1 expressions:1 even:5 plays:2 appear:1 section:5 expressed:1 goes:1 waals:2 new:3 net:1 body:6 edited:1 outgoing:1 whose:1 modify:1 here:3 atoms:9 growing:1 standard:3 equations:4 change:3 obtained:2 incoming:2 larger:3 resulting:2 pick:1 usually:1 decouple:2 changes:2 plotted:1 diameter:5 ekstrom:1 replace:1 neutrons:1 decrease:2 total:3 hegerfeldt:4 would:1 breakup:5 contains:2 negative:1 tightly:1 france:1 few:5 nucl:1 therefore:4 taken:4 theoretical:7 more:6 introducing:1 composite:3 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quant-ph9905091.txt |@word represent:1 concept:3 consider:3 desirable:1 four:9 consists:1 devoted:1 transiting:1 dimensionality:1 depend:1 charge:1 those:1 stable:1 rham:1 uchebn:1 zaved:1 orthogonal:1 very:1 wave:9 lyapunov:1 emphasized:1 difference:1 condition:2 leads:1 presented:3 did:1 positions:1 configurational:1 enclosing:1 inertial:3 force:7 direct:2 atomizdat:2 second:1 enclosed:2 further:1 theory:10 sum:1 selected:1 uniform:1 above:1 new:1 method:3 coefficient:1 fiz:1 component:1 interdependent:1 answers:1 behaviour:3 free:1 groups:1 represented:1 const:1 along:9 equations:13 change:1 obtained:5 allows:3 ourself:1 readily:2 use:2 covariant:1 therefore:1 correspondents:1 more:3 becomes:1 under:1 odinger:1 curvature:1 correspondingly:1 virtue:2 known:1 imbedding:4 must:2 states:2 account:2 mc:1 equation:10 values:1 concepts:1 modifies:1 example:1 tab:2 stated:1 process:1 accept:1 dxo:7 dxl:1 dxk:3 dxj:10 dxi:5 sense:2 νo:2 occur:1 absolute:4 rather:1 gordon:2 description:7 may:12 law:1 lines:9 correspond:1 sk:1 secs:1 so:5 specifying:1 allow:1 sl:1 move:9 satisfied:1 paper:2 including:1 motions:1 mentioned:1 its:1 sν:1 chosen:1 interesting:1 differently:1 derivative:1 dxν:5 dai:2 sω:1 they:1 now:2 dirac:1 always:1 university:1 magnitude:1 metrization:3 found:2 referred:1 differential:4 formulate:1 energy:1 principles:2 related:1 operator:3 quantum:12 eq:5 enclosure:2 special:2 goo:11 goi:1 space:19 content:1 izv:1 denoted:1 linear:1 interactions:5 possibility:1 standard:1 completely:1 york:1 definition:2 interaction:1 geometry:3 transition:1 motion:6 isotropic:11 expedient:1 hence:5 go3:5 first:1 pseudoeuclidean:1 xi:7 geodesic:10 another:2 impossible:1 little:1 rewritten:1 eqs:1 system:3 construct:1 too:1 kµ:3 dt2:3 postulate:4 popov:1 statement:2 moscow:3 translation:2 than:1 was:2 see:3 determined:1 modern:1 generalization:1 any:9 relatively:6 zero:1 convenient:1 answering:1 transference:1 isolated:2 potential:6 build:4 finding:1 coincide:2 formulas:1 broglie:7 shall:3 correlation:3 connected:2 gauss:1 measured:2 prolongation:1 considered:4 clear:1 points:3 principle:1 velocity:3 physics:1 lying:2 gauge:1 find:1 parameters:1 aω:1 state:1 should:8 do:1 establishes:1 klein:2 de:9 words:1 dt:1 aν:1 ds:1 covering:2 fields:6 arxiv:1 dpo:1 dpi:1 view:3 characteristics:2 set:2 observer:3 frame:9 respect:1 namely:2 sec:2 result:2 surfaces:4 dpµ:1 gravitation:2 tensor:7 nonmetricity:1 distinctive:2 definite:1 written:1 between:3 geometric:5 conditions:3 terms:1 however:3 hypothesis:3 here:1 taking:1 according:1 quantization:1 etc:1 connection:3 distinction:2 requests:1 holonomic:1 whole:3 mechanics:4 point:5 dimensional:2 table:4 considers:1 described:8 microparticle:1 trajectory:3 describes:2 basic:6 ph:1 abstract:1 arises:1 corresponding:1 sufficient:1 photon:4 observers:2 external:1 c2:6 c1:3 present:1 conception:2 look:1 formalization:1 will:5 euclidean:2 while:1 behavior:1 irrespective:1 property:2 detailed:1 microparticles:2 vol:1 vi:2 metric:9 thus:3 surface:4 ij:1 il:1 io:1 different:2 author:2 journal:1 make:1 geometrization:3 quant:1 connectedness:1 physical:1 higher:1 trajectories:3 v3:6 v4:24 changing:1 reference:7 schr:1 pµ:1 well:2 vyssh:1 obviously:2 components:4 coordinate:1 soviet:1 manifold:10 less:1 newton:1 obtain:2 ideas:1 photons:5 spread:1 skl:4 remaining:1 momentum:2 take:2 possible:3 press:1 formal:2 semiclassical:1 necessary:3 particle:10 follows:2 velocities:1 specific:1 collect:1 arbitrary:1 stationary:1 essential:1 because:2 classical:10 some:4 specified:2 nonzero:3 acquaintance:1 describing:2 electromagnetic:2 