text
stringlengths 0
190k
|
|---|
quant-ph9906073.txt |@word limited:4 similarity:1 desirable:5 four:49 entropy:9 anticorrelated:5 consists:1 equiprobable:1 whose:3 u3:1 violate:1 contained:1 presents:2 groundwork:1 swap:1 under:10 conjecture:12 intriguing:1 ble:1 p1:9 every:2 affect:2 believed:2 basics:1 cause:4 solution:7 convenience:5 vector:10 math:1 mp2:1 force:1 specially:2 deutsch:9 consistent:7 α2k:1 trusting:1 pulse:1 feasibility:3 merkle:2 second:20 implemented:8 machines:1 subchannel:6 even:63 nel:1 errors:63 ˆy:1 specification:3 selected:2 while:33 decoding:4 above:20 new:41 increasing:2 told:3 coefficient:1 notions:1 never:3 equals:2 here:10 represented:9 entire:1 logarithmic:1 calculate:31 obtained:41 luther:2 property:5 study:2 changed:1 approaches:3 ignoring:2 calculations:2 permit:2 advantages:2 suitable:2 changes:4 ρx:9 secure:58 classification:1 explained:9 purifying:2 replace:5 rχ:2 sloane:1 rρ:1 total:17 univ:2 unit:6 opponents:1 cheating:15 would:26 motivate:1 chooses:12 leaks:1 call:12 therefore:23 type:25 tell:4 preserved:2 separated:2 successful:4 naive:5 wars:1 aware:1 phone:1 reversible:1 excellent:4 hold:4 must:53 rζ:1 word:7 permits:1 work:42 mi:2 itself:2 concepts:2 example:26 give:4 bennett:23 organized:1 implementations:16 involve:1 indicates:2 want:3 times:13 advancing:1 absolute:1 preferably:1 end:2 recovery:1 carriers:3 provide:21 verify:6 feature:1 recovers:1 machine:5 how:17 answer:2 gate:16 ordinary:1 preferable:2 brassard:19 description:1 replacing:3 ancilla:7 insecure:5 after:23 minimized:1 lab:1 wrong:16 summarize:3 law:2 parallel:4 types:4 attempt:7 effective:8 ρnm:1 summing:2 complexity:4 maintain:2 algorithms:1 ultimate:6 correlation:2 operate:3 order:24 operations:9 restriction:2 interpretation:1 over:27 inconclusive:19 expects:1 thesis:12 experimentally:1 fidelity:13 before:16 manuscript:1 fit:1 personal:6 writing:2 better:22 distinguishing:5 fig:8 hidden:7 easier:1 overcome:5 maximal:7 them:71 affected:4 combination:2 prevented:1 safe:1 heinzen:1 steane:2 effects:2 they:78 represents:1 meas:1 reasonably:1 alternately:1 reasonable:5 each:135 went:3 side:2 mean:3 signing:1 schemes:43 financial:1 principles:3 used:109 combining:6 laboratory:4 extract:4 projections:5 divincenzo:7 network:26 restricted:8 crucial:8 particles:74 re:2 mζ:1 conjectured:1 diagonalized:2 got:4 rn:8 ri:1 interchanging:1 numerical:1 log2:4 linear:4 assured:1 gardiner:1 given:46 free:6 standard:27 vazirani:2 assures:1 corrects:3 estimate:6 muller:2 r2:4 created:5 messages:6 days:1 tolerant:6 creates:10 iae:1 isi:1 disturbed:2 arccos:1 corrections:2 generalizations:3 purpose:2 already:13 features:1 coding:6 rank:2 qkd:1 channels:35 fantasy:3 2a2:1 another:28 electronic:1 hood:1 toy:1 similarly:1 29th:1 amsterdam:1 needed:2 rates:2 too:10 postulate:1 john:4 listen:1 enhancing:2 tool:6 leaking:1 direct:1 α2n:1 somewhat:1 shortly:1 maintaining:2 distance:24 showed:1 