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quant-ph9701019.txt |@word neighbors:1 iǫ2:1 logarithms:1 sci:2 consider:5 represent:2 desirable:2 results:5 leads:2 roy:2 generalize:1 higher:2 computation:16 edu:2 consists:1 remarkably:1 preferable:1 meaningfully:1 issues:2 gr:1 extra:1 whose:2 preserves:1 boghosian:3 calculate:1 disposal:1 tt:3 april:1 contained:1 factoring:3 containing:1 environment:1 does:2 weyl:4 unclear:1 under:7 discovering:1 include:3 worth:3 resources:1 alternating:1 amplitudes:2 hibbs:1 advantage:2 returning:1 far:4 implicitly:1 rise:1 differently:1 wave:2 stat:1 electron:1 wishes:1 every:3 cellular:6 ninomiya:2 matrices:1 condition:1 ibm:1 four:2 nonrenormalizable:1 presented:5 positions:4 notes:1 colors:1 large:6 solved:2 vector:2 wolfram:1 science:5 small:5 eigenvalues:3 noted:1 inserting:1 force:1 l2d:2 deutsch:2 dealing:1 direct:1 sign:2 go:2 second:4 street:1 enhancement:2 invariant:2 dynamics:11 implemented:6 odd:3 seth:1 canonical:3 even:6 index:2 predictions:1 appear:1 advantageous:1 d2:4 section:8 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quant-ph9701020.txt |@word partial:1 consider:3 caused:2 results:3 existing:2 cooperative:13 edu:1 follow:1 contributions:3 devoted:1 whose:2 knill:1 subjected:1 show:2 tr:3 factoring:1 environment:12 monotonically:1 marks:2 advantage:1 very:6 exact:1 condition:2 paz:2 level:1 guo:2 small:2 eigenvalues:2 commented:1 lloyd:1 computation:6 deutsch:1 direct:1 approximation:1 rate:6 cost:3 eigenspace:2 further:3 dynamics:1 implemented:1 even:1 what:4 nonlinear:2 stands:1 sum:1 expressed:3 decoding:2 above:2 new:2 method:1 contrast:1 satisfy:1 degree:1 respectively:1 equals:1 here:3 atoms:1 desired:1 china:3 coupling:10 obtained:2 ψ2l:5 study:1 larger:3 suggests:2 amount:1 usually:1 makes:1 sci:1 transformations:2 extra:1 unitary:3 undergone:1 superpositions:1 jozsa:1 h1i:2 h1j:2 h1l:3 therefore:1 ψl:1 memory:6 encode:4 goldenberg:1 type:3 more:4 sort:1 bennett:1 becomes:1 operators:2 under:2 correspondingly:1 particular:2 foundations:1 cases:1 involve:1 science:4 equation:1 reviews:1 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quant-ph9701021.txt |@word concept:5 ceases:1 issued:1 magnetic:12 results:2 leads:1 consists:2 follow:1 expressions:2 centers:1 excludes:1 const:1 calculate:3 passage:2 charge:10 monotonically:1 caused:2 include:2 worth:2 very:3 wave:3 electron:38 every:1 resonant:1 exact:1 superlight:2 try:1 discrete:1 coincidences:5 small:2 challenge:1 prevent:1 work:1 compensated:1 direct:2 second:1 premature:1 further:1 even:3 ˆz:2 experiment:4 above:1 new:13 method:2 exchange:1 eksp:1 component:10 here:2 separation:1 κu:1 along:9 strong:2 equations:5 change:3 violate:1 obtained:3 convert:1 involved:1 study:1 changed:2 allows:2 completely:1 commonly:2 periodic:2 permit:1 usually:1 resonance:1 changes:4 pearle:1 diameter:1 projection:2 plenum:1 decrease:2 apply:1 total:2 unit:2 use:1 takes:2 would:2 process:1 noting:1 call:1 averaging:1 type:1 more:6 separated:1 zh:1 formally:2 under:1 curvature:2 particular:2 known:3 cases:1 hold:2 must:8 me:8 account:2 sphere:1 equation:5 averaged:2 oscillator:1 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quant-ph9701022.txt |@word represent:1 partial:1 consider:4 rev:3 magnetic:8 results:3 scalar:3 commute:1 expressions:1 contributions:4 scr:1 regularize:1 const:1 under:1 divergent:7 seemingly:1 splitting:1 refractive:2 bounding:1 affect:1 difference:1 exact:1 condition:1 treating:1 did:1 positions:1 eigenmodes:1 detected:1 small:2 deutsch:4 sin4:1 sin2:5 sign:2 zero:4 correlator:1 linear:1 index:2 what:3 sub:1 fine:1 sum:8 near:6 above:1 new:1 net:1 contributes:1 method:1 paradoxical:2 satisfy:1 full:1 leh:1 equals:2 here:2 behaviour:1 cos2:1 separation:1 obtained:4 institute:1 changed:1 ravndal:8 ignoring:1 resulting:2 usually:1 cancellation:1 via:2 scaled:1 total:10 use:1 would:1 positive:1 give:1 m4:1 nucl:1 approach:1 therefore:3 bender:2 more:1 flat:1 becomes:1 potentially:1 dirichlet:2 normalized:1 hold:1 must:1 high:1 integrating:1 equation:1 work:1 values:2 following:1 example:3 plate:1 calculation:1 sphere:1 effectively:1 candelas:4 calculated:2 axis:1 regularization:8 oslo:2 holds:1 significance:1 instead:2 sin:3 map:1 emulate:1 after:2 vaccum:1 plane:5 coming:1 wave:1 parallel:3 realized:1 effective:1 light:2 element:1 so:3 order:2 talk:1 operations:1 furnished:1 over:1 expects:1 kong:3 including:1 still:1 its:1 before:1 energies:1 vicinity:1 absence:1 degrees:1 mail:2 norway:1 transparently:1 non:4 walls:2 subtraction:1 they:2 half:3 now:4 transparent:1 easily:2 term:3 finite:6 spacetimes:1 university:1 barton:3 l7:1 l4:1 mode:2 each:1 2l:3 found:3 mean:1 homogeneous:1 schemes:1 24l:2 energy:43 frequency:1 expect:1 quantum:3 our:1 out:2 shown:1 space:2 since:1 lagrangian:2 denotes:1 particles:1 get:1 integrated:5 theory:2 free:4 standard:2 approaches:2 e0:4 e2:6 interaction:6 could:1 similarly:1 length:1 first:5 symmetry:1 zπ:1 clear:1 given:5 perturbation:1 their:1 leading:3 πn:1 system:2 2ωn:3 imposing:1 too:1 realization:1 utken:3 recovered:1 gives:4 a31:1 shell:6 exactly:2 part:9 somewhat:1 b237:1 b236:1 hays:2 second:3 correlators:2 preparation:1 lowest:1 fluctuation:1 correction:2 seen:1 any:3 gravity:1 metallic:5 instance:2 8m2:1 heisenberg:6 akad:1 electric:7 opposite:2 who:1 simplify:1 nothing:1 measured:1 don:1 consequences:1 kk:1 average:1 electrons:1 principle:1 physics:2 ned:1 quantity:1 phenomenon:1 show:1 discovered:1 spaces:1 finn:2 keywords:1 trivial:1 d3:1 outside:1 should:1 jan:1 only:3 integrate:2 do:2 distance:3 dependent:4 between:7 expectation:2 dz:1 fields:3 arxiv:1 approaching:1 ignored:1 physically:1 see:3 result:9 heavy:1 interacting:2 definite:1 diverge:1 boundaries:4 written:1 closed:1 simplest:1 invariant:1 boundary:6 conditions:5 terms:5 however:2 spectroscopic:1 analyzed:1 configuration:1 come:1 both:2 cos:2 cot:2 2θn:1 region:1 equal:2 propagation:1 casimir:18 contribution:4 finds:1 point:2 simple:1 dimensional:1 regulated:3 cancel:4 zeta:2 considering:1 locally:1 due:4 been:3 hinds:1 describes:1 ph:1 ann:1 direction:1 