avoid:2 everything:1 does:1 assuming:1 particles:15 demonstrated:1 equivalent:1 each:2 properties:9 oo:1 oj:2 basis:1 o:11 simulation:1 mixed:1 plan:1 cambridge:1 christoffel:1 into:1 soo:2 einstein:2 frames:1 transfer:2 initial:2 quadratic:1 gik:6 misner:1 function:1 form:8 m2:1 but:1 construction:1 aµ:10 russian:4 line:3 evident:1 daµ:1 minkowski:3 up:1 po:3 problem:2 similar:1 called:3 originating:1 associated:1 ln:1 defined:3 ak:1 describe:3 influence:1 rahm:1 formulation:1 formalism:9 constructed:2 no:11 field:9 other:1 papers:3 test:6 generates:1 separate:1 models:1 nonmetric:2 symbol:1 problems:3 n4:1 dτ:2 required:1 together:1 n8:1 depth:1 mass:10 fact:1 n1:1 n2:1 n3:1 starting:1 n5:1 n6:1 n7:1
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quant-ph9905092.txt |@word consider:1 interference:2 leads:1 computation:19 denotes:4 deterministic:10 languages:8 th:5 qacc:2 applied:1 amplitudes:3 string:1 straightforward:1 orthogonal:1 very:2 continues:2 every:2 difference:3 condition:5 disturb:1 mo:4 large:1 item:1 vector:2 terminating:3 programme:1 focs:2 sign:17 zero:10 further:3 defines:1 machines:1 theory:3 aim:1 sum:5 current:2 above:3 new:5 coefficient:1 impact:1 processing:2 respectively:5 here:1 desired:1 groups:1 others:2 path:6 xδ:4 great:1 1qfa:4 allows:2 resulting:1 conjunctive:1 automaton:33 changes:3 uniquely:1 logically:1 total:3 use:4 takes:2 would:1 prove:2 remains:2 contains:1 negative:2 properties:1 automata:37 therefore:1 means:1 type:4 more:7 formally:1 operators:1 reversible:3 known:1 cases:1 must:4 word:35 mm:6 science:3 equation:3 work:2 modified:3 believes:1 remain:1 values:4 halts:1 following:6 root:1 example:10 proof:6 compare:1 process:1 arise:1 accept:2 states:14 council:1 sense:1 keep:1 occur:2 end:2 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quant-ph9905093.txt |@word fredenhagen:1 represent:4 concept:1 consider:2 issued:1 rovelli:1 results:9 four:1 eds:2 scalar:3 commute:7 generalize:2 foundations:1 hyperboloid:6 follow:1 expressions:6 displaying:2 localized:1 reynaud:7 devoted:2 certainly:3 inverse:2 depend:2 superpositions:1 indices:4 paris:3 concerned:1 equivalence:5 finally:2 weyl:1 preserved:6 th:4 under:25 breach:1 analogous:1 include:2 worth:2 division:3 witten:1 outside:1 very:2 b188:1 translations:1 brossel:1 choice:5 electron:10 manipulated:3 dispersions:1 fall:9 emphasized:1 difference:1 condition:3 preuss:1 leads:1 cunningham:2 prize:1 solves:1 purely:2 positions:12 henri:1 solution:1 maggiore:1 solved:1 vector:7 dealt:2 inversions:1 optics:1 equation:6 benjamin:1 smaller:1 force:1 relativit:1 direct:3 lubanski:1 zero:1 evaluated:6 equal:2 rigorous:1 further:1 canonical:4 even:1 aim:4 sud:1 essence:1 stands:1 clock:1 giving:1 diag:2 section:2 xρ:1 expressed:4 uniform:3 heron:1 annals:2 intersect:2 sup:2 new:1 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quant-ph9905102.txt |@word consider:4 magnetic:28 leads:3 roy:1 scalar:12 generalize:1 consists:1 chair:1 quasi:1 those:1 th:1 applied:1 wave:11 witten:6 exact:2 condition:1 generalised:1 entire:1 hamiltonian:2 pacs:1 solution:3 solved:3 vector:3 small:1 eigenvalues:2 noted:4 sukhatme:1 cosh:2 matrices:1 zero:16 dedonder:1 even:1 tkachuk:2 section:2 indian:1 above:1 contrast:2 simultaneously:1 here:2 address:1 along:2 strong:4 equations:2 ukraine:1 institute:1 study:3 studied:4 reports:1 prior:1 periodic:1 zhdanov:1 useful:1 superpotential:5 unit:1 would:2 positive:1 finally:3 nucl:1 theoretical:1 separated:1 becomes:2 operators:4 odinger:1 berlin:1 particular:1 must:1 springer:1 junker:1 equation:6 levai:1 following:4 example:1 india:1 states:3 susy:32 numbers:1 partner:3 axis:1 breaking:8 feature:2 how:1 zaxis:1 sin:4 may:6 after:2 plane:1 cannata:3 generalise:1 sy:5 sx:2 sectors:1 coupling:2 explicit:2 correspond:1 so:5 fundamental:1 subsequently:1 order:3 move:1 paper:3 statistical:2 existence:1 satisfies:2 its:1 before:1 interesting:4 sα:1 inclusion:1 parts:1 systems:1 mail:2 supersymmetry:6 non:9 affected:1 greater:1 band:4 now:4 discuss:1 eigenvalue:5 term:1 2w:1 always:1 university:1 sufficiently:4 mode:1 each:2 found:1 2k:1 square:3 energy:21 