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quant-ph9505013.txt |@word spherical:2 duflo:1 consider:1 similarity:1 particular:2 paper:1 relation:1 solutions:1 substituting:1 trivial:2 find:1 causes:1 principal:1 ıp:1 position:1 group:7 chosen:1 affine:2 depend:1 selfsimilar:1 than:1 only:1 permanent:1 choose:1 under:1 might:1 hill:1 p2:1 insight:1 dk:1 means:1 translations:2 wave:4 joint:1 dx:1 report:1 condition:1 formal:1 evolution:1 dµl:2 particle:3 hamiltonian:2 always:1 arxiv:1 solution:4 large:1 admissible:3 vector:5 math:2 2m:2 anal:1 limit:1 pertains:1 referred:1 homogeneous:1 often:1 exists:1 some:1 related:1 applicable:1 see:1 measure:1 quantum:4 our:2 dµ:1 ultimately:2 satisfying:1 space:2 nuclear:1 since:3 chaos:1 research:1 state:1 daubechies:2 decomposition:2 wavelet:5 invariant:2 boundary:1 conditions:1 minimal:2 2ma2:2 importance:1 derived:1 however:1 free:1 reason:1 objects:1 comm:1 here:1 groups:1 address:1 consideration:1 dubna:1 hilbert:2 meyer:1 interaction:1 central:1 mcgraw:1 institute:1 uncertainty:1 equal:1 quantization:2 hψ:1 a2:2 opinion:1 uniquely:1 hyderabad:1 symmetry:3 minimises:1 into:1 within:1 apt:1 transform:1 dimensional:1 references:1 apl:1 respect:2 subm:1 cv:2 given:1 deep:1 basis:1 sake:1 strictly:1 preprint:1 system:1 cv0:2 int:1 describes:2 treat:1 basic:3 taken:1 ph:1 type:1 speaking:1 systems:2 function:2 formally:1 form:4 solitons:1 exactly:1 odinger:8 but:1 so3:1 packet:2 func:1 atom:1 x2:2 quasiclassical:1 translation:1 level:1 potential:3 present:1 must:1 case:2 distance:1 singapore:1 october:1 look:2 science:2 equation:9 will:1 technical:1 near:1 determined:1 suppose:2 following:1 problem:4 similar:3 russia:1 grossmann:1 mechanics:2 ictp:1 unitary:1 constant:1 moore:1 defined:1 certain:1 abstract:1 india:1 generalization:1 general:2 states:1 sidharth:1 say:1 point:1 close:1 ax:1 ic:1 hydrogen:1 physical:3 lie:3 functions:1 possibility:1 no:1 rather:1 self:4 get:1 trieste:1 other:1 quant:1 actual:1 pure:1 mathematics:1 theor:1 simplicity:1 infinity:1 superposition:1 excitation:1 centre:3 may:1 after:1 problems:3 v0:1 meaning:1 plane:1 scale:1 waves:1 representations:1 choice:1 class:1 normalization:1 schr:8 well:1 dadb:2 nottale:1 exp:1 representation:4 model:1 requires:1 fractals:1 left:1
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quant-ph9505015.txt |@word concept:1 consider:10 alternatives:2 four:18 anticorrelated:1 calculate:1 tr:1 finally:3 protocols:4 worth:1 sent:3 risk:1 very:1 notes:2 says:10 second:15 implemented:3 even:5 what:4 axes:4 nec:1 above:7 new:1 here:1 cos2:7 address:2 directions:1 along:45 obtained:4 technical:1 unproved:1 usually:2 bob:50 useful:1 secure:8 highly:1 cheating:2 proceed:1 prove:1 chooses:5 next:6 noting:1 m1:9 m2:24 encode:12 until:2 formally:1 knows:3 successful:6 particular:1 known:1 cases:5 iii:3 none:1 tokyo:1 learn:11 following:10 example:1 proof:2 ma1:27 flavor:1 bennett:7 india:1 states:24 assumptions:1 performed:3 axis:43 information:11 goal:1 answer:2 sin:5 brassard:6 product:2 plane:1 introduced:1 allow:1 sigact:1 aiken:1 mx2:66 mx1:44 course:2 paper:2 innovative:1 japan:2 ieee:2 before:3 symmetry:1 chosen:15 cryptology:1 permanent:1 choose:12 setting:1 correspondence:1 non:1 propose:1 break:1 they:3 now:7 university:1 crypto:1 orthonormal:1 σ2x:8 σ2y:8 σ2b:9 obtains:3 measure:1 quantum:9 laboratory:1 eq:1 out:5 shown:2 since:20 rev:7 research:1 particles:21 shows:3 standard:1 difficulty:2 york:1 pairs:1 yaxis:1 computers:1 honest:2 american:1 first:20 tama:1 features:1 probability:5 xy:1 another:1 given:2 similarly:1 eqs:1 least:1 perfectly:3 bits:2 store:5 memo:1 contribute:2 tapster:1 wiesner:2 