arises:1 corresponding:2 quantities:1 essentially:1 eigenfrequencies:1 present:1 case:4 survey:1 pacs:1 value:1 will:11 while:3 situation:1 endpoints:3 opt:1 thus:8 surprisingly:1 surface:3 obeying:1 confining:2 d14:1 different:1 generic:1 divergences:2 same:2 quant:1 plates:8 dimensionless:1 gets:1 φn:1 independent:1 investigated:1 numerical:1 effect:3 hand:3 scharnhorst:3 levels:1 moving:1 infinite:7 recent:1 obviously:2 concrete:1 position:8 left:1 spherical:3 b192:1 just:3 mol:1 obtain:1 yet:1 previous:1 adv:1 density:29 photons:3 lett:2 wet:1 transformation:1 euler:7 real:1 around:1 fys:2 vacuum:22 confined:3 using:2 continue:1 either:1 completely:1 because:3 methods:2 some:2 regularized:6 b2:6 provided:1 dimensions:1 cavity:1 electromagnetic:1 normal:1 integration:1 does:1 assuming:1 proc:1 l3:1 although:1 about:1 most:2 freedom:1 dependence:3 cutoff:1 presence:1 maxwell:3 within:2 integral:1 lies:1 references:1 qed:1 there:4 much:1 low:1 way:2 analyze:1 was:2 function:3 form:1 but:3 volume:1 atom:3 line:1 made:1 minkowski:1 inside:2 up:1 us:2 placed:1 limit:2 ωn:10 ue:7 fluctuations:10 problem:2 similar:2 called:1 ub:5 diverges:7 constant:8 abstract:1 contribute:2 meaningless:1 uio:2 general:6 dθ:2 physical:2 again:6 extending:1 no:4 when:8 vanishes:2 virtual:1 field:16 other:5 spatial:1 you:1 massless:3 variation:1 bounded:1 structure:2 longer:1 d20:1 interval:1 4l:2 mass:2 affects:1 requires:1
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quant-ph9701023.txt |@word neighbors:1 represent:1 concept:3 consider:3 interference:7 forbidden:1 rod:2 results:5 leads:1 roy:1 scalar:3 go:1 gm:2 instantaneous:2 localized:2 soc:1 compact:1 particles:51 keith:1 statistics:1 james:4 kγ:1 finally:1 stable:1 ontological:1 presumed:1 magnetic:1 p2:1 amplitudes:5 string:11 far:5 frequencies:1 springer:1 wave:77 bjorken:2 electron:14 rotational:1 difference:2 condition:4 dim:2 riemann:3 ρc2:1 positions:1 solution:2 d2:1 discrete:1 convenience:1 vector:10 small:5 equation:3 upper:1 force:1 zi:6 oscillation:7 dealing:1 consistent:2 sin2:1 direct:1 pulse:2 sign:2 consists:3 zero:8 invariant:6 copenhagen:1 estimated:2 goes:3 even:8 what:3 morse:1 sun:2 section:9 interactions:6 expressed:2 uniform:2 consistently:1 19th:1 experiment:5 above:4 boundary:1 new:1 increasing:1 method:1 edited:1 simultaneously:2 exchange:1 respectively:3 never:1 component:3 equals:2 here:6 les:2 separation:1 berkeley:1 represented:1 ratio:1 drell:2 appears:2 change:5 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quant-ph9701026.txt |@word represent:1 partial:1 consider:1 four:3 rˆ:29 whose:1 calculate:6 fellowship:1 eigenbasis:1 tr:1 finally:7 pˆr:2 under:1 pˆx:1 coor:1 dilatons:7 straightforward:1 choice:1 sons:1 figs:1 difference:1 annihilated:1 altering:1 knight:1 integrated:1 leave:1 discrete:1 differential:1 section:2 eigenvalues:1 optics:2 noted:1 inserting:1 hillery:1 cosh:1 linear:1 even:1 appear:1 specification:1 axes:1 reminiscent:1 above:2 capital:1 new:5 contrast:1 satisfy:1 exponentials:1 degree:1 lange:1 here:1 understanding:1 ranges:1 cylindrical:1 groups:1 others:1 logarithmic:1 obtained:1 ultra:1 rdr:5 twamley:1 simultaneous:1 products:1 action:4 makes:1 plotted:1 buˇzek:3 ix:1 marginal:1 condensates:1 derivatives:1 use:1 quasi:3 proceed:2 working:2 commun:1 positive:1 negative:2 explicitly:2 nential:1 more:3 chapter:1 becomes:2 operators:9 distribution:4 labelled:4 particular:2 must:7 e2µ:1 ρd:1 integrating:1 equation:2 work:2 oscillator:7 ρl:1 fock:4 following:1 ions:1 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quant-ph9701027.txt |@word consider:8 magnetic:1 saves:1 four:1 scalar:3 computation:11 edu:1 go:2 expressions:3 reasoning:1 aua:1 aug:1 petersburg:2 include:1 presentation:2 norm:5 division:1 very:1 differently:1 wave:7 electron:4 lecture:1 difference:2 matrices:12 riemann:1 presented:1 notes:1 discrete:2 vector:12 small:1 c01:1 dmitri:1 grateful:1 deutsch:2 direct:1 sign:1 ators:1 street:1 further:1 machines:1 linear:3 index:1 nonlinear:2 richard:2 sum:1 pobox:1 current:1 ˆa:2 poles:1 new:2 boost:1 method:1 3d:2 satisfy:1 full:2 respectively:1 component:2 here:3 protection:1 consideration:4 equations:5 change:5 hamiltonian:1 broken:1 vectors:8 schumacher:1 hospitality:1 changes:1 foundations:1 projection:1 logical:1 apply:2 neutrino:1 tools:2 unit:1 use:2 positive:1 hilbert:2 few:3 ψi:1 scope:1 theoretical:2 minor:1 more:6 introducing:1 operators:9 corrected:1 mira:1 tested:1 projective:1 cases:2 resemblance:1 isomorphism:2 ma:1 quantized:1 science:2 equation:1 work:1 det:4 following:1 vlasov:4 example:3 numbers:3 computers:4 figure:5 relativistic:18 bennett:1 states:7 sphere:5 lorentz:12 stereographic:1 sharp:1 spb:1 information:2 rather:1 write:1 instead:3 map:1 express:1 description:2 algebra:1 may:1 turing:2 after:1 plane:1 cambridge:1 representations:2 data:2 computations:1 light:3 author:1 correspond:3 su:7 st:2 so:6 fundamental:1 sl:5 representation:8 paper:2 london:2 mentioned:1 style:1 group:17 temporal:2 fig:6 main:2 correspondence:3 wolfgang:1 functional:3 effects:1 they:1 gate:7 own:1 nov:1 now:1 yu:2 articles:1 2v:1 electro:1 alex:1 always:2 university:2 level:1 2d:2 2a:1 each:2 2n:1 spinor:3 weyl:2 society:2 extended:1 poincare:1 quantum:37 eq:26 special:1 really:1 ru:1 shown:1 matrix:8 space:7 particles:7 re:2 race:1 print:1 formula:1 xσx:1 correct:1 benjamin:1 wiley:1 theory:19 quite:1 c00:1 approaches:1 complicated:1 usual:7 interaction:1 benioff:1 transition:1 programming:1 david:2 length:1 produce:2 massive:6 corrections:1 today:1 qn:1 first:3 coding:1 number:3 directly:1 impossible:1 size:1 rewritten:1 introduction:2 system:13 relations:5 their:1 john:1 tommaso:1 part:1 authors:1 than:2 coefficients:1 wide:1 kind:1 penrose:1 annihilation:3 russia:2 false:2 boston:2 modern:1 null:4 demonstration:1 any:5 ray:2 constructions:1 built:1 convenient:1 internal:2 build:1 analogy:1 poster:1 fcr:1 trace:1 opposite:1 algebraic:1 jul:1 formulae:2 device:1 pages:1 especially:1 considered:5 feynman:4 proceedings:2 electrons:3 principle:2 mechanical:2 charged:3 physics:13 show:2 