feinberg:1 isospectral:1 quantum:12 laboratory:1 out:3 emerges:1 shown:4 matrix:2 discrete:2 rev:3 particles:1 investigation:1 nontrivially:1 issue:1 math:1 theory:1 free:2 standard:1 khare:1 e1:3 dunne:2 could:1 motion:9 first:1 franko:2 given:11 publication:1 introduction:1 least:1 indicate:1 unbroken:5 tool:1 exactly:4 part:1 than:1 see:1 future:1 str:1 ktf:1 lowest:2 generality:1 spectrum:6 seen:1 seek:2 any:1 strength:2 note:4 potential:11 k4:3 channel:1 shall:4 nishnianidze:1 involving:2 pair:1 considered:1 points:1 exp:1 mechanical:1 kz:4 physics:3 merit:1 rotating:11 purely:2 solutions:6 keywords:1 d2:2 ground:9 based:1 parameters:1 written:2 ksz:2 only:2 integrable:3 hamiltonians:13 do:2 dependent:1 lviv:3 dz:10 words:1 gen:1 arxiv:1 remove:1 investigate:1 view:1 set:1 exists:1 depends:3 result:1 w0:2 subject:1 eigenfunctions:1 state:10 various:1 isical:1 however:1 both:6 essentially:1 last:1 ua:2 connection:1 0e:1 nonrelativistic:1 period:2 dimensional:2 proved:1 addition:1 been:3 pb:1 permanent:1 ph:1 choose:3 obtained:3 arises:1 supersymmetric:3 concerning:1 cos:4 recalled:1 spin:17 present:4 case:15 unlike:1 tanh:1 appearance:1 value:2 hau:1 will:3 while:1 b02:8 situation:1 unitary:3 coupled:1 iq:1 thus:12 vx:1 vy:1 vz:1 normalisable:2 different:2 perform:1 same:2 complex:1 quant:1 pauli:1 used:1 levels:1 moving:3 purpose:1 potentials:2 schr:1 modes:3 scenario:1 framework:1 well:2 without:1 components:1 coordinate:1 calcutta:1 model:3 dimension:1 posses:1 being:1 λz:3 obtain:5 previous:1 preprint:1 conclusions:1 point:3 had:2 transformed:1 lett:3 nicolai:2 solvable:1 transformation:4 real:5 spinless:2 easily:1 february:1 burns:1 apart:1 loss:1 necessary:1 like:2 particle:16 follows:2 performing:1 ivan:1 methods:2 b0:15 b2:2 eiqz:1 investigating:1 cooper:1 lead:1 destroys:1 illustration:1 broken:6 imaginary:1 about:1 amado:1 dependence:1 introduced:1 own:1 presence:4 previously:1 within:1 andrianov:1 references:1 determine:1 operator:1 hep:1 strictly:1 there:1 way:2 was:1 function:6 complete:1 form:5 enough:1 ioffe:1 line:2 true:2 he:1 iqz:1 whether:1 us:4 problem:6 similar:1 called:1 mechanics:9 ac:1 constant:9 abstract:1 describe:3 exist:3 corresponding:3 moves:1 irrespective:1 functions:2 no:2 when:12 field:29 other:3 mathematics:1 briefly:1 models:2 problems:1 implies:1 factorized:1 orbit:1 4k:3
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quant-ph9906001.txt |@word concept:2 partial:1 consider:2 magnetic:1 particular:1 four:6 consists:1 amplification:1 tr:1 noncompact:1 charge:1 th:2 case:2 straightforward:2 orthogonal:1 wave:1 exact:1 leads:2 hamiltonian:3 vector:4 gauge:1 markov:1 upper:1 consistent:1 approximation:2 second:1 further:1 port:3 linear:2 bilinear:1 established:1 expressed:2 current:1 poles:1 ˆf:5 ˆj:4 ˆl:1 method:2 body:1 outgoing:1 full:1 here:1 trung:1 equations:4 incoming:1 study:2 vectors:2 resulting:1 constitutive:1 action:1 fourier:1 spatially:1 replace:1 apply:2 use:2 takes:1 positive:1 scheel:6 next:1 process:1 introducing:2 operators:8 emission:1 varying:1 known:2 iii:2 states:1 account:1 valued:2 quantized:2 equation:4 work:1 oscillator:1 fock:2 freedom:1 following:1 spontaneous:6 example:4 exchanged:1 give:3 calculation:1 high:1 performed:2 goal:1 acta:1 profile:1 simplicity:1 description:1 algebra:1 may:1 max:1 after:1 applications:1 plane:1 waves:1 forschungsgemeinschaft:1 effective:1 deutsche:1 su:2 element:1 so:2 specifying:1 fundamental:6 representation:4 order:2 typical:1 reservoir:1 amplifying:8 satisfied:1 including:2 satisfies:1 excitations:1 its:1 diagonalized:1 derive:2 group:1 decay:7 matrices:2 temporal:1 solving:1 microscopic:2 systems:3 schmidt:1 them:1 splitter:1 introduce:1 ǫij:2 ρˆin:4 now:1 okl:1 dielectric:6 term:1 level:1 sufficiently:1 each:1 universit:1 2k:1 differential:1 barnett:2 related:2 inhomogeneous:1 frequency:5 changed:1 quantum:6 eq:7 special:1 out:1 shown:2 matrix:3 space:2 integrates:1 since:3 rev:8 gˆj:4 ra:4 issue:1 shows:1 theory:5 dung:1 diagonal:1 free:1 approaches:2 dirk:1 universally:1 starts:1 motion:1 isotropic:1 δij:1 hence:1 first:4 variables:5 huttner:1 channels:1 simplified:1 