transferred:1 rarity:1 crepeau:2 polarizer:1 generality:1 mind:1 argument:5 randomly:6 manuscript:1 any:16 angle:1 mermin:1 efficient:2 note:3 take:1 rediscovered:1 formulas:1 rhs:1 who:1 encodes:6 letter:1 pair:3 measured:2 salvail:1 later:1 principle:1 fact:1 cheat:2 substituting:1 based:1 should:17 only:7 ardehali:2 emitting:1 his:13 goes:8 cryptography:1 get:1 σ1a:9 σ1y:8 σ1x:4 international:1 him:12 podolsky:2 arxiv:1 she:29 shi:1 wrote:1 set:14 decides:12 detection:1 see:3 alternative:1 best:1 learns:9 cheaters:4 review:1 state:22 between:1 ability:1 however:10 succeed:2 news:1 both:15 cos:4 against:7 called:2 harvard:1 login:1 arbitrarily:3 among:1 corresponds:1 oblivious:10 considers:2 conference:1 pp:2 asks:10 been:6 strategy:3 expected:1 ph:1 systems:1 direction:1 describe:3 flight:1 θb:17 concerning:1 θa:17 angles:1 spin:32 present:3 case:13 value:16 choices:2 applies:1 thus:8 them:1 iv:3 ii:7 technology:3 same:5 tells:8 quant:1 infeasible:1 used:2 rabin:2 center:1 epr:4 without:4 laboratories:1 protocol:16 less:1 rosen:2 obtain:2 yes:6 kanagawa:1 source:1 belongs:9 lett:5 theorem:2 sagamihara:1 rules:1 unlimited:5 period:3 entangled:1 bit:17 multiplexing:1 loss:1 particle:26 follows:3 signal:1 dishonest:1 alice:61 wooters:1 unstable:1 either:16 arbitrary:1 spins:8 sends:2 successfully:1 some:2 proceeding:2 measurements:4 does:17 assuming:2 proc:1 demonstrated:1 measures:21 scientific:1 power:5 processing:1 perpendicular:1 step:9 although:1 bangalore:1 about:10 attacks:1 o:1 ot:10 computational:1 appropriate:4 references:1 determine:2 einstein:2 elementary:1 additional:2 her:6 transfer:10 there:3 question:4 long:3 was:4 smolin:1 jun:1 but:15 gain:2 encoded:15 mb2:27 he:46 october:1 whether:5 maximum:2 us:1 tell:2 below:2 problem:1 similar:3 agree:4 mechanics:2 computing:5 defined:4 measurement:10 general:1 peres:1 again:1 no:4 corporation:1 ekert:3 when:2 other:2 briefly:1 my1:65 my2:42 palma:1 prepares:2 cryptographic:1 correlated:1 assume:17 microelectronics:1 cheater:3 time:3 having:1
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quant-ph9505016.txt |@word consider:1 rev:3 desirable:1 results:1 four:1 computation:14 go:1 whose:1 inverse:1 tr:1 factoring:1 conjecture:1 very:2 every:1 resonant:1 experimentally:1 level:1 turns:1 large:2 solved:1 deutsch:11 pulse:1 zero:1 further:1 theory:1 even:2 appear:1 nand:1 establishes:1 new:2 public:2 satisfy:1 simultaneously:1 respectively:1 teleportation:1 here:1 operating:1 along:3 obtained:2 sending:1 technical:1 goldwasser:1 exceptionally:1 through:1 suggests:1 published:1 action:1 via:2 family:1 a23:2 unit:1 use:2 feb:1 figure:2 prove:1 toffoli:2 call:1 therefore:1 stage:1 type:5 theoretical:2 more:2 shamir:1 composite:1 carrying:1 known:2 foundations:1 ibm:1 science:2 work:2 infinitesimal:1 values:1 following:1 proof:3 control:8 ions:1 indicated:1 bennett:2 haroche:1 implementations:1 states:2 performed:5 axis:4 information:1 united:1 provide:1 verify:1 gate:31 parameter:1 sin:8 brassard:1 simplicity:1 irrational:2 may:3 earlier:1 applications:1 constants:1 efficiently:1 natural:1 third:2 computations:1 register:1 explicit:1 their:2 complexity:1 so:1 block:2 allow:1 operations:1 symbols:2 paper:3 london:7 existence:1 cold:1 ieee:3 perfect:1 rapidly:1 forms:1 systems:2 non:1 universality:2 sooner:1 framework:1 effects:1 symposium:1 oxford:3 rotation:4 now:2 irrationality:2 easily:1 always:1 university:1 presented:2 realistic:1 arrow:1 each:3 simplified:1 2n:4 ed:1 society:1 quantum:21 laboratory:2 operation:8 eq:1 out:2 divincenzo:4 shown:4 matrix:4 res:1 since:2 induces:1 rz:3 performs:1 issue:1 math:1 linear:1 interactions:1 diagonal:2 