charles:1 contemporary:1 registers:1 relation:5 keywords:1 networks:3 occupation:1 q2:2 based:1 simulating:1 title:1 merger:1 aψ:2 histories:1 universal:1 should:5 jan:1 only:4 local:1 columns:1 postscript:1 do:2 notation:3 shirkov:1 between:11 ϕr:5 ϕl:5 cannot:1 report:1 alexander:3 typos:1 processes:2 conditions:1 arxiv:1 roger:1 fixed:1 view:2 set:1 see:2 computer:3 sec:1 result:2 qti:2 interacting:1 review:1 definite:1 irh:2 state:9 simplest:1 invariant:3 approach:2 positron:1 qubits:6 harvard:1 uψ:2 bose:3 eipx:1 both:2 essentially:1 bogoliubov:1 qft:6 many:3 sty:1 etc:3 σy:3 σx:2 figures:1 qubit:16 expression:2 otherwise:1 ck:3 fields:3 nonrelativistic:4 reasons:1 royal:2 corresponds:5 dimensional:2 church:1 respect:1 cp:5 pp:1 described:12 transformations:5 due:10 workshop:1 electrodynamics:1 ph:2 algebras:1 ak:3 systems:3 determinant:3 σi:3 modelling:1 angles:1 c1:37 c0:33 spin:6 nicolai:1 those:1 case:1 pacs:1 behavior:1 spbu:1 property:1 iy:3 unitary:11 vol:1 vi:1 secondary:2 im:2 cone:2 quantization:3 ava:4 different:2 σz:2 same:2 unity:3 complex:10 quant:2 split:1 pauli:1 finite:3 used:7 hand:1 v3:1 v4:1 purpose:1 necessity:1 reflection:1 programs:1 components:1 coordinate:11 model:6 subgroup:1 gates:4 rindler:1 half:1 using:6 paul:1 speed:1 rotation:7 integer:2 application:1 photons:4 point:3 seems:1 passive:1 simple:4 valid:1 c11:1 c10:1 transformation:13 momentum:1 possible:2 press:1 dirac:2 bit:5 formal:1 necessary:4 like:7 particle:13 steps:2 essential:1 mathematical:1 because:2 often:1 creation:3 phenomena:1 erase:1 statistic:2 ipx:1 describing:1 2c0:2 2c1:2 comments:1 does:1 commutators:1 proc:1 limitations:1 ba:1 journal:2 bu:1 step:1 properties:6 about:1 discussed:3 compatible:1 act:1 backus:1 organizers:1 22n:1 computational:1 rotations:4 isomorphic:1 twostate:1 references:1 operator:4 qed:2 spinors:4 interacted:1 support:1 there:7 describes:1 way:1 was:1 function:2 form:1 some:14 δkk:2 but:6 neutral:1 construction:1 true:2 auxiliary:1 october:1 up:1 us:4 fermi:3 diagrams:1 similar:3 called:1 mails:1 ab:1 abstract:1 describe:2 denote:1 multiparticle:1 moves:1 physical:2 functions:3 no:5 field:6 definitions:1 other:5 spatial:5 department:1 massless:4 conclusion:1 briefly:2 kinds:1 superposition:1 vocabulary:1 models:2 commutator:1 meaning:1 bounded:2 rqc:1 included:2 anticommutator:1 time:1 4d:4
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quant-ph9701028.txt |@word secondly:1 partial:2 illustrates:2 equalities:1 desirable:2 focus:1 four:8 ρt2:3 follow:1 research:1 whose:1 inverse:1 const:2 alamos:1 tr:1 nonlocal:4 finally:1 under:4 indicating:1 amplitudes:9 presently:1 advantage:1 orthogonal:1 very:1 bratislava:1 print:1 condition:4 quantitatively:1 level:1 tra:1 knight:2 trb:1 t2:9 science:1 small:1 eigenvalues:3 optics:1 smaller:1 zi:1 zk:2 hillery:2 second:1 design:2 further:4 implemented:1 even:3 employ:1 what:3 nonlinear:1 sub:1 section:1 expressed:3 current:1 new:1 satisfy:1 simultaneously:2 ibid:1 ρab:1 respectively:1 ρai:1 here:1 plenio:1 operating:2 address:1 represented:1 consideration:2 equations:2 obtained:2 great:1 institute:1 vectors:4 amount:4 procedure:5 schumacher:3 action:2 implement:1 devices:1 uniquely:1 buˇzek:2 via:3 spatially:1 fµ:2 imme:1 highly:1 specified:2 put:2 apply:1 should:4 manipulate:1 use:3 proceed:1 would:7 positive:3 negative:4 e0:1 classically:3 wj:1 going:1 therefore:1 criteria:1 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quant-ph9701029.txt |@word secondly:3 consider:6 springer:2 priori:10 young:1 rev:22 lack:1 commun:1 results:8 quadrature:1 entropy:19 during:1 parameterization:1 consists:2 expressions:1 manipulations:1 toledo:1 foug:2 devoted:1 inverse:1 tracing:2 arthurs:1 alamos:1 tr:9 orthonormalized:1 containing:1 finally:2 program:1 restriction:1 those:2 th:1 under:16 kapur:1 stochastic:1 indicating:1 case:16 straightforward:3 orthogonal:2 very:3 dynamic:1 implicitly:1 conditions:5 wave:2 print:1 electron:2 every:1 orientations:1 traced:2 husimi:2 difference:1 exact:3 condition:11 dimensionality:1 jurˇco:1 smithey:4 mc:1 level:21 opt:9 turns:1 ford:1 large:4 discrete:9 convenience:1 vector:2 phase:3 math:3 affect:1 small:1 eigenvalues:3 trr:1 optics:2 equation:3 proof:1 gerlach:3 α2i:1 consistent:1 maximization:2 direct:1 second:5 design:1 dordrecht:1 estimated:6 odd:1 port:1 canonical:9 even:3 index:1 what:6 ˆs:3 appear:1 apparatus:3 ˆx:20 ˆy:15 section:8 mathematical:1 analogously:1 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quant-ph9701030.txt |@word concept:1 rev:1 results:1 eds:1 privman:1 follow:1 technique:1 tr:1 factoring:1 presents:1 finally:1 under:1 must:1 norm:1 applied:3 endowing:1 straightforward:3 rise:1 wave:4 worst:1 turns:1 solution:1 adjust:1 small:2 eigenvalues:3 second:1 further:1 index:1 errors:2 sum:1 above:2 method:1 satisfy:1 full:1 degree:2 never:1 here:3 desired:1 iσy:1 objects:1 others:1 extreme:1 remark:1 leaves:1 allows:2 later:1 permutation:1 changes:1 mutual:1 useful:1 bounds:1 requiring:1 highly:1 viz:1 apply:1 univ:1 usa:1 prove:1 give:1 negative:1 next:2 call:1 therefore:1 criteria:2 more:4 israel:1 permutations:2 trait:1 operators:1 apparent:1 odinger:2 normalized:4 known:2 circumstances:1 keeping:1 science:2 work:1 obvious:1 γe:2 following:1 example:1 stated:1 december:1 sense:1 pieces:2 states:5 minimum:1 numbers:1 want:1 arise:1 sharp:1 occur:1 respective:1 united:1 advantage:1 provide:3 s2:5 discussion:1 holds:1 damage:2 dydz:1 write:1 criterion:4 optimal:1 product:1 intended:1 may:3 max:1 after:1 mapping:2 factored:1 produce:2 inst:1 cambridge:2 choice:1 unentangled:1 clarkson:1 effective:2 revzen:1 rather:2 so:2 enter:1 definitions:1 horne:1 essence:1 years:1 episodes:1 paper:1 its:5 before:1 thank:1 interesting:1 coordinates:1 actually:1 distinguishing:1 degrees:4 systems:5 defining:1 maximal:4 non:2 mention:1 walls:2 they:2 now:1 transparent:1 easily:2 always:1 university:1 arrows:1 trap:1 each:1 ed:1 reduce:1 obtains:1 measure:9 quantum:10 our:6 eq:2 out:1 shown:1 matrix:7 space:3 since:1 interference:3 ajk:1 dxdy:1 cause:1 occurs:1 foundation:1 linear:1 written:1 pub:1 