relations:4 directly:2 dispersive:1 given:4 necessarily:2 guest:1 introduction:2 system:4 least:1 assumption:1 zeros:1 scheme:3 2ωa:1 holomorphic:1 part:1 completes:1 distance:1 was:2 approximations:1 rate:3 submitted:1 annihilation:2 matter:4 amplitude:1 dielectrics:4 fluctuation:4 nonradiative:1 any:2 note:4 gkk:5 potential:1 generalized:2 green:4 channel:4 formulas:1 play:1 electric:2 germany:1 but:2 device:7 gruner:2 class:1 tensor:1 radiating:1 considered:1 later:1 kn:6 principle:2 drastically:1 absorbing:12 supported:1 rotating:1 purely:1 relation:8 d3:3 slov:1 causality:2 written:1 local:2 over:1 achieve:1 continuity:1 dependent:1 beam:1 platz:1 continuum:1 fields:2 arxiv:1 µ2z:1 observed:1 see:1 gunnar:1 sec:3 devices:6 dyadic:2 3c3:1 satisfying:1 commutation:5 review:1 dipole:1 symmetric:1 state:6 µk:3 between:1 physikalisches:1 approach:2 terms:7 chizhov:1 eˆk:3 jk:1 interface:2 both:1 equal:3 quantization:6 hω:1 γij:1 otherwise:1 arbitrarily:1 relevant:1 simple:1 harmonic:1 dimensional:3 ensures:1 described:2 transformations:1 wien:1 three:1 anisotropic:2 degrees:1 ph:2 hardly:1 field:11 corresponding:1 kronig:3 photon:2 requires:3 kramers:3 external:1 c2:3 2ǫi:1 applied:1 reciprocal:1 theoretisch:1 ǫi:5 transformation:7 ǫr:1 near:2 couplings:1 procedure:1 planar:1 unitary:2 coupled:1 phenomenological:4 iv:2 ii:2 ij:3 im:3 media:9 radiation:1 unity:1 complex:5 quant:2 several:1 independent:1 oik:2 schiller:1 effect:1 ρˆout:3 uˆ:1 acknowledgement:1 well:2 without:2 consistency:1 position:1 model:1 bodies:4 left:1 λs:1 construct:1 λt:1 being:3 obtain:1 rest:1 sources:1 atomic:1 macroscopic:1 polarization:2 density:5 absorption:2 regarded:1 iω:1 friedrich:1 other:1 combine:1 theorem:4 input:6 excited:3 read:1 possible:1 vacuum:2 press:1 using:1 like:1 follows:3 reduces:1 benefit:1 yields:3 arbitrary:6 output:4 jˆ:1 permittivity:4 because:1 qed:4 classical:2 creation:2 some:3 electromagnetic:6 does:1 welsch:9 noise:5 stefan:1 agreement:1 ǫkl:3 ˆbj:2 properties:1 extension:3 tracing:1 discussed:1 recognized:1 introduced:2 bloch:1 presence:5 maxwell:4 integral:3 jena:2 hermitian:1 weyl:1 operator:9 bosonic:4 institut:1 additional:1 long:1 start:1 accordingly:1 fˆk:1 fˆj:2 gik:1 gij:1 function:6 medium:5 complete:1 form:2 oll:6 regard:1 jul:1 ho:1 atom:9 iµ0:1 dissipative:1 applying:1 embedded:1 characteristic:1 us:4 d21:2 limit:1 ωa:4 problem:4 general:1 single:1 ti2:5 formalism:1 constructed:1 again:1 when:2 rewriting:1 application:1 valid:2 role:2 briefly:1 models:1 prepared:2 dissipation:4 auxiliary:1 dω:3 assume:2 nonmagnetic:3 ti1:7 together:3 equivalently:1 time:3 starting:1
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quant-ph9906002.txt |@word now:2 measurements:3 interpretation:5 pointing:1 show:1 being:2 magnetic:1 summarized:1 repeatability:1 obtain:12 actions:1 rotated:5 founded:1 paper:2 through:1 higher:1 foundations:3 go:1 expressions:2 find:1 projection:16 expansion:2 whose:4 derive:2 symmetry:1 measure:3 functions:1 contained:1 should:3 forms:1 finally:3 other:1 treatment:2 under:2 evidenced:1 exposition:1 save:1 lies:1 transformation:3 take:1 identical:1 case:4 them:2 amplitudes:4 compute:1 quantph:1 means:2 very:1 devised:1 results:1 expectation:6 introduce:1 number:1 units:2 ones:1 every:1 axes:2 they:4 formula:3 press:4 using:5 respectively:1 outcomes:1 matrices:3 condition:2 eigenvalue:5 products:1 particle:1 presented:2 validity:2 follows:1 university:3 arxiv:1 unnecessary:1 yield:1 occurs:1 twice:1 vector:11 yields:1 arbitrary:1 eigenvalues:4 limit:3 discussion:1 characterized:1 measuring:1 requirement:1 because:1 ei:12 transform:1 polar:4 therefore:1 principles:2 literature:2 see:1 elements:8 b1:1 b2:1 measurement:4 quantum:9 further:1 eq:5 alternative:2 yet:1 obey:1 even:1 shown:2 matrix:12 labour:2 furthermore:1 ensures:1 below:1 its:3 similarly:2 state:9 features:1 use:1 simplest:1 new:7 row:1 approach:2 method:4 shows:1 satisfy:1 multiplied:3 bi:1 replaced:1 eiϕ:1 theory:2 extend:1 adding:2 initially:3 upon:1 yale:1 component:12 however:1 bj:7 quite:1 here:2 references:1 found:3 represented:1 along:9 refers:1 change:6 proceed:1 