princeton:2 approximations:2 zero:29 1l:3 preparation:6 matter:1 solomon:1 unconditionally:1 tion:1 1n:5 minus:3 extracting:1 boston:2 modern:1 mind:3 raw:8 seen:7 seem:1 unaffected:1 tells:15 contents:1 relatively:1 estimated:1 mermin:3 person:2 thoroughly:1 thorough:3 transmit:9 effectiveness:8 reversed:9 decoheres:1 optimizes:6 shall:40 object:1 simplify:4 optimized:2 ensure:1 letter:9 phase:3 coil:1 coin:1 bsc:8 don:1 treats:1 calculated:19 bracket:1 tech:2 principle:15 hamming:14 sum:6 came:1 dover:1 incorporate:1 signatures:1 distances:8 lewis:1 meetings:1 probe:20 implying:1 attempts:6 solutions:4 subtle:1 analogue:1 randomize:2 elect:4 just:5 implementation:3 explain:12 announce:1 adequate:2 organizes:1 do:30 erasure:3 dm:2 neumark:1 establishes:1 cryptography:93 yielded:1 despite:3 unfortunately:12 method:4 bad:2 34th:1 release:2 transporting:1 erroneous:1 reference:1 clarified:3 sensitivity:2 richer:1 detection:2 pads:1 cloning:9 holding:1 discussions:6 disturbing:2 ainit:3 rarity:2 best:11 techniques:13 said:5 capacity:6 tensor:8 away:10 ensures:1 yet:17 symmetric:40 secured:1 simplest:7 c2k:17 caves:5 approach:22 preserve:2 terms:32 extend:4 nature:2 weak:25 however:40 wi:5 wt:1 unnormalized:1 news:1 improve:8 suggested:28 received:11 cos:69 cot:1 fault:6 against:75 planned:1 receives:8 receiver:19 distinction:1 qubit:33 0n:4 col:2 2nh:1 appeared:2 nˆ:1 hers:1 unprotected:1 polynomial:13 oblivious:9 trust:2 conference:2 puts:1 basis:104 trapdoor:2 three:21 been:9 much:65 interest:5 basic:13 expected:6 formalized:1 derives:1 θj:3 digits:1 deeper:1 attacker:1 coherent:25 spin:22 unproven:5 applied:6 exception:1 miquel:1 remaining:3 aim:1 near:5 suppose:18 applies:9 vernam:1 leaves:5 procedure:8 schumacher:3 iy:2 seven:4 2βj:1 memoryless:1 ip:2 ii:1 ij:3 im:24 interacts:2 id:6 trusted:9 perform:31 suggest:18 make:9 quant:6 split:1 mixtures:1 several:14 infeasible:2 independent:17 i2:26 hand:12 normalization:1 niu:1 weakly:3 kept:8 scenario:2 programs:1 reprinted:1 epr:35 academic:1 simulated:1 telephone:2 claims:4 investments:1 left:5 protocol:51 proposed:4 3p2:5 distribute:3 3p4:1 ideas:1 identify:9 transforms:1 human:1 facts:1 yamamoto:1 eigenstates:2 projection:19 adding:1 eli:6 monitored:1 infinitely:1 had:6 evidences:2 transformed:3 projects:5 easy:9 technological:4 accumulating:1 tolerable:1 opt:5 usable:1 advances:2 disagreement:1 possible:74 spanned:4 possibly:5 highly:2 advanced:3 apart:4 bistable:1 performing:21 alice:202 specific:8 private:1 states1:1 arbitrary:2 invaluable:1 security:118 ivanovic:1 right:4 theorists:3 deal:10 people:5 sends:26 successfully:1 confusing:1 ignore:2 dense:1 fourth:1 linearly:1 unavoidably:3 steps:8 shamir:2 pose:1 ψx:2 translated:1 binomial:1 substitution:2 bangalore:1 permitted:22 proceed:1 chapter:60 limitation:1 attacks:87 ranges:1 o:34 distinct:1 plus:4 spins:6 commit:6 slightly:1 raised:3 presence:2 wineland:2 