effect:1 inevitable:1 definition:5 interaction:2 computers:2 iterative:1 place:1 hence:1 retain:1 generalizations:1 first:1 variables:1 number:1 done:1 another:1 given:2 πj:2 eqs:1 achieved:1 system:3 their:1 variational:1 gives:1 continuous:1 environmental:1 part:1 anandan:1 than:2 cyclic:1 zero:1 amplitude:1 minus:1 function:6 vector:2 ann:1 mind:1 defect:1 generalization:1 say:1 conjugate:1 intertwining:1 seen:1 any:4 min:3 latter:1 note:2 forces:1 measures:2 most:1 decohered:1 representation:1 phase:1 acknowledgements:1 measured:1 eigenfunctions:1 especially:1 considered:2 clear:2 sometimes:1 error:4 exp:1 camb:1 physics:1 fact:3 precise:2 shor:1 particularly:1 show:2 supported:1 minimizing:3 chuang:1 find:1 knowledge:1 aφ:1 situations:1 state:5 should:2 jan:1 only:8 explicitly:1 developed:2 mechanics:1 subspaces:1 notation:1 zurek:1 cannot:1 despite:1 podolsky:1 arxiv:1 notational:1 national:1 j3:2 depends:2 computer:4 result:1 discussions:1 optimum:1 best:1 techniques:1 said:1 inequalities:1 shimony:1 enough:1 between:2 available:1 wd:1 however:1 extent:1 article:1 configuration:1 come:1 both:1 essentially:1 many:1 taking:1 equal:1 etc:1 bristol:1 distinction:1 mann:1 among:2 characterization:1 simple:2 assertions:1 maximize:1 moreover:2 complication:1 described:1 basis:3 three:1 ph:1 arises:1 corresponding:1 coherence:2 zeilinger:1 representative:1 maximally:2 spin:1 present:1 quotation:1 case:1 pacs:1 will:5 while:1 behavior:1 aij:1 laflamme:1 vj:1 thus:1 them:2 need:1 ij:1 grant:1 make:2 same:3 clearly:1 complex:2 quant:1 largest:1 several:1 independent:2 temporary:1 see:4 singapore:1 mozyrsky:1 hand:1 ion:1 phy:1 entanglement:16 destruction:3 weakly:1 schr:2 maximizing:1 minimize:2 epr:1 analysis:1 obviously:1 without:1 solve:1 coordinate:1 arising:1 know:2 λv:1 λu:1 rosen:1 press:1 world:1 preprint:1 ny:1 bell:1 except:1 lett:2 easy:1 real:7 putative:1 eigenvalue:6 possible:2 test:1 entangled:11 confined:2 using:2 necessary:1 helpful:1 particle:1 follows:1 interestingly:1 continue:1 arbitrary:3 become:1 mathematical:2 indications:1 because:2 successfully:1 some:2 proofs:1 provides:1 proc:1 object:1 scientific:1 minimization:1 combines:1 although:2 hilbert:3 bz:1 schulman:4 central:1 would:1 freedom:4 introduced:1 slightly:3 soc:2 own:1 dilemma:1 significant:1 garg:1 into:1 within:2 due:1 references:2 einstein:1 operator:4 interacted:1 there:3 was:3 φjk:1 form:3 but:3 construction:1 true:1 characteristic:1 maximum:1 below:1 ui:1 verification:1 problem:3 aa:1 phil:1 constant:1 corrective:1 defined:2 abstract:1 measurement:1 influence:1 general:1 av:2 formalism:1 physical:1 again:2 functions:6 paradox:1 no:3 when:4 application:2 other:1 potsdam:1 department:1 you:2 separate:2 meaning:1 important:2 recent:1 longer:1 original:2 phonon:1 time:2 decoherence:6 having:3 once:1
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quant-ph9701031.txt |@word consider:1 maximum:2 rev:1 magnetic:1 varying:1 desirable:1 results:2 leads:2 gn:1 increase:1 depend:1 collisions:2 γu:9 environment:2 finally:1 kσ:6 applied:2 worse:1 straightforward:1 far:1 induce:1 wave:43 2γx:2 affect:1 emphasized:2 rebounds:1 condition:4 treating:1 entire:5 presented:1 did:1 issue:1 large:11 settle:1 science:2 small:16 chuang:1 noted:1 mozyrsky:2 prevent:1 says:1 cosh:2 second:1 further:1 even:3 will:10 what:2 errors:1 apparatus:1 expressed:1 reminiscent:1 experiment:1 above:5 boundary:1 new:1 method:2 satisfy:1 impact:1 outgoing:3 degree:6 relates:2 respectively:1 applies:1 lem:1 here:7 desired:1 explore:1 objects:3 possibility:1 sinh:3 path:2 strong:1 change:1 incoming:1 study:4 larger:1 allows:2 experience:1 example:2 pinning:2 suggests:2 amount:1 resulting:1 pick:1 changes:1 involves:1 appropriately:1 situations:1 maximizing:1 treatment:1 2δk:1 brought:1 decrease:1 frame:1 establish:1 2δx:1 use:3 usa:1 recalling:1 positive:1 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quant-ph9702004.txt |@word gr:2 similarity:1 results:4 ala:3 roy:1 go:1 ros:2 consider:1 calculate:1 young:1 th:5 under:1 anharmonic:2 divergent:3 advantage:1 choice:1 mixing:4 condition:1 solution:1 large:2 solved:1 zh:2 consistent:1 d7:1 rigorous:1 further:2 even:2 sun:1 sum:2 expressed:1 en:18 new:1 method:15 satisfy:1 justification:2 fiz:1 eksp:1 here:2 ranges:1 met:1 clns:1 illustration:1 logarithmic:2 obtained:3 shift:1 studies:1 appropriately:2 via:1 would:1 chi:1 next:1 calculation:2 ψi:1 ψn:17 chu:2 bender:2 taken:1 becomes:1 known:3 must:1 account:1 science:1 equation:8 work:1 oscillator:2 remain:1 l129:1 example:1 process:2 accept:1 states:2 sense:4 regularization:7 end:1 dalgarno:2 recovers:2 trieste:1 instead:2 ordinary:4 parameter:4 may:1 after:2 dx2:1 wave:4 fm:1 constants:1 ambiguous:1 advocated:1 effective:1 sk:3 so:2 sc:10 order:11 displayed:1 through:2 existence:1 its:1 energies:7 interesting:1 solving:1 defining:1 into:2 non:3 propose:1 introduce:1 bound:1 newman:1 half:1 now:1 nor:1 easily:2 february:1 name:1 always:1 university:2 establishing:1 mean:1 differential:3 ei:1 energy:2 expect:1 combining:1 quantum:2 laboratory:1 eq:20 out:6 since:3 rev:2 ref:1 correct:1 foundation:1 turning:1 theory:2 standard:2 approaches:1 term:1 e0:1 care:1 nodal:1 hence:3 teor:1 south:1 first:3 utilized:1 calculational:1 aharonov:1 given:3 perturbation:12 rewritten:1 eqs:1 least:1 needed:2 convention:1 final:1 gives:3 zeroth:2 part:1 x0:21 chong:1 x4:2 tion:1 perturbative:1 sees:1 correction:1 say:1 seen:1 recover:1 efficient:1 lim:1 note:2 mix:1 neither:1 beirut:1 unperturbed:1 unless:1 though:2 denominator:1 letter:1 treats:1 adopt:1 typeset:1 traditional:3 regards:1 usual:1 physics:1 12a:1 12b:2 12c:1 show:3 lewis:2 supported:1 substituting:1 d2:1 ground:3 ratio:6 jan:1 only:4 explicitly:1 integrable:6 carolina:1 dz:4 dy:9 justified:1 arxiv:1 acknowledgments:1 london:1 qm:5 national:1 see:1 result:7 nuclear:1 diverge:2 state:7 correctly:2 between:2 boundary:4 conditions:4 recently:2 wu:2 multiplies:1 jetp:1 both:2 ill:1 chosen:1 comes:2 arbitrarily:2 point:3 polynomial:1 been:1 ph:1 abstract:1 firm:1 quantities:4 assigning:1 present:1 value:3 