obtained:7 deriving:1 cos:88 r1:6 r2:6 just:1 vectors:4 allows:1 quantization:9 cx:8 turn:1 important:1 simply:1 procedure:2 published:1 hence:3 importantly:1 expression:4 automatically:1 first:2 key:1 appropriately:1 twodimensional:1 cn:8 probability:9 iϕ:1 obtaining:6 corresponds:2 due:1 down:4 directions:1 cy:8 square:6 done:1 completed:1 operator:16 respect:8 earlier:1 unit:6 defined:7 iei:4 given:2 verifying:1 transformations:3 leads:1 prove:1 introduction:1 positive:2 eqs:3 initial:4 system:8 been:1 next:1 their:7 intermediate:3 m1:2 interpret:1 way:3 basic:1 ph:1 was:2 final:5 a2:1 more:3 function:1 dualism:1 direction:17 corresponding:3 form:10 both:1 quantities:1 operators:14 m2:2 convert:1 jul:1 direct:2 task:2 angles:11 known:1 c2:1 c1:1 spin:61 than:2 present:1 derivation:2 applied:4 mf:2 defines:1 since:3 characterize:1 submitted:1 mi:10 up:3 value:7 mj:1 information:1 while:2 itself:1 suppose:4 three:4 amplitude:5 were:4 those:1 situation:2 enables:1 proves:1 example:1 eigenvector:3 projections:1 mechanics:7 instead:1 result:1 constant:1 coordinate:5 ai:8 aj:1 thus:2 argument:3 general:3 eqn:1 ij:2 sought:1 r12:2 orthogonal:1 seek:1 r22:2 r21:2 axis:10 tedious:1 again:1 different:1 us:2 etc:2 arguments:1 make:1 agency:1 when:4 same:7 evidently:2 how:2 unity:1 setting:1 quant:1 generalized:16 pauli:4 plane:1 finding:1 resulting:1 proved:1 mutually:1 sin:82 cambridge:2 conclusion:1 hermiticity:2 formulas:2 calculation:2 used:2 shall:1 may:2 ladder:3 become:1 derived:4 ultimately:1 hand:1 a1:1 most:1 involving:1 connected:1 but:2 r11:2 date:1 changing:1 measured:1 recent:1 eigenvectors:23 land:8 values:2 required:1 correspond:2 physics:2 original:2 squaring:2 without:1 so:1 satisfied:1 components:13 sets:1 moreover:2 observables:2 starting:2 order:1 quantity:3
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quant-ph9906003.txt |@word concept:2 partial:1 consider:12 squared:4 separates:1 results:1 scattered:1 leads:7 consists:2 landau:1 iu2:5 optical:1 farhi:1 whose:2 depend:3 calculate:12 λn2:1 interactions:1 tn:5 nπ:14 finally:1 according:18 present:3 th:2 under:2 stochastic:1 analogous:4 include:2 sent:1 p2:4 hibbs:1 outside:7 far:2 frequencies:3 rise:3 k02:3 wave:79 electron:1 sons:2 every:1 summarized:1 bounding:1 experimentally:2 difference:2 condition:8 entire:6 obvious:1 subsets:2 level:7 did:1 induction:1 t2:9 t3:5 damped:1 large:1 detected:1 discounting:4 small:1 eigenvalues:1 setup:3 upper:2 tel:4 measurable:2 literature:1 cosh:1 past:1 rate:17 value:1 qualitatively:1 renormalizes:1 will:2 predictions:1 plays:1 combined:1 section:12 axes:1 uniform:1 current:15 experiment:13 above:13 lifshitz:1 kleinert:1 expresses:1 ever:1 method:2 contrast:2 coefficient:9 q1:2 2ma2:2 respectively:1 never:2 component:2 here:1 atoms:2 free:3 consideration:1 along:2 sine:1 equations:4 appears:1 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quant-ph9906009.txt |@word proposition:9 concept:2 partial:8 consider:12 maximum:1 rev:1 results:9 leads:2 eds:1 scalar:26 commute:1 generalize:2 computation:2 foundations:1 consists:1 follow:2 expressions:3 reasoning:3 gh:1 whose:1 certainly:1 tx:4 effort:1 tr:34 alberti:1 finally:4 program:1 those:1 th:1 under:6 stochastic:3 analogous:1 must:1 alternating:1 case:13 conjecture:12 advantage:1 orthogonal:3 very:1 focus:1 corollary:9 p1:5 every:5 additional:1 entries:1 mixing:1 matrices:14 condition:1 milburn:1 3h1:1 map:1 riemann:1 immediately:2 level:1 turns:2 notes:1 list:1 large:1 vector:15 morozova:10 indices:5 entropy:2 markov:1 der:1 relative:1 application:1 mn:5 neighborhood:5 version:1 dealing:1 zg:1 b23:13 riesz:5 surrounding:1 second:11 deutscher:1 go:1 nondecreasing:1 further:8 nauki:1 linear:2 even:1 index:3 what:3 developed:1 appear:5 diag:5 section:10 expressed:1 infinitesimal:1 en:2 goes:2 8c:3 dn1:9 method:1 3d:1 full:1 degree:2 respectively:1 component:2 equals:8 here:7 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quant-ph9906010.txt |@word sci:1 similarity:1 particular:1 results:2 content:1 inverse:1 ingredient:1 applied:2 wave:9 electron:3 condition:1 margarita:1 smithey:1 presented:1 transmission:1 