obtaining:4 bound:17 combine:6 down:4 lies:1 raises:2 old:3 reducing:6 methods:3 rely:5 compression:1 waits:1 amazingly:1 suffice:1 initial:11 available:13 transform:1 why:2 way:39 m1:1 was:65 iˆ:4 decoded:1 singleparticle:2 form:17 piron:1 concatenated:1 differences:2 conclusively:3 encodes:3 subchannels:1 failure:1 encoded:12 removed:3 true:3 lncs:5 c2γ:2 versions:1 inside:1 attached:1 distinguishability:9 devices:34 until:2 dordrecht:1 unanimous:2 attaches:3 jauch:1 b1:4 promises:2 adopt:2 guesses:3 zeno:2 computing:18 request:9 abstract:3 proven:17 evidence:3 peres:17 proves:1 exist:6 φabc:3 distributions:2 check:4 physical:6 nk:2 nm:1 no:52 whereas:1 tossing:1 goldreich:1 reality:5 composite:1 factorizable:1 unambiguously:3 role:6 ambitious:1 papers:3 test:9 intend:1 superposition:2 phoenix:1 models:3 preceding:1 uniformly:1 transported:1 palma:2 parities:15 faster:4 assume:15 together:26 reception:1 time:55 n1:1 n2:17 1st:1 logarithms:1 concept:2 managed:1 remarkable:1 separates:1 focus:3 ρaµ:1 roy:2 manages:1 computation:17 certainly:4 amplification:82 technique:8 environment:6 finally:9 analogous:6 string:88 advantage:7 orthogonal:46 keeping:6 choice:12 trouble:1 exact:6 discovered:1 impressive:1 solves:2 level:21 did:4 accidentally:1 leave:4 solved:16 recall:4 h2n:2 prevent:1 mn:2 says:1 securely:1 prediction:2 sign:7 sθ1:2 sθ2:2 sθ4:2 dev:1 port:1 repeaters:5 adds:1 appear:2 axes:9 shares:2 current:2 goes:1 lifshitz:2 shared:9 unrestricted:1 satisfy:1 ˆp:3 lange:1 understanding:1 cos2:5 groups:3 kilometers:5 alone:2 along:8 appears:7 change:13 sending:4 noticeable:1 popescu:2 vectors:13 step:12 commonly:1 ineffective:1 suggestion:7 usually:18 bob:221 genuinely:1 tasks:6 useful:23 extra:1 inducing:3 merely:1 prefer:2 logical:4 eiφj:1 randomizing:2 inverses:1 additive:2 working:7 prove:21 positive:12 visit:1 predictions:2 emits:1 live:1 going:2 memory:68 encode:10 scope:2 theoretical:3 today:3 introducing:1 share:5 acceptable:3 eiφ3:2 clue:2 cases:25 effort:2 easiest:1 logarithm:3 valued:1 ibm:1 collision:2 originally:1 focs:4 modified:12 eavesdropper:39 fock:2 values:8 hope:2 following:17 modifies:1 arrive:4 claim:2 figure:2 predict:2 expanding:1 permutations:1 substring:5 celsius:1 performed:21 allowed:3 counting:1 distinguishable:4 occur:4 tremendous:1 redundancy:6 requirements:4 sphere:6 fortunately:4 s2:55 discussion:16 s4:20 write:8 till:8 pure:83 optimal:114 parameter:3 secures:1 inputs:2 product:12 huge:5 may:30 fed:1 applications:8 produce:4 designed:7 improving:8 representations:2 destructive:1 data:49 eighth:2 raimond:1 natural:5 succeeded:2 whenever:4 maybe:1 approximation:2 purify:1 explicit:4 yielding:1 purification:20 so:51 block:25 ˆz:1 sc:17 definitions:1 talk:2 typical:2 exclusive:3 acts:2 noteworthy:1 indeed:13 mainly:7 soc:4 years:9 course:4 statistical:3 differs:1 peterson:1 still:45 ieee:13 mµ:2 derive:20 group:6 sγ:33 interesting:9 sα:5 decreases:2 