eigenstate:1 while:1 au:3 endpoints:1 taking:1 procedure:4 a24:1 a29:2 examined:1 italy:1 make:2 same:1 quant:1 finite:7 independent:3 used:1 columbia:1 numerical:4 upon:3 v0:1 v1:4 purpose:2 normalization:1 lower:1 well:2 contact:1 parametric:2 dimension:1 left:1 comment:3 proposed:4 being:1 obtain:1 assigned:1 ithaca:1 cornell:1 priori:1 lett:1 theorem:1 excited:2 real:1 possible:2 using:6 necessary:1 like:1 follows:1 sissa:2 separately:1 mathematical:1 because:2 regularized:3 provided:1 obtaining:1 does:1 proc:1 journal:1 wavefunctions:1 agreement:1 expansion:1 revtex:1 carried:1 extension:1 numerator:1 dependence:1 practical:2 chow:2 soc:1 previously:1 h0:2 numerically:1 functional:1 appropriate:1 square:6 references:1 sov:1 assumed:1 strict:2 way:1 function:4 form:6 keung:1 but:4 justify:2 convergence:1 line:1 made:1 infinity:1 up:1 limit:4 similar:2 jσ:4 mechanics:2 defined:2 universal:1 chan:1 proven:1 general:1 examine:1 exist:1 our:2 physical:1 functions:6 vanishes:2 guardiola:2 ny:1 points:2 department:1 briefly:1 calculating:2 astronomy:1 ghost:4 turbiner:1 together:1 augmented:1 once:1
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quant-ph9702005.txt |@word sector:3 concept:1 consider:2 similarity:2 squared:1 magnetic:7 splitting:1 leads:1 latter:1 grateful:1 go:3 contributions:3 depend:1 disposal:1 send:1 tn:5 charge:1 critical:5 tk:6 tf:5 sent:1 digit:1 φns:3 hibbs:4 very:2 observables:1 end:1 choice:1 bjorken:1 electron:11 every:1 fall:1 experimentally:4 difference:5 fractal:8 hamiltonian:1 positions:1 t2:2 tubes:9 t1:5 large:3 vector:8 small:1 ree:9 noted:1 smaller:2 force:1 winds:1 zero:5 pass:1 prof:2 index:1 errors:1 plays:1 section:2 expressed:2 experiment:32 goes:3 fractional:1 new:3 increasing:1 consisting:1 full:2 deduces:1 never:1 here:2 experimentalist:3 path:25 along:1 change:3 obtained:3 compute:1 study:1 stretching:1 allows:6 action:5 suitable:1 changes:1 involves:1 york:2 via:10 projection:1 scales:1 marked:1 screens:3 addressed:1 decrease:1 apply:1 resolutions:1 total:2 propagators:1 unit:1 takes:3 give:1 only:3 next:1 zig:2 chapt:1 call:2 hadron:1 taken:1 yardstick:5 schulman:2 ψf:5 becomes:3 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quant-ph9702006.txt |@word sergei:1 dewitt:3 partial:1 consider:1 rev:3 hats:1 results:1 leads:1 scalar:2 commute:1 generalize:1 controversial:1 2r2:3 whose:1 certainly:2 depend:2 pˆi:3 pˆk:3 pˆj:2 removal:1 pˆr:11 manifolds:1 under:2 forbidden:2 fax:1 straightforward:1 orthogonal:1 rise:1 distort:1 choice:3 putting:1 affect:1 emphasized:1 matrices:1 condition:6 school:1 solves:1 hamiltonian:13 applicable:2 leave:1 solved:2 pˆ2:3 eigenvalues:1 degeneracy:1 l2a:1 consistent:2 arnimallee:1 second:18 dynamics:4 canonical:14 even:1 index:1 kinetic:1 brackets:8 sum:1 batalin:1 experiment:1 above:4 lifshitz:1 ˆi:1 ˆj:5 ˆk:1 ever:1 method:3 satisfy:1 altogether:1 degree:2 modify:3 here:2 others:1 represented:1 path:4 extrema:1 equations:9 change:1 every:1 antisymmetric:1 suitably:1 larger:1 allows:3 contradiction:1 resulting:1 poisson:7 published:1 action:1 successors:1 relation:3 jackiw:1 uniquely:2 via:6 pla:1 classification:2 extra:7 replace:1 sliced:1 contradictions:1 total:1 univ:1 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quant-ph9702009.txt |@word partial:3 consider:2 grateful:1 revealed:1 increase:2 amplification:2 alamos:4 concerned:1 young:1 send:3 th:1 sent:1 versus:1 shielding:1 advantage:1 very:1 rise:2 choice:1 selleri:1 securely:1 immediately:1 presented:1 conceive:1 eve:38 leave:1 noted:1 prevent:1 version:1 deutsch:1 miller:1 prediction:1 second:3 incidentally:1 even:3 what:1 errors:3 access:5 experiment:2 above:1 new:3 method:20 full:2 chose:2 newyork:1 respectively:3 intercepts:1 along:8 observing:1 obtained:3 sender:1 institute:1 popescu:1 vectors:1 exiting:1 implement:1 composed:1 via:1 useful:1 secure:5 plenum:1 outcomes:1 p46:1 use:6 probabilities:2 positive:1 next:4 discrepancies:1 few:1 therefore:1 encode:1 theoretical:1 more:2 introducing:1 knows:6 organized:1 company:1 particular:1 known:2 must:4 account:2 science:1 work:1 intercepted:1 instantaneously:1 remain:1 ρu:2 learn:2 following:4 strategies:1 arrive:1 example:4 compare:1 weaker:1 give:3 bennett:4 share:1 purposes:1 states:7 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quant-ph9702010.txt |@word represent:1 req:2 provided:1 maslov:4 show:5 moments:1 developed:1 equalities:2 tcs:6 nφ:1 paper:1 relation:8 solutions:5 expressions:1 eigenstates:1 q1:11 naturwissenschaften:1 imb:11 secondly:3 should:1 imq:1 only:4 hxp:2 systems:4 easy:1 theorem:1 momentum:3 real:1 p2:1 iωt:2 similar:1 account:2 number:1 methods:1 they:2 polytechnic:1 using:2 dt:1 now:1 exact:3 condition:1 easily:1 hxx:12 necessary:1 particle:1 hamiltonian:9 fields:1 university:1 arxiv:1 differentiating:1 solution:6 t0:1 ternov:2 investigate:3 pˆ2:1 reasonable:1 arbitrary:2 analytical:1 2m:2 optics:1 atomic:1 mathematical:1 because:1 constructing:1 classical:5 sequence:1 variations:2 some:1 direct:1 ωt:6 q21:3 depends:1 us:2 quantum:5 further:2 satisfied:3 special:2 even:2 aim:1 nuclear:1 since:3 find:1 particles:2 state:1 belov:3 izv:1 example:2 reb:4 according:3 conditions:4 method:2 math:1 satisfy:3 condensed:1 recently:1 integrals:1 minimization:6 mω:4 equivalent:2 obtain:6 mir:1 quite:1 vuzov:1 iωm:2 q2:6 dx:1 described:1 equations:5 simpler:1 obtained:3 cos:3 tomsk:2 conviction:1 many:1 taking:2 uncertainty:9 equal:1 called:1 motion:1 hψ:1 ims:1 symplectic:1 assumed:1 hence:3 coh:1 first:3 xk:1 study:2 follows:1 into:2 potentials:2 moscow:3 harmonic:3 approximate:2 dimensional:1 phase:1 xx:3 references:1 bose:1 operator:1 production:1 operational:1 illustrate:1 pp:1 feb:1 second:2 basis:2 trajectory:8 initial:2 system:8 been:3 iq2:1 ordinate:1 defined:1 cauchy:4 therefore:3 statement:1 bagrov:2 ph:1 was:1 const:4 function:7 nauka:2 wkb:3 corresponding:1 complete:1 form:1 operators:1 exactly:1 odinger:10 but:1 fortschr:1 coherent:8 construction:2 particular:3 x2:1 schr:10 x0:3 denote:1 potential:2 present:1 must:3 case:11 obeying:1 p0:2 valued:1 coefficients:2 dubey:1 type:1 equation:12 work:1 oscillator:3 q22:3 value:2 annihilation:1 matter:1 determined:1 were:3 following:5 problem:5 xˆ:5 averages:1 russia:1 result:1 mechanics:1 constant:3 almost:1 certain:1 abstract:1 describe:1 ages:1 general:3 states:9 single:1 minimum:1 pˆ:5 sense:1 mωr:1 any:2 fizika:1 constructed:2 hpx:3 relationship:3 eq:4 hpp:12 when:2 detail:1 check:1 note:2 complex:3 quant:1 neighbourhood:1 widely:1 solve:1 guarantee:1 parameter:3 sin:3 difficult:2 heisenberg:8 wave:1 calculation:1 used:2 closest:1 shall:2 may:1 symbol:1 time:1 minimized:1 possible:1 firstly:3 moment:1 representation:1 linearization:1 choice:1 cases:1 branches:1 minimize:3 obviously:2 mass:1 calculations:1 exp:4 mechanical:3 coordinate:2 quadratic:4 otherwise:1 physics:6 fact:1