optics:5 ville:2 approximation:1 linear:1 even:1 established:1 nonlinear:2 plays:1 analogously:1 expressed:1 fractional:19 new:1 method:2 respectively:1 component:1 beck:1 active:1 change:2 institute:2 study:2 periodic:1 fourier:26 measuring:3 extra:1 marginal:1 visible:1 sgn:1 establish:1 use:2 takes:1 would:1 intensively:2 imω:3 more:1 nauka:1 formally:1 knows:1 odinger:3 normalized:2 employed:1 reconstructed:1 science:1 equation:3 oscillator:9 zhao:1 fock:1 obvious:1 example:4 compare:2 process:2 cited:1 states:3 information:7 needs:1 provide:1 maps:1 opt:4 parameter:1 sin:10 map:4 product:1 description:1 mendes:1 after:1 inst:1 ff:2 data:1 man:8 jiang:1 fibers:1 explicit:1 inform:1 green:13 representation:1 order:2 wigner:3 developed:1 pulses:1 lasers:3 satisfies:1 ieee:2 better:1 lu:1 systems:1 they:1 now:1 discuss:1 tran:1 2x:1 mode:1 acoustic:1 ed:1 gaussian:1 related:2 frequency:5 obtains:1 quantum:25 eq:1 out:1 shown:1 tombesi:1 rev:3 research:1 semiconductor:4 investigation:1 print:1 formula:2 math:1 theory:1 mω:13 possibility:1 advantages:1 york:1 publ:1 ltd:1 onto:1 first:1 probability:6 variables:3 xy:1 done:2 πa:1 unitarity:2 system:1 relations:2 their:1 realization:1 gives:2 relationship:3 moscow:2 optical:8 x2:4 thai:1 iωt:2 determines:1 see:4 determined:2 amplitude:1 were:1 russia:1 lines:1 say:1 angle:1 depending:2 studying:2 potential:1 coincide:1 modulus:3 gω:5 leontovich:1 connected:2 phase:4 observation:1 raab:1 coincides:1 proceedings:1 exp:13 physics:1 fact:2 lebedev:2 show:1 random:1 relation:3 aπ:1 based:1 parameters:3 elucidated:1 analytic:16 only:1 factor:3 elucidates:1 means:2 dependent:1 joint:1 dx:3 dy:4 dv:1 reconstruct:1 du:3 procedures:1 evolution:4 arxiv:1 qe:1 vision:1 view:2 conversions:1 kernel:11 bertolotti:1 physically:1 ωt:10 observed:1 namely:1 recently:1 dµ:2 satisfying:1 state:3 between:1 approach:5 terms:2 suggested:2 both:1 last:1 cot:6 equal:1 etc:1 connection:3 symplectic:3 context:1 contribution:1 mechanics:4 point:1 corresponds:1 pr:1 kernels:2 described:2 pt:1 describes:1 applying:2 ph:1 lohmann:1 iµ:1 noncommutative:6 case:1 laser:1 appearance:1 value:1 aim:1 replaced:1 property:1 procedure:2 ix:1 vogel:1 vol:2 thus:2 reads:3 2uu:1 different:2 propagation:1 same:1 complex:4 quant:1 arguments:1 used:8 iop:1 uses:1 potentials:1 identity:2 schr:3 modes:1 makes:1 well:1 analysis:12 coordinate:1 usual:2 proposed:2 being:1 shape:1 transforms:3 aspect:1 mathematically:1 signals:10 lett:1 versa:1 iπ:2 iφ:1 real:3 aspects:1 quasidistribution:2 harmonic:8 press:1 using:1 formal:1 like:3 signal:29 arbitrary:2 output:1 essential:1 replacement:2 methods:4 successfully:1 some:3 b0:1 b2:1 employment:1 describing:4 electromagnetic:1 measurements:1 2xy:2 provides:3 demonstrated:1 inserting:2 ba:4 equivalent:3 processing:6 conventional:1 2m:1 properties:5 raymer:1 waveguides:1 extension:1 faridani:1 introduced:3 soc:1 image:1 integral:4 references:1 inverting:1 sov:2 operator:3 risken:1 statistics:1 initial:5 transform:35 nova:1 u2:1 appl:2 analyze:1 was:7 function:27 form:2 jun:1 but:1 idea:1 rozprawy:1 consist:1 2πi:3 2πk:2 up:2 us:2 below:1 2πv:1 russ:1 distribution:6 semiclass:1 similar:1 called:2 detailed:1 constant:2 ko:8 abstract:1 describe:4 am:1 tomography:14 cables:1 physical:2 functions:4 no:1 arctan:5 application:1 other:4 role:1 conclusion:1 conventionally:1 problems:1 interferometric:1 meaning:1 important:2 variable:2 seismic:1 structure:1 vice:1 lanl:1 mancini:1 time:10
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quant-ph9906012.txt |@word scalapino:1 sci:1 consider:2 switched:1 rev:4 results:3 gx:1 four:3 computation:1 consists:1 devoted:1 whose:1 depend:1 fokker:1 segments:3 technique:1 tr:8 environment:2 tail:2 under:2 γf:1 p2:1 belonging:1 very:3 tends:3 account:1 wave:21 figs:1 difference:2 exact:1 rotating:1 obvious:1 level:1 joined:15 damped:2 leave:1 solved:1 differential:1 small:1 inspection:1 lapse:3 limitations:1 slower:1 trend:1 dealing:1 approximation:2 located:3 second:11 plenum:1 pass:1 dynamics:1 linear:5 sub:1 rate:1 selected:1 current:2 experiment:1 above:8 flowing:2 new:4 acknowledgments:1 satisfy:2 