forms:1 decreased:1 main:21 decryption:2 non:59 introduce:6 underneath:1 transmissions:4 equidistant:1 half:9 arriving:2 now:24 discuss:15 nor:4 term:13 equality:1 name:3 didn:3 crypto:7 establishing:1 possibilities:6 realistic:10 classify:1 ann:2 significantly:1 commuting:1 revised:1 breakthrough:2 year:1 approximated:1 eq:20 ep:10 tried:1 living:1 shown:11 space:23 furthermore:17 cancels:1 increase:4 transforming:1 seriously:1 investigation:2 turing:6 suggesting:5 formula:3 receiving:6 correct:31 shows:6 earlier:2 theory:31 seventh:1 possibility:19 quite:5 complicated:26 bayes:2 remainder:28 inevitable:1 care:3 advance:10 fixed:1 derivation:3 language:1 interacted:1 programming:4 honest:4 inverts:1 place:1 u4:1 βj:1 first:53 origin:1 intuition:7 fetched:1 symmetry:1 withstand:2 u1:1 2p3:4 huttner:11 simplified:4 long:36 directly:6 vote:2 impossible:5 message:10 open:5 size:6 interchange:2 little:2 necessarily:6 checked:3 unitarity:6 caught:1 1a:4 1b:3 bits:154 cite:2 gives:4 fraction:3 season:1 proving:6 tapster:2 criticize:1 undesired:2 representing:3 than:61 wide:4 impractical:3 third:4 wiesner:6 require:8 transferred:1 distill:3 future:20 were:35 outcome:2 published:2 3p3:1 correction:92 argument:9 generalization:6 say:18 recover:1 saw:1 any:136 computationally:5 efficient:9 aside:1 converges:1 note:21 equipment:1 potential:1 take:11 online:5 objective:1 davies:3 wonder:1 switching:2 channel:91 sure:3 trace:1 opposite:7 removes:1 price:2 keeps:9 drummond:1 formulae:1 pair:19 analytically:2 probes:34 especially:5 surprising:7 considered:21 average:29 later:22 implications:4 phonons:1 diagonals:1 typically:1 mabuchi:1 laws:2 langlois:1 shor:10 show:20 cheat:4 contemporary:1 sible:1 notations:2 spaces:1 fifth:1 realizing:1 frequent:1 ratio:1 ensembles:3 state:256 analytic:2 only:120 explicitly:8 equipped:5 robb:1 info:2 quantph:2 get:29 expectation:1 sss:2 satisfied:1 2mc:1 cannot:55 nearly:1 secondary:1 reveal:1 regarding:23 consist:2 podolsky:1 yield:14 summary:2 though:1 discussing:1 16th:1 ignored:2 eavesdropping:20 signs:3 bounds:13 relative:1 namely:4 ignores:1 impressions:1 uncorrelated:1 nonlocality:1 ability:13 fails:1 detect:2 enlightening:1 ways:9 review:4 definite:1 qubits:49 enough:8 between:59 geometric:1 reading:3 checks:1 αn:4 notice:2 vertical:1 originated:1 comp:6 points:1 concentrate:4 comm:1 jk:8 analyzed:2 come:1 repeating:1 implementing:4 many:48 according:7 contract:1 called:22 enabling:1 σx:1 concentrates:2 expression:5 comes:2 among:5 solving:1 overview:1 authenticity:1 pos:1 2αn:2 maurer:1 iterations:1 moreover:6 considers:6 considering:2 destroyed:1 combines:1 capable:1 encryption:2 absence:1 shortening:1 workshop:1 deposited:1 combined:4 prototype:7 hardly:1 wants:7 direction:12 enable:13 unsafe:1 dieks:1 formed:1 photon:4 observers:1 bms:6 observe:1 covers:1 irrelevant:2 those:6 case:141 hughes:2 engineering:1 teleport:2 guessed:1 promising:2 