possibility:1 davidovich:2 completely:1 york:1 put:1 jozsa:2 interaction:3 computers:4 circuit:1 exhibited:1 first:3 simplifies:1 manuscript:1 number:1 done:1 another:1 given:3 similarly:1 obtainable:1 types:1 scheme:1 bits:1 trapped:1 rsa:1 rivest:1 than:1 target:9 showed:1 second:2 submitted:1 appealing:1 providing:1 reviewing:1 already:1 weinfurter:3 any:8 angle:3 built:1 efficient:1 lim:2 parks:1 note:2 instance:1 algorithms:1 mit:2 accuracy:3 shall:1 most:1 class:3 constructed:1 considered:1 later:1 points:1 mechanical:2 physics:1 fact:1 shor:2 signatures:1 particularly:1 show:1 supported:1 trivial:1 networks:3 just:1 implementation:1 ox1:1 controls:1 should:1 iei:3 only:4 explicitly:1 black:1 factor:1 adequate:4 do:1 cryptography:1 means:1 syst:1 ones:1 report:1 processes:1 arxiv:1 consisting:4 nθ:1 common:1 nα:1 fixed:1 view:2 set:5 constructing:2 exists:2 undergoes:2 computer:2 college:1 result:3 discussions:1 ieiφ:1 currently:1 state:5 between:2 numerous:1 brune:1 notice:1 barenco:4 recently:3 qubits:6 however:1 key:2 sleator:3 improve:1 both:2 cos:8 realizable:1 last:1 many:1 annual:1 raimond:1 context:1 logic:1 qubit:15 experimental:4 generalisation:1 relevant:1 point:3 simple:1 royal:1 sequences:2 moreover:2 conference:1 perspectives:1 basis:3 three:10 been:1 int:1 much:1 threaten:1 ph:1 fig:4 dots:1 corresponding:1 sufficient:2 precision:2 repertoire:2 denote:4 spin:5 present:1 plain:1 reliable:1 transformation:4 will:2 aij:1 shafi:1 unitary:7 almost:1 itself:1 ie:2 containing:1 unaffected:3 develop:1 generic:1 radiation:1 same:2 clearly:2 iα:1 quant:1 digital:1 finite:1 trivially:1 effect:2 possible:2 ion:2 uses:1 entanglement:1 lower:2 off:1 traps:1 zagury:1 nevertheless:1 no:2 analysis:1 preprints:1 realised:1 gates:17 proposed:2 thanks:2 multiples:1 letting:1 conforming:1 preprint:2 zoller:2 had:1 lett:1 input:3 remaining:1 iφ:2 kingdom:1 lcs:1 read:1 showing:1 iβ:2 3pu:1 press:1 bit:16 mod:2 lincoln:1 imposed:1 permuting:1 either:1 arbitrary:4 output:3 security:2 signal:1 because:1 qed:1 classical:4 sequence:2 conditional:1 specified:1 eiα:3 eiβ:1 cavity:1 replicas:4 comments:1 does:1 adleman:1 proc:8 refer:1 problems:1 processing:1 analysed:1 clarendon:1 eiφ:1 properties:1 transformations:1 integers:1 about:2 constraint:1 o:1 practical:2 range:1 ensure:1 greatly:1 introduced:1 road:1 soc:6 computational:1 realisation:1 there:3 forward:1 was:1 form:4 but:4 construction:3 irreversible:1 applying:1 boldface:1 problem:1 adriano:1 similar:2 cryptosystems:2 cirac:2 defined:2 certain:1 universal:17 evidence:1 single:3 our:1 defines:1 effected:1 drafts:1 variety:1 ekert:3 when:3 other:2 papers:1 department:1 realisable:1 a13:2 a12:4 june:1 important:1 palma:1 structure:1 network:5 algorithm:1 fund:1 starting:1 required:1 reversible:1 requires:1 having:1
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quant-ph9505017.txt |@word concept:1 consider:6 results:3 existing:1 leads:1 eds:4 scalar:1 overlap:1 grateful:1 mcmullin:1 go:1 reasoning:1 careful:1 depend:1 deterministic:2 finally:3 analogous:5 include:1 worth:2 already:1 blasi:1 laws:1 very:7 tends:1 springer:2 wave:19 every:2 interpreting:1 anonymous:1 emphasized:2 difference:2 condition:3 generalised:6 hamiltonian:3 positions:4 t2:7 t1:7 large:1 vector:6 postselection:3 small:1 shows:2 equation:1 prevent:1 occurrence:1 dealing:2 zero:2 dualistic:1 reznik:2 further:1 click:1 canonical:1 even:4 will:9 appear:2 apparatus:4 section:8 abl:10 bergman:3 experiment:12 goes:3 new:3 supporting:1 outgoing:4 respectively:2 here:4 asymmetry:4 possibility:1 directions:1 path:26 along:2 quite:3 deduced:2 obtained:2 search:1 incoming:4 oxford:2 involved:1 