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quant-ph9702011.txt |@word represent:3 measurements:1 sci:1 qian:1 interference:3 magnetic:7 particular:7 results:1 adjective:1 roy:4 scalar:2 commute:1 generalize:3 parameterization:4 remarkably:1 research:1 contributions:3 discern:1 whose:3 simon:6 depend:1 concerned:1 ali:1 editors:1 nonlocal:1 passage:1 environment:2 finally:2 alvarez:1 under:3 analogous:1 include:1 dutta:1 belonging:1 supported:1 amplitudes:1 returned:1 orthogonal:4 far:1 emphasizes:1 wave:10 electron:1 monopoles:1 ertmer:1 interpreting:1 got:1 experimentally:1 associated:2 difference:7 pati:3 brihaye:1 four:1 exponential:1 hamiltonian:7 issue:2 henri:1 list:1 applicable:1 involution:1 vector:7 reich:1 rev:58 eigenvalues:4 unifying:1 1940s:1 equation:4 unaware:1 degeneracy:3 rohrlich:3 force:1 findings:2 direct:1 literature:1 approximation:2 fold:2 rate:1 datta:1 incidentally:2 dynamics:1 chem:3 linear:1 koenig:1 what:3 abc:1 sub:1 section:1 axes:1 current:3 quadrupole:2 sequential:1 above:8 fractional:1 new:3 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quant-ph9702012.txt |@word descartes:3 splitting:2 psyche:1 edu:4 battle:2 oldest:1 seemed:1 shattered:1 concerned:2 environment:1 lord:1 garden:1 sitting:1 very:1 gravitate:2 fall:1 forking:1 did:6 knight:1 small:2 brave:1 miller:1 go:1 copenhagen:1 fapp:4 even:4 established:1 what:1 captain:1 reminiscent:1 version:1 relocate:1 method:2 edited:3 christian:1 gathered:1 men:1 french:1 others:2 alone:1 luis:1 great:1 merely:1 plenum:1 thought:1 planck:1 feb:1 would:7 vol:11 going:1 therefore:8 more:4 horses:1 quant:1 odinger:3 central:1 iii:1 cat:3 reviews:1 remain:3 itself:2 strategies:1 spontaneous:1 abner:1 intricate:1 sought:2 united:1 hoc:1 rather:3 embarrassingly:1 ghirardi:3 sword:1 acta:1 fudge:6 irrational:1 after:1 ronald:1 lay:1 cambridge:2 appealed:1 proclaimed:1 goal:1 elusive:1 conscious:3 cosmology:1 so:6 cloaking:1 tall:1 talk:1 helv:1 wigner:3 help:3 hugh:1 years:2 course:2 scientist:1 through:1 still:3 its:2 before:3 la:1 resorting:1 followers:1 hidden:1 might:1 weber:1 eugene:1 fool:1 non:3 evening:1 weakness:1 distilled:1 cutting:1 tails:8 they:6 oxford:7 now:1 shadows:1 netherlands:1 dirac:1 university:5 prosperi:1 man:1 found:2 went:2 luck:1 scheme:1 meta:4 computable:1 quantum:11 happen:1 es:2 out:2 god:1 content:1 ren:1 got:1 theory:1 localization:1 quite:1 reason:2 surely:2 york:1 put:3 could:2 david:3 place:1 think:1 exotic:1 feel:1 primary:1 reached:1 ring:1 horse:1 necessarily:1 unknown:1 top:1 their:5 too:1 john:1 final:1 speculates:1 lot:2 happily:1 albert:3 took:1 alas:1 somewhat:1 manifestation:1 fooled:1 july:4 than:4 albeit:1 hundred:1 unfortunately:1 penrose:3 bother:2 matter:3 were:4 ingenious:1 remained:3 modern:1 mind:2 interpretation:1 comfortable:1 saw:1 metaphysics:6 paths:1 genuine:1 able:1 gravity:5 sciences:1 potential:2 new:3 mit:1 heisenberg:1 though:1 who:2 jorge:1 most:2 nothing:2 awe:1 camp:2 metaphysical:4 shortly:1 face:1 reestablished:1 enterprise:1 physics:8 partisan:1 fact:1 queen:2 discovered:1 purely:1 subtle:1 fine:1 ground:1 naturalistic:1 loinger:1 cloak:1 ox2:1 only:3 princeton:4 mend:1 riding:1 moses:1 do:1 his:13 preferred:2 despite:1 him:3 krishna:1 arxiv:1 roger:2 worries:1 london:2 obscure:1 gell:2 view:1 declared:1 opposed:2 fair:1 seat:1 college:1 result:1 apologies:2 declined:1 surmised:1 nuclear:1 review:7 monstrous:1 definite:1 state:2 dlp:3 neither:1 publishers:1 joy:1 omn:2 however:1 kluwer:1 many:2 uncertainty:1 minds:1 facet:1 unh:4 conducting:1 passing:2 mann:2 among:1 liked:1 tone:1 bell:2 wall:8 cf:1 karel:2 maintained:1 away:2 indefinite:1 decohere:2 accomplishing:1 perspectives:1 locally:1 three:1 been:2 much:3 ph:1 hepp:2 search:1 sound:7 kuchaˇr:2 premature:1 spontaneously:2 trick:2 while:2 voice:1 almost:2 von:1 thus:2 them:1 commander:1 ii:1 good:3 pedestal:1 italy:1 perhaps:2 algorithmically:1 clearly:2 discourse:2 tumbling:1 split:2 largest:1 physical:3 privileged:1 everett:4 upon:1 hand:1 off:1 nevertheless:1 well:1 bohr:7 bohm:3 academic:1 without:1 jersey:1 easing:1 charged:1 just:5 localize:2 yet:3 death:1 borges:1 kirk:1 thinking:1 had:3 appeared:1 questioned:1 save:2 kingdom:1 around:1 possible:2 press:5 world:1 bit:1 prominent:1 wolfson:1 like:3 niels:1 quantal:5 www:4 right:1 neumann:1 classical:5 belonged:1 some:2 back:2 born:1 curious:1 lead:1 bottom:1 schr:3 knew:1 truth:1 reaching:1 shimony:2 although:1 worthy:1 sixty:1 about:3 actual:2 boldly:1 emperor:1 own:2 into:2 clifton:1 due:1 down:1 references:1 einstein:2 refined:1 your:1 there:4 long:2 way:1 was:25 happy:2 rimini:1 but:8 he:17 characteristic:1 called:2 mechanics:1 gone:1 irish:1 rightly:1 ad:1 elegant:1 am:43 deep:1 exist:1 obtuse:1 ship:1 constructed:1 again:3 heinemann:1 no:12 when:1 reality:1 field:1 other:1 really:1 poor:3 star:1 faction:1 fell:1 utterly:1 culprit:1 together:2 time:2 decoherence:2 once:2