edited:1 degree:1 mel:1 never:1 here:1 behaviour:1 yannouleas:1 mev:27 ansatz:1 represented:3 path:1 dissipated:1 equations:3 deduced:2 obtained:2 burstein:1 institute:1 study:2 studied:3 abrikosov:1 published:1 action:1 scutaru:1 studies:1 love:1 ase:1 treatment:1 decrease:1 total:1 establish:2 asymptotic:2 would:4 next:3 choosen:1 calculation:1 nucl:5 therefore:2 taken:4 det:1 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quant-ph9906019.txt |@word magnetically:1 precise:1 measurements:2 consider:1 csic:1 caused:1 magnetic:2 indicating:1 amplifier:1 results:2 gy:1 dbm:3 depend:1 technique:2 groundstate:1 ıa:1 under:1 dramatically:2 montevideo:1 belonging:1 supported:1 amplitudes:1 orthogonal:2 very:3 frequencies:2 conditions:1 wave:12 electron:1 refractive:13 mixing:2 locked:1 difference:1 squares:1 level:11 nagel:1 large:8 optics:2 degeneracy:1 possibility:1 smaller:1 prediction:2 pulse:2 rate:2 doppler:2 design:1 enhancement:2 further:1 theory:2 spectral:1 index:14 nonlinear:1 trapping:2 section:2 near:1 cell:13 experiment:2 new:1 3a:1 increasing:1 method:4 thin:2 coefficient:1 magnetometry:1 danzmann:1 led:1 submitted:1 arb:1 respectively:3 modify:1 here:1 atoms:3 following:2 zibrov:2 relaxation:4 path:1 extrema:1 obtained:5 instituto:1 trans:1 spite:1 institute:1 study:2 studied:1 resulting:1 permit:1 resonance:9 narrow:1 diameter:5 named:1 see:1 wicht:1 explained:1 electromagnetically:2 welch:1 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quant-ph9906020.txt |@word pointing:1 maximum:1 rev:4 results:1 generalize:1 edu:1 query:1 expressions:1 inverse:1 calculate:1 leung:1 speeded:1 factoring:1 monotonically:1 worth:1 norm:5 fax:1 g4:1 amplitudes:4 g2:1 advantage:2 zhang:2 far:1 affect:1 exact:1 høyer:2 condition:4 notations:1 gui:1 large:1 vector:4 science:2 small:11 radio:1 smaller:1 tel:1 second:1 chen:1 further:1 implemented:1 even:1 what:2 plays:1 appear:1 sum:2 cooking:1 henceforth:1 version:3 new:2 journal:1 3d:4 satisfy:1 respectively:2 here:1 following:2 china:2 represented:1 along:1 obtained:2 search:20 study:1 studied:2 leaving:1 alamos:1 usually:2 implement:1 narrow:1 changes:2 involves:1 plotted:5 composed:1 useful:2 marked:16 replace:2 inverses:1 unit:1 plot:4 use:2 working:1 contains:1 next:1 taken:1 theoretical:1 more:2 becomes:1 foundations:1 cases:2 must:1 high:1 avoiding:1 equation:2 des:1 cancellations:1 geometry:1 grover:22 values:7 believed:1 hansen:1 example:1 beijing:2 give:2 bennett:1 states:3 walsh:5 g3:1 counting:1 rather:1 orthogonal:1 recovers:1 write:1 very:1 instead:1 sin:25 brassard:3 simplicity:1 product:2 may:3 suppose:1 after:6 derived:1 applications:1 produce:2 summarize:1 realized:2 maybe:1 algorithms:2 order:3 operations:3 gershenfeld:1 over:1 satisfied:4 paper:1 through:4 still:3 ieee:1 acknowledge:1 chosen:1 li:3 better:1 lu:1 fig:13 mail:1 lx:1 versus:9 them:1 tsinghua:3 optimal:3 rotation:11 now:1 discuss:1 matched:1 easily:1 inversion:7 hereafter:1 university:2 each:2 found:5 2i:2 ei:3 another:1 society:1 frequency:1 measurement:1 quantum:29 our:1 operation:6 out:1 shown:2 matrix:6 space:3 restricted:1 crucial:2 increase:3 eprint:11 denoted:1 formula:2 ref:2 shows:1 gate:1 numerical:1 differ:1 inversions:4 approaches:2 put:3 jozsa:1 definition:1 language:1 recast:1 times:1 βe:1 βg:1 first:2 initial:4 probability:3 omitted:1 e2iδ:4 number:7 set:1 done:1 approximately:2 directly:1 zalka:5 qnew:1 given:5 long:2 construct:4 realization:1 siam:1 scheme:1 williams:1 imperfect:1 explanation:2 exactly:1 took:1 authors:2 than:3 showed:2 iteration:3 zero:2 contrary:1 amplitude:15 deciphering:1 sees:1 generality:1 rewrite:1 generalization:1 seen:1 recover:1 clearly:1 mountain:1 chem:1 angle:12 lin:1 instance:5 absorbed:1 generalized:4 effectiveness:1 formulas:1 towards:1 though:1 neatly:1 reach:2 fails:1 letter:2 phase:35 analytically:1 average:3 typeset:1 proceedings:1 βei:1 physics:3 shor:2 vandersypen:1 rotating:2 relation:1 lloyd:1 keywords:1 ca:1 tapp:2 situations:1 heavily:1 distributed:1 written:3 should:1 iei:1 only:4 experiment:1 factor:9 do:2 his:1 means:1 overall:1 nearly:2 areas:1 prime:1 arxiv:1 yield:1 