vectors:3 allows:1 approaches:1 contradiction:1 suggests:5 calculations:1 usually:1 placing:1 spacetime:1 der:1 composed:1 useful:1 projection:1 outcomes:2 hardy:3 addressed:1 durham:4 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quant-ph9505018.txt |@word secondly:1 externally:1 concept:3 consider:5 chain:1 locations:1 results:3 four:1 commute:2 computation:32 expressions:1 issues:1 relationships:1 whose:1 dimensionality:1 violate:1 transferred:1 financial:1 involve:1 tr:2 environment:1 neighbours:1 efficiencies:1 swap:1 th:1 under:3 analogous:1 eiq:1 belonging:1 straightforward:1 eip:1 very:3 differently:2 every:10 cellular:1 fall:1 affect:4 difference:1 generalised:1 entire:1 swapping:1 level:1 did:1 turns:1 conceive:1 solution:2 large:1 small:1 eigenvalues:1 configurations:1 coordinate:1 deutsch:7 approximation:2 second:4 design:1 pass:1 machines:6 linear:2 even:6 established:1 what:1 errors:2 sub:3 richard:1 find:1 ˆa:1 above:2 new:3 ˆj:2 method:3 satisfy:1 compact:1 full:1 degree:1 never:1 component:2 here:2 contemplate:1 objects:1 others:1 alone:1 quite:1 change:1 deduced:1 obtained:3 study:1 composing:1 through:2 within:1 published:1 conveniently:1 history:1 composed:3 emerge:1 tasks:2 useful:1 secure:1 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quant-ph9505019.txt |@word sci:1 consider:4 results:2 grateful:1 expressions:1 alamos:5 finally:1 present:4 sent:1 very:2 trouble:1 condition:2 transmission:2 large:1 solved:2 vector:2 small:2 work:1 trend:1 past:2 second:6 even:1 errors:2 rate:1 selected:1 nec:2 above:2 new:2 satisfy:1 mel:1 address:2 along:11 change:2 extreme:1 sending:1 sender:1 published:1 bob:29 spatially:1 secure:8 requiring:1 polarizers:2 chaum:1 langlois:1 counts:1 alamitos:1 cheating:5 eψ:2 would:1 insecurity:1 eφ:4 chooses:1 therefore:1 selects:2 until:1 more:1 separated:1 initiated:1 foundations:1 must:1 me:1 none:1 reveals:1 tokyo:1 science:1 pretend:4 learn:3 following:4 dec:1 example:2 ma1:12 stated:1 expanding:4 bennett:3 india:1 states:11 indicates:2 assumptions:6 honest:1 occur:2 axis:11 preferably:1 information:3 goal:1 sixties:1 symposium:1 parameter:3 sin:8 brassard:5 product:2 may:2 insecure:1 after:2 applications:2 tries:1 third:5 whenever:8 complexity:5 so:1 fundamental:1 keeps:2 first:7 order:1 least:1 ith:5 indeed:1 over:1 satisfied:3 paper:2 committed:9 japan:2 ieee:4 its:1 before:2 thank:1 chosen:8 lo:3 cryptology:1 late:1 permanent:2 systems:1 decades:1 correspondence:1 motivated:1 safe:1 they:2 now:7 instances:2 always:1 crypto:1 sufficiently:1 entirely:1 schemes:1 reduce:1 σ2b:4 society:1 obtains:1 measure:1 quantum:16 really:1 shown:1 since:1 research:2 particles:13 performs:1 correct:1 m2b:4 34th:1 weaknesses:1 standard:1 york:1 jozsa:1 computers:1 success:1 feasible:2 initiate:2 sigact:1 there:1 features:1 probability:4 succeeds:1 email:1 approximately:3 impossible:2 guess:1 similarly:5 eqs:1 system:1 relations:1 attack:2 scheme:1 store:5 authors:1 perfectly:1 wiesner:2 see:2 matter:1 crepeau:3 were:1 toward:1 result:2 comput:1 angel:1 outstanding:1 mind:2 randomly:2 tells:5 relatively:1 angle:7 efficient:2 able:1 note:3 instance:1 build:1 measures:4 reach:1 most:2 pair:5 coin:1 measured:1 why:1 salvail:1 later:1 detectors:1 principle:1 show:3 discovered:1 based:4 should:4 only:5 ardehali:3 achieve:1 do:3 his:4 cryptography:3 σ1a:4 international:1 arxiv:1 summary:1 she:24 shi:1 pioneering:1 set:1 unpublished:1 depends:1 computer:2 usefulness:1 eliminating:1 discussions:1 subject:1 cheaters:4 review:2 state:19 between:2 tens:2 conditions:1 checks:4 check:1 terms:6 opening:2 jp:1 however:5 news:1 cos:12 many:2 uncertainty:1 according:1 against:9 