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quant-ph9702013.txt |@word secondly:2 monte:1 leighton:1 arrives:1 consider:15 springer:1 similarity:3 says:2 magnetic:21 desirable:2 results:8 leads:3 rapid:1 latter:2 grateful:2 go:6 follow:1 contributions:8 cases:2 localized:1 certainly:2 depend:1 advantage:1 disposal:1 switched:1 passage:1 tn:1 answered:2 finally:9 does:15 infinitesimally:2 tk:2 th:1 ti:1 tf:1 presentation:1 sent:1 ta:1 deforming:1 interacting:1 digit:1 φns:6 hibbs:14 nul:2 outside:5 far:3 alternatives:1 assuming:2 translations:1 conditions:1 wave:31 indication:3 electron:23 putting:3 figs:4 fall:1 inequivalent:2 experimentally:7 bubbles:1 difference:18 fractal:14 rn:1 condition:1 arrange:1 tubes:3 hamiltonian:3 xexp:4 vertex:2 solution:5 t0:8 bohn:1 large:10 discrete:1 vector:26 demonstrated:1 section:5 small:8 gauge:2 ree:14 inspection:1 noted:1 draws:1 bessel:4 correct:2 smaller:3 compensated:1 sin2:2 direct:1 13a:1 approximation:2 winds:3 second:3 displays:1 pass:3 rigorous:2 qualitatively:1 estimated:1 carlo:1 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quant-ph9702014.txt |@word aguilera:1 represent:1 partial:1 consider:6 magnetic:1 excellent:1 results:1 leads:1 entropy:4 go:2 follow:1 expressions:1 worked:1 tr:2 finally:1 edward:1 those:4 th:1 under:2 lack:1 broadly:1 very:2 wave:1 fan:1 difference:2 exact:2 immediately:1 level:11 did:1 turns:1 solution:1 solved:1 differential:2 optics:2 noted:1 miller:1 approximation:1 second:1 prairie:1 arnold:1 further:1 dynamics:2 implemented:1 canonical:1 even:1 will:1 appear:1 giving:2 section:2 mechanics:1 current:3 ˆb:4 version:2 above:2 ˆi:4 ˆj:2 occupation:1 ˆl:1 method:1 ˆn:4 satisfy:1 condensed:1 led:1 respectively:1 here:1 ˆ2n:1 mep:13 address:1 based:3 trung:1 equations:14 obtained:3 buck:2 spontaneous:1 study:3 studied:4 allows:4 eberly:1 periodic:1 resulting:2 resonance:1 suitable:2 via:4 useful:1 extra:1 reichel:1 plenum:1 viz:1 use:1 feb:1 takes:1 working:2 levine:1 e1:1 next:1 comparing:1 live:1 therefore:2 conservation:1 more:4 introducing:1 becomes:1 operators:54 emission:2 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quant-ph9702015.txt |@word represent:3 saturating:1 consider:2 discards:1 equalities:1 results:4 computation:1 edu:2 go:1 causes:1 number:1 referring:1 contained:1 uniqueness:1 present:3 under:1 stochastic:1 must:2 worth:1 sent:6 case:6 random:3 straightforward:1 rise:1 polarization:1 choice:3 summarized:1 iuv:3 presented:1 transmission:8 cause:1 who:3 eve:47 t0:4 t1:11 large:1 convenience:1 settle:1 interchanging:1 succession:1 cmu:2 noted:1 measuring:5 employing:6 consistent:5 rate:4 further:1 theory:1 employ:2 what:3 errors:9 advantageous:1 incompatible:2 brief:1 expressed:2 waiting:1 above:1 values:1 consisting:1 edited:1 full:2 simultaneously:1 respectively:1 applies:1 understanding:1 represented:2 along:1 calculate:1 sending:1 involved:3 leaves:1 changed:1 allows:1 prior:1 amount:1 bennett:1 action:3 california:1 bob:17 fourier:1 makes:3 involves:1 f0:2 followed:3 griffiths:3 family:3 logical:1 alamitos:1 use:5 feb:1 dxy:15 would:3 remains:2 chi:1 chooses:1 next:1 noting:1 call:3 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quant-ph9702018.txt |@word concept:2 consider:2 blanchard:6 results:1 themes:1 go:1 causes:1 whose:2 deterministic:4 countdown:1 device:1 norm:1 orthogonal:1 very:1 wave:5 summarized:1 exact:1 level:2 knight:1 solution:1 vector:2 miller:1 direct:1 jump:1 second:1 perspective:2 dynamics:4 haag:7 theory:14 even:3 what:2 plays:1 stands:2 selected:2 experiment:4 localized:1 above:1 suppose:1 ever:2 seeks:1 postulates:1 κk:1 1987b:1 κf:1 1987a:2 here:1 represented:1 invented:1 equations:1 knowledge:1 incoming:2 institute:1 study:2 allows:1 reason:1 specialize:1 changes:1 honor:1 projection:1 family:1 complying:1 vii:1 plenum:1 marked:1 total:1 unit:1 plot:1 use:1 metaphor:1 takes:1 would:8 commun:2 probabilities:2 positive:2 contains:1 next:1 vol:1 nucl:1 taken:1 today:1 more:1 becomes:1 operators:1 odinger:2 aware:1 normalized:1 particular:2 foundations:1 cases:1 must:3 states:2 equation:6 work:1 theories:2 values:1 concepts:1 following:2 meet:1 spontaneous:1 example:1 history:1 f2:1 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quant-ph9702019.txt |@word measurements:2 consider:2 blanchard:4 leads:1 go:1 follow:1 causes:1 inverse:1 const:1 deterministic:3 unanswered:1 finally:1 stochastic:1 conjecture:1 finkelstein:1 very:1 alternatives:1 wave:10 every:1 experimentally:2 difference:1 exact:3 themes:1 presented:1 did:1 turns:1 solution:2 noiseless:1 honor:1 small:1 der:1 verifiable:1 miller:1 second:2 pass:1 dynamics:2 salam:1 haag:2 linear:1 even:1 what:5 stands:1 apparatus:1 experiment:1 above:1 flowing:1 new:3 increasing:1 acknowledgments:1 contrast:1 counters:1 philippe:1 evolving:1 pushing:1 here:2 sink:3 berkeley:1 path:1 change:1 obtained:1 drops:1 incoming:4 institute:2 leaves:1 allows:1 completely:1 suggests:2 poisson:1 stressed:1 action:1 changes:1 options:1 involves:1 extra:1 plenum:1 herzog:1 feb:1 would:6 commun:1 positive:1 contains:2 vol:1 theoretical:1 more:3 becomes:1 odinger:3 known:2 foundations:1 hold:1 potential:1 must:1 sample:1 science:1 equation:2 believes:1 deficiencies:1 following:2 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quant-ph9702020.txt |@word represent:1 pointing:1 global:4 focus:1 four:7 rapid:1 scalar:2 computation:27 stochastically:1 go:2 decisions:1 row:4 whose:3 simon:3 const:24 calculate:1 graph:1 deterministic:1 tr:5 factoring:1 former:1 finally:3 compensate:1 restriction:1 preserved:1 th:3 under:1 analogous:1 indicating:1 lack:1 returned:1 straightforward:1 orthogonal:6 very:1 tends:1 dell:1 results:10 isomorphism:4 every:3 decide:2 entries:3 exact:1 condition:2 arrange:1 leads:1 obvious:1 subsets:1 presented:2 did:1 turns:4 solution:8 occurs:1 large:9 discrete:3 convenience:1 dealt:1 small:3 upper:1 quicker:2 grateful:1 deutsch:14 direct:2 second:4 cost:1 evaluated:1 further:1 estimated:1 columns:2 canonical:1 even:3 what:4 errors:1 xor:1 appear:2 invertible:2 incompatible:1 giving:1 section:8 expressed:3 uniform:3 waiting:1 above:6 expresses:1 satisfy:2 led:1 never:1 component:1 answers:1 behaviour:1 along:11 quite:1 equations:2 appears:2 change:1 referring:1 box:1 study:1 larger:5 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quant-ph9702021.txt |@word limited:3 sci:1 consider:3 pointing:2 ali:2 rev:14 varying:1 resistance:25 four:1 roy:8 ge:1 commute:1 computation:15 maxima:2 consists:3 involved:1 localized:1 