analytical:1 qj:2 requirement:2 multiplying:1 constructing:2 exists:1 bounds:3 see:7 computer:8 result:1 enhanced:1 terms:1 techniques:1 phases:2 state:34 various:1 between:3 theta:7 geometric:1 email:1 recently:2 nature:2 confusion:1 however:3 untouched:1 jm:6 uτ:12 suggested:1 both:1 cos:11 improved:1 efficiency:1 many:1 annual:1 according:1 figures:2 expression:1 boyer:2 arbitrarily:1 cn:1 simple:6 acted:1 dimensional:1 pati:2 simply:1 iterations:9 transformations:2 basis:9 addition:1 encryption:1 been:2 validating:1 yan:1 expected:2 ph:11 pi:6 lett:4 cerf:1 corresponding:1 great:1 niu:2 last:1 those:1 case:2 look:1 iτ:5 will:5 near:1 replaced:2 behavior:1 iφ:2 35th:1 unitary:4 thus:4 encouragement:1 ignoring:1 ie:10 different:2 author:1 realizing:1 same:2 any:1 shorter:1 unity:1 complex:1 quant:12 largest:1 phi:6 used:6 peaks:3 closest:1 i0:2 i2:1 effect:2 gingrich:2 relies:1 database:2 makes:1 analysis:1 without:2 solve:1 experimental:1 dimension:1 stringent:1 proposed:3 less:1 rotated:1 obtain:1 shape:1 using:5 rotates:2 wei:1 except:2 improvement:2 signals:1 reasons:1 treatment:1 easy:2 transformation:5 chuang:2 gave:1 iθ:5 iγ:5 iβ:4 term:1 iζ:4 increases:1 press:1 integer:1 loss:1 rotate:1 like:1 mismatching:2 separately:1 communications:1 steps:3 arbitrary:9 replacement:1 successfully:1 some:2 searching:5 b7:2 b0:5 specified:1 duration:1 b8:5 matching:17 lead:2 eiζ:1 eiθ:4 does:1 prof:1 nmr:2 equivalent:1 bj:15 step:2 revtex:1 eiφ:5 hadamard:5 properties:1 about:3 certainty:1 o:1 range:1 rotations:7 jβ:13 references:1 operator:3 proportional:1 fortsch:1 span:2 there:5 approximate:3 fast:1 los:1 function:3 form:2 jun:1 but:2 failure:1 larger:1 highest:1 up:1 kumar:1 problem:2 constant:1 computing:2 abstract:1 general:4 single:1 adversely:1 constructed:1 mosca:2 no:1 whereas:1 when:18 tight:2 other:4 role:1 department:2 symposium:1 elements:1 zhou:1 problems:1 prepared:3 a0:3 peak:1 vectors:2 song:1 jones:2 faster:1 algorithm:38 lanl:11 curve:1 together:3 parallelism:2 time:1 serious:1 requires:3 original:7
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quant-ph9906021.txt |@word consider:3 magnetic:1 comparatively:1 results:7 roy:1 quadrature:4 computation:1 remarkably:2 2r1:7 gr:1 calculate:1 paris:1 pˆk:4 pˆj:3 pˆl:6 send:2 thapliyal:1 finally:1 squeezing:24 pˆv:7 sent:3 ingredient:1 case:4 amplitudes:1 orthogonal:1 fav:4 experimentally:4 arrange:1 splitter:1 school:1 positions:2 notes:1 tripartite:3 pˆ1:11 discrete:2 pˆ3:9 bangor:1 small:2 refer:1 optics:5 work:1 tel:2 consistent:1 zero:7 greenberger:1 even:4 will:2 what:1 ˆu:5 assistance:1 version:1 issues:1 above:1 shared:2 ˆj:4 ˆl:6 method:1 3e:1 satisfy:1 outgoing:3 αin:4 simultaneously:1 respectively:1 teleportation:36 here:4 reported:1 represented:1 obtained:2 sending:2 trans:1 sender:6 funded:1 action:1 resonance:1 bob:17 via:4 achievable:2 apply:1 total:3 unit:1 use:1 would:2 contains:1 daad:1 partite:7 tele:1 criteria:1 more:4 becomes:7 operators:7 normalized:1 particular:2 known:1 detects:1 iii:1 must:1 states:19 springer:1 science:2 originally:1 averaged:1 values:2 following:1 drops:1 example:1 attain:1 figure:1 give:1 bennett:2 distillation:1 reconstructed:1 indicates:1 minimum:2 numbers:1 want:1 inseparability:2 tan:1 verlag:1 information:4 needs:3 soc:1 rather:1 write:1 criterion:4 pure:2 answer:1 optimal:1 parameter:1 sin:2 brassard:1 teleport:2 db:4 after:2 epsrc:1 modest:1 plane:1 realized:1 light:1 yielding:3 ghz:2 provide:1 claire:14 so:1 allow:1 representation:2 order:1 superscript:1 operations:2 superimposing:2 help:1 indeed:1 choose:1 produced:2 course:2 through:3 fidelity:25 still:3 before:1 perfect:5 group:1 chosen:4 exhibits:2 writing:1 better:3 absence:1 compelling:1 systems:3 wales:1 might:1 eugene:1 non:3 fig:3 walls:1 now:7 easily:2 2r:9 always:1 university:1 2x:1 identified:1 displacements:3 2e:6 mode:48 2n:3 polzik:1 mean:1 schemes:1 doing:1 einstein:1 gaussian:1 related:1 extended:1 connect:1 combining:1 quantum:23 laboratory:1 operation:2 eq:5 special:1 shown:2 network:2 quantify:1 rev:9 projected:1 denotes:1 participants:1 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