etc:1 arbitrarily:6 co:1 cl:1 simple:2 period:5 oblivious:1 considers:2 conference:1 pp:3 generality:1 due:1 been:4 secret:2 azimuthal:5 expected:1 ph:5 m1a:4 direction:3 enable:1 θn:2 spin:15 protocols:6 unproven:1 expanded:1 value:2 will:2 suppose:1 error:1 misalignment:1 annual:1 thus:1 primitives:3 technology:7 any:3 quant:5 φi:19 several:2 φn:1 used:1 uses:1 recent:1 proceed:1 unconditionally:1 epr:17 without:1 laboratories:1 protocol:17 proposed:5 being:2 tossing:1 obtain:4 useful:1 previous:1 kanagawa:1 preprint:5 had:10 easy:1 iφ:2 sagamihara:1 march:2 rules:1 unlimited:4 possible:1 dark:1 entangled:4 press:1 using:2 bit:26 like:1 helpful:1 particle:17 signal:1 alice:26 steps:2 arbitrary:1 security:5 spins:2 therein:2 deal:1 sequence:2 sends:1 some:1 happens:2 provided:1 proceeding:3 breakthroughs:1 measurements:1 does:4 eliminate:1 proc:1 demonstrated:1 who:3 run:1 power:4 problems:1 processing:1 mayers:3 bangalore:1 rearranging:1 about:3 cosθ1:4 accepts:1 practical:2 commit:1 primitive:1 previously:2 commitment:20 down:3 variable:1 references:3 elementary:1 her:4 transfer:1 tama:1 long:7 los:6 way:2 was:2 opens:1 interest:1 smolin:1 jun:1 mb1:7 mb2:5 he:2 made:1 up:4 us:1 tell:1 demonstrate:1 problem:1 similar:1 agree:3 mechanics:2 wants:6 computing:4 abstract:1 measurement:3 am:1 θi:34 chau:2 flight:1 quantph:1 archive:5 again:1 no:2 corporation:1 when:6 reality:1 polar:5 briefly:1 describe:2 prepares:2 cryptographic:1 microelectronics:1 time:7 requires:1 decision:1
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quant-ph9505020.txt |@word represent:2 concept:1 customary:1 remarkable:1 four:4 eds:1 entropy:25 shimony:1 follow:1 expressions:1 content:1 calculate:1 tr:1 nonlocal:25 under:3 stochastic:1 applied:2 supported:1 amplitudes:1 very:1 void:3 wave:1 orientations:6 difference:7 condition:6 leads:2 randomness:16 presented:3 transmission:11 large:2 convenience:2 coincidences:1 indices:1 eigenvalues:2 warszawa:1 optics:1 work:1 za:1 fold:3 second:2 value:3 greenberger:4 linear:5 even:3 established:2 what:3 incompatible:3 sum:1 axes:2 expressed:1 experiment:2 goes:1 new:4 acknowledgments:1 satisfy:1 edited:1 degree:1 respectively:2 never:3 answers:5 test:1 address:1 directions:6 based:8 along:2 strong:2 violate:1 obtained:2 involved:1 study:1 studied:1 lr:3 makes:4 involves:1 plotted:3 composed:2 named:1 projection:4 marginal:4 polarizers:13 outcomes:14 addressed:1 decrease:1 apply:1 total:2 unit:1 plot:4 confidence:2 projector:2 usa:1 commun:1 probabilities:26 positive:5 predictions:2 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quant-ph9505021.txt |@word circles:1 illustrating:1 pendulum:1 show:1 over:1 packet:1 maximum:1 symbols:1 sphere:1 radius:2 same:1 momenta:1 angular:1 tho:18 shown:1 strength:1 classical:2 bottom:1 chosen:1 dashed:1 thick:1 range:1 coordinates:1 li:1 equal:1 fig:5 ensure:1 circle:1 integrated:1 ls:4 function:1 case:3 exchange:1 trajectories:1 but:1 wave:1 step:1 plane:1 equidistant:1 marked:1 during:1 line:2 spin:4 tls:35 down:1 interaction:1 solid:1 up:1 orbit:4 motion:2 si:1 steps:1 thin:1 time:3 top:1
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quant-ph9505022.txt |@word partial:2 consider:1 reinhold:1 instantaneous:1 localized:1 compact:1 inverse:1 tr:5 finally:1 those:2 norm:4 applied:1 orthogonal:3 wigner:3 wave:4 corollary:1 isomorphism:1 every:9 experimentally:1 exact:2 condition:2 dim:1 hamiltonian:1 t2:14 solution:1 t1:30 large:2 vector:3 shows:2 challenge:1 bd:4 consistent:5 measurable:1 cosh:1 imply:1 value:2 dynamics:21 implemented:2 linear:18 even:3 what:2 nonlinear:30 invertible:2 section:1 selected:1 mycielski:1 new:1 ˆj:2 ˆk:1 