whose:3 dimensionality:1 depend:2 calculate:2 iii:1 segments:3 show:14 nonlocal:1 removal:1 environment:1 tail:1 program:1 those:6 excluded:1 under:5 mutandis:1 nodes:1 include:2 presentation:2 division:3 random:1 string:1 advantage:1 very:17 p0j:4 continues:3 01m:1 01n:1 results:17 electron:5 every:1 figs:1 algorithm:1 emphasized:2 difference:2 matrices:4 høyer:1 condition:3 paz:1 tang:1 upj:6 incoherent:2 hamiltonian:5 transmission:29 positions:1 z12:1 decreasing:2 z11:1 large:8 discrete:1 convenience:1 phase:4 succession:3 small:7 optics:1 noted:4 lloyd:2 upper:8 zn:9 smaller:3 nonrandom:1 10m:1 trend:2 cond:1 grover:1 among:1 direct:1 cosh:3 second:1 pass:1 defines:1 distance:1 machines:3 theory:1 even:4 lesser:1 what:1 errors:1 essence:1 fluctuates:4 rate:2 morse:1 trivial:1 sum:7 probably:1 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quant-ph9702022.txt |@word partial:3 consider:2 gesztesy:1 results:1 leads:1 known:1 alt:1 reˇ:1 gr:2 compact:1 whose:1 certainly:1 dimensionality:3 depend:1 technique:1 restriction:1 those:1 under:3 worth:1 ta:4 case:4 amplitudes:2 straightforward:2 g0:1 very:1 frequencies:1 wave:10 specific:1 φnm:1 difference:1 condition:2 four:1 hamiltonian:3 transmission:2 solution:3 try:1 admissible:2 differential:1 eigenvalues:1 gossard:2 equation:4 mm:1 smaller:1 alhassid:1 zero:1 evaluated:3 further:1 folk:1 haake:1 spectral:2 aim:1 adds:1 combined:1 giving:1 pandey:1 expressed:2 find:4 current:1 experiment:3 above:3 suppose:4 consisting:1 coefficient:1 full:2 exchange:1 respectively:1 component:3 equals:1 here:2 diagonal:1 ranges:1 cylindrical:1 kudrolli:1 2ka:2 eikx:3 consideration:1 εn:2 change:1 obtained:2 remark:1 institute:2 involved:1 study:1 larger:1 allows:2 amount:1 action:1 resonance:9 studies:1 inspires:1 missing:1 plotted:1 composed:1 diameter:1 named:2 classification:1 explained:1 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quant-ph9702024.txt |@word represent:1 since:1 peshkin:3 chain:2 rev:6 magnetic:53 global:3 results:1 per:2 contributions:2 2r0:4 clarification:1 charge:20 under:1 webb:1 multielectron:1 case:6 shielding:14 string:25 very:2 wave:5 electron:61 matsuda:1 associated:1 difference:1 wipe:1 condition:1 level:4 positions:1 t2:2 solution:1 large:2 vector:6 small:2 round:1 measuring:2 zh:1 approximation:2 zero:6 enclosed:12 odd:7 situated:1 even:9 bruynseraede:1 interatomic:1 appear:1 morse:1 sum:4 contributed:1 thickness:3 experiment:7 above:4 lifshitz:1 contributes:1 edited:2 measurements:1 respectively:2 component:1 atoms:1 ramsey:2 separation:3 represented:4 path:3 along:9 equations:1 appears:1 change:3 obtained:3 antisymmetric:1 institute:1 shift:24 study:1 larger:1 periodic:2 resulting:1 poisson:1 action:4 studies:1 cancellation:1 composed:2 yamada:1 santa:1 explained:2 altshuler:1 total:1 conventional:4 feb:1 would:1 stated:1 suppl:1 ψn:1 therefore:1 m2:1 slater:1 entails:1 more:1 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quant-ph9702025.txt |@word represent:2 concept:2 rev:6 magnetic:62 global:1 four:6 expressions:2 charge:5 th:2 divergent:7 amplitudes:2 string:45 eilθ:4 very:1 assuming:1 wave:34 electron:29 putting:1 difference:10 al2:17 2rr:1 condition:2 al1:17 exponential:1 presented:1 ref:2 solution:2 vector:3 enclosing:1 small:10 hk2:1 direct:2 sign:1 zero:3 equal:1 further:2 odd:1 gm:2 b01:1 morse:1 sum:1 ψl2:1 ψl1:1 thickness:2 experiment:5 international:1 component:3 cylindrical:3 separation:4 represented:8 path:1 equations:2 eikr:2 logarithmic:4 obtained:9 institute:1 shift:1 studied:3 leaving:1 amount:2 kρ0:1 products:1 suitable:1 changes:1 cancellation:1 involves:1 derivatives:2 conventional:1 feb:1 superpositions:1 would:6 remains:3 positive:1 fl2:4 negative:1 comparing:1 therefore:3 type:1 theoretical:3 gyromagnetic:2 becomes:1 odinger:2 carrying:1 basically:1 cases:1 iv:1 mg:1 mc:4 shielded:24 equation:8 work:2 cancellations:1 ere:1 values:4 thin:2 about:1 fulfil:1 example:2 decoupled:1 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quant-ph9702026.txt |@word limited:2 concept:3 semantic:1 consider:2 zhang:1 interference:11 magnetic:4 both:3 results:1 leads:3 ginzburg:1 supplement:2 constants:1 gk:3 ammonia:2 certainly:2 essentials:1 equivalence:4 topic:1 those:1 th:1 stable:1 γc:2 γb:2 include:1 applied:2 supported:1 antiferromagnetism:1 very:3 rise:4 puzzles:1 electron:2 sons:3 every:1 onsager:1 emphasized:2 difference:2 exact:9 condition:2 randomness:3 incoherent:2 hamiltonian:16 nucleates:1 expectation:10 large:1 vector:1 dealt:1 small:7 eigenvalues:1 gor:1 commented:1 degeneracy:6 lagrangian:1 tem:1 oscillation:1 consistent:3 sin2:1 literature:1 approximation:6 zero:8 doubt:1 perspective:1 rigorous:1 further:1 spontaneously:3 odd:1 approached:1 even:6 what:1 giving:1 section:2 while:5 current:2 ˆc:3 above:3 ˆg:1 new:5 ˆk:1 method:4 body:3 condensed:5 justification:1 simultaneously:1 notions:1 ibid:3 respectively:2 modify:3 equals:1 here:12 atoms:3 condmat:1 explore:1 free:4 address:1 standard:1 appears:2 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quant-ph9702027.txt |@word represent:2 partial:1 consider:1 rev:6 results:1 leads:1 proposition:4 entropy:8 computation:1 contributions:1 particles:2 terms:1 calculate:6 tr:11 cess:1 those:1 under:9 ingredient:1 division:1 conjecture:1 straightforward:3 very:2 every:3 experimentally:1 matrices:4 condition:6 generalised:1 p4:1 level:1 tra:1 knight:3 trb:2 leave:2 generalize:2 optics:2 deutsch:1 direct:3 second:1 rigorous:1 further:3 choices:1 theory:3 even:1 what:1 appear:1 witnessed:1 section:1 analogously:1 above:4 new:1 increasing:2 satisfy:8 degree:4 ρab:13 here:2 desired:1 plenio:3 directions:1 consideration:1 change:2 violate:2 obtained:2 great:1 involved:2 reason:2 suggests:3 amount:4 survey:1 procedure:1 pictorial:1 action:2 suitable:1 composed:1 useful:1 divide:1 private:1 decrease:1 apply:1 operational:2 use:4 feb:1 would:5 prove:3 distinct:3 positive:3 contains:1 ψj:2 classically:1 ψi:2 therefore:11 taken:3 metric:3 decomposable:1 more:6 preserving:3 successful:1 operators:5 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