clausthal:2 full:1 component:1 here:3 groups:1 others:1 affiliated:1 strong:2 equations:1 change:1 orthomodular:1 institute:1 vectors:2 leaving:1 suggests:1 bd1:3 bd2:2 suitable:4 changes:1 uniquely:2 via:1 projection:2 family:6 explained:1 expect:1 apply:1 inc:2 additive:2 eψ:2 commun:1 probabilities:1 positive:3 negative:1 ψt:10 properties:2 ψj:1 ψk:2 bialynicki:2 call:1 therefore:2 taken:1 conservation:1 becomes:2 operators:3 odinger:27 everywhere:1 known:4 foundations:1 hold:2 iii:3 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quant-ph9505023.txt |@word searle:12 writings:1 saves:1 consists:5 localized:2 whose:1 aggregations:1 presents:1 under:5 ontological:12 activation:1 rise:1 every:1 conceive:1 solution:2 unrelated:1 unconditioned:1 force:1 pragmatic:1 consistent:1 direct:1 likely:3 implemented:2 even:4 incompatible:2 above:6 new:14 ever:1 consisting:4 evolving:8 simultaneously:4 notions:1 never:1 here:9 met:1 represented:13 obtained:2 employees:1 approaches:2 stressed:1 changes:3 attractor:1 divide:1 explained:7 objectively:1 psychological:9 univ:1 landscape:1 spoke:1 would:15 chooses:1 noting:1 call:2 therefore:5 strike:1 type:1 until:3 separated:1 berlin:1 hole:3 hold:1 must:19 me:2 room:1 rights:1 pursue:1 work:5 theories:1 macroscopically:1 neurons:1 concepts:2 akin:2 my:3 example:11 give:2 involve:1 want:1 cites:2 end:4 provide:4 feature:4 very:5 imbedded:1 significance:1 answer:3 symposium:1 ordinary:1 actuality:3 description:9 replacing:1 earlier:2 predicated:1 law:1 meaningful:2 heidelberg:1 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quant-ph9506005.txt |@word limited:2 consider:2 rev:4 elektron:1 brownian:3 results:4 leads:5 scalar:4 supplement:1 computation:1 expressions:1 lptens:1 reynaud:6 whose:2 certainly:1 dimensionality:1 violate:2 paris:3 characterises:2 braginsky:1 γt:1 presents:1 preserved:1 th:2 under:3 include:1 kν:1 applied:6 amplitudes:1 very:2 frequencies:11 induce:1 electron:5 ξqq:2 sensitivity:1 aµ:3 affect:2 associated:1 difference:3 matrices:2 condition:3 four:1 transmission:1 positions:4 ford:1 large:1 solved:1 vector:2 indices:1 relation:9 optics:1 commented:1 upper:2 rohrlich:1 force:53 version:1 cff:2 consistent:3 direct:1 modified:1 second:1 noise:2 further:2 d4:2 linear:4 even:2 sud:1 stands:1 deeply:1 sum:1 lhomond:1 uniform:1 consistently:1 transfered:1 goes:1 sup:3 new:2 propre:1 erieure:2 χf:9 satisfy:5 exchange:2 ma:1 component:1 here:1 agreement:1 behaviour:1 cours:1 objects:1 coupling:1 equations:2 appears:1 obtained:6 delimited:1 wesley:1 leaves:1 studied:2 allows:2 kubo:1 survey:2 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quant-ph9506006.txt |@word premi:1 consider:1 lagrangian:2 elektron:1 global:1 brownian:1 results:2 exceeding:1 leads:5 eds:1 scalar:3 computation:3 expressions:6 contributions:3 lptens:1 reynaud:7 whose:2 inverse:1 depend:1 paris:3 equivalence:6 environment:1 compensate:1 th:2 stochastic:1 characterised:3 very:3 frequencies:14 rise:2 induce:2 wave:1 electron:1 govern:1 resonant:1 verh:1 matrices:2 four:1 cmm:4 level:1 diverging:1 positions:1 mb:2 mirror:15 small:3 optics:1 der:1 smaller:2 force:13 cfi:2 consistent:3 direct:1 approximation:5 located:2 zero:3 noise:3 enhancement:1 equal:1 further:3 implemented:1 linear:5 spectral:3 sud:1 appear:1 sum:1 lhomond:1 consequent:1 reminiscent:1 consistently:1 sup:3 new:4 propre:1 contributes:2 erieure:2 satisfy:5 never:1 component:1 here:1 governing:1 directions:1 equations:5 appears:2 obtained:8 incoming:7 exemplified:1 wesley:1 involved:2 changed:1 δqi:1 δqj:4 stressed:1 resonance:3 conveniently:2 spacetime:1 involves:1 emerge:1 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quant-ph9506007.txt |@word limited:5 consider:2 brownian:1 results:2 leads:1 eds:1 quadrature:2 lptens:1 reynaud:6 χf:4 depend:1 paris:3 technique:1 braginsky:3 environment:1 finally:2 squeezing:1 th:2 under:4 kλ:3 stochastic:1 characterised:2 eikonal:1 case:2 kρ:2 very:1 frequencies:12 rise:2 induce:5 wave:8 endpoint:2 govern:1 affect:3 difference:1 dominate:2 riemann:3 level:3 positions:6 bypassed:1 math:1 small:1 gauge:2 optics:2 round:1 smaller:3 2k0:2 hk0:3 approximation:1 zero:3 further:2 dynamics:1 port:1 theory:2 spectral:3 sud:1 adds:1 appear:2 giving:2 sum:1 beaten:1 lhomond:1 consistently:1 sup:3 new:1 propre:1 increasing:2 erieure:2 consisting:1 mp:3 coefficient:1 led:1 exchange:1 mω:5 component:1 here:1 directions:1 along:2 quite:1 equations:1 deduced:1 obtained:3 shift:2 vectors:1 amount:1 resulting:1 action:2 resonance:1 linearised:2 fourier:2 changes:1 polonica:1 plenum:1 total:1 univ:1 planck:12 unit:2 undergone:1 takes:1 positive:1 give:1 arms:1 jaekel:6 france:3 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quant-ph9506015.txt |@word gw:7 limited:1 vorticity:1 remarkable:1 rev:6 magnetic:1 results:2 produce:1 existing:1 four:1 scalar:11 microwave:2 fig1:1 sci:1 denotes:1 compact:1 inverse:1 terms:3 schiff:1 integral:2 ott:1 technique:1 tr:16 nonlocal:2 ıa:1 tanaka:1 must:1 eikonal:1 ın:1 fond:1 orthogonal:3 very:6 dokl:1 wave:30 algunos:1 every:1 selleri:1 experimentally:2 emphasized:1 sssr:1 exact:1 special:3 notations:1 europhys:3 obvious:1 level:5 transmission:1 die:1 list:1 solution:1 discrete:2 vector:8 small:1 div:2 optics:3 equation:4 configurations:2 rohrlich:2 neighborhood:1 imbert:2 ten:1 dealing:1 direct:1 second:2 noise:1 displays:1 pass:1 chem:2 linear:1 even:3 nothing:1 what:1 plays:1 a66:1 d2:1 section:3 brief:1 expressed:1 thickness:1 current:1 axial:1 version:2 sobre:1 boundary:1 new:3 a336:1 waveguide:1 method:3 filled:1 satisfy:1 full:2 evanescent:4 ibid:2 divergence:1 never:2 here:1 understanding:1 operating:1 ansatz:1 making:2 concluding:2 const:2 along:1 standard:1 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quant-ph9506023.txt |@word externally:1 concept:1 sci:1 rev:4 magnetic:1 dynamic:1 results:3 bφ2:1 go:1 putterman:5 expressions:1 research:1 contributions:1 bremsstrahlung:3 calculate:1 flash:2 behave:1 stable:1 spec:1 sound:3 conjecture:1 returned:1 far:5 tends:1 intriguing:1 induce:1 wave:2 every:1 stays:1 experimentally:2 bubbles:1 feeble:1 condition:1 hamiltonian:6 turns:2 solution:1 t0:2 leave:1 sand:1 vector:2 dealt:1 small:3 inspection:1 equation:2 dis:1 claudia:1 application:1 work:1 eberlein:6 occurrence:1 periodicity:1 hindered:1 estimates:1 direct:1 pulse:4 200nm:1 surrounding:2 zero:11 further:1 dynamics:1 chem:1 remarkably:1 shining:1 spectral:6 index:5 appear:1 clock:1 trivial:1 section:1 dr2:1 remain:1 uniform:2 experiment:2 abt:1 above:5 judicious:1 values:1 body:4 barton:3 led:1 degree:1 component:2 here:2 atoms:2 water:12 cylindrical:1 compressed:2 groups:1 others:1 consideration:1 dissipated:1 strong:1 equations:1 stresses:2 great:1 identifiable:1 involved:1 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quant-ph9506025.txt |@word ψcs:2 consider:1 squared:1 focus:1 leads:1 eds:2 quadrature:1 terms:3 alamos:2 program:2 squeezing:2 those:2 under:1 alberta:1 thorne:1 include:1 division:1 zhang:1 very:1 p0:3 wave:5 nieto:12 2rs:1 groups:1 annihilated:1 exits:1 hamiltonian:4 suffices:1 michael:1 t0:1 large:1 math:7 science:1 optics:1 noted:1 2k0:2 katriel:5 zj:2 zk:1 dealing:1 consistent:2 sin2:4 za:2 cosh:10 zero:1 rigorous:1 further:1 odd:4 canonical:4 even:6 will:2 what:1 t2n:1 giving:1 sum:1 annals:1 goes:1 new:3 occupation:1 method:10 satisfy:4 confluent:1 here:3 understanding:2 cos2:3 sinh:7 investigating:1 concluding:1 path:1 z1:2 z2:1 obtained:4 exemplified:1 involved:1 study:5 studied:5 drt:1 commonly:1 round:1 suggests:1 published:1 complicated:2 makes:1 useful:1 hermite:1 plenum:2 malkin:1 names:1 circumvent:1 use:2 theor:1 proceed:1 would:2 analytic:1 positive:1 pedagogical:1 their:2 ψn:1 therefore:9 calgary:2 theoretical:1 more:5 lowering:2 operators:22 odinger:1 ip0:3 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quant-ph9506026.txt |@word secondly:1 sci:1 consider:4 magnetic:1 global:1 results:3 leads:1 eds:1 follow:2 looking:1 aligned:1 depend:1 universe:1 paris:1 subjected:1 deterministic:3 environment:1 summarised:1 those:1 th:2 under:1 stochastic:1 divergent:4 case:2 very:1 wave:9 affect:1 condition:4 hamiltonian:3 positions:1 notes:1 t2:1 solution:2 integrated:1 small:1 force:1 direct:1 literature:1 second:1 further:1 dynamics:3 theory:7 even:4 appear:1 apparatus:2 giving:2 interactions:1 above:2 kicked:17 never:1 here:4 atoms:1 behaviour:7 possibility:4 situation:3 along:1 equations:3 implicit:1 obtained:2 involved:1 studied:1 allows:1 simultaneous:2 uniquely:1 4a2:1 extra:1 substitution:2 highly:4 stern:3 summation:1 apply:1 causal:1 linearly:1 readily:1 plot:4 conventional:1 would:1 found:1 next:1 classically:4 ψn:1 therefore:1 taken:4 themselves:1 type:1 separated:1 entrance:1 formally:1 started:1 becomes:2 odinger:3 particular:3 known:2 cases:2 iv:1 iii:1 evolves:1 springer:1 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quant-ph9506027.txt |@word sci:1 consider:3 pointing:1 rev:2 varying:1 alternatives:3 splitting:2 follow:2 depend:1 paris:1 subjected:4 deterministic:2 passage:2 environment:2 present:1 under:2 circumstances:1 divergent:1 division:1 labels:1 orthogonal:3 far:2 wave:13 every:1 mixing:1 experimentally:1 condition:1 splitter:1 randomness:1 level:1 transmission:1 positions:3 developing:1 convenience:1 small:1 consistent:1 second:2 notwithstanding:1 further:2 dynamics:2 functioning:1 employ:2 nonlinear:2 apparatus:2 selected:1 wavelike:1 above:3 new:1 acknowledgments:1 contrast:2 coefficient:1 kicked:7 component:2 here:3 behaviour:21 explore:2 separation:2 active:1 path:5 along:2 equations:1 arena:2 chaotic:10 study:3 ignoring:1 resulting:1 makes:1 broglie:1 followed:1 search:1 merely:1 outcomes:2 pp:1 stern:1 univ:1 takes:1 would:6 remains:2 next:2 few:1 taken:1 themselves:1 type:1 more:3 introducing:1 started:1 becomes:2 odinger:2 virtue:2 particular:1 foundations:1 potential:4 must:6 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quant-ph9506028.txt |@word represent:1 concept:3 partial:3 consider:3 pti:1 similarity:1 crucial:3 global:1 results:3 illustrated:1 eds:4 proposition:18 entropy:1 ρt0:3 lahti:1 follow:1 expressions:2 research:1 reasoning:1 issues:3 ptj:2 devoted:1 whose:4 certainly:1 tr:6 tp:1 tn:7 finally:1 those:3 ti:4 analogous:2 circumstances:3 worth:1 xti:2 ingredient:3 potentially:1 proved:1 summand:1 takes:1 orthogonal:2 very:3 bilinear:1 choice:1 suggesting:1 every:1 difference:2 matrices:1 condition:1 generalised:22 entire:3 unlike:2 hamiltonian:2 supports:3 notes:1 t2:9 t0:9 t1:13 singularly:1 discrete:1 vector:5 progress:2 manifestly:2 glued:1 noted:3 programme:5 occurrence:1 htn:4 consistent:13 direct:2 dimensional:3 generalisations:1 second:1 perspective:1 further:2 copenhagen:1 canonical:10 even:5 synthesis:1 what:3 zinn:1 developed:1 appear:5 wide:3 incompatible:3 trivial:1 specification:1 selected:1 while:1 find:2 current:1 version:6 suspect:1 inferences:1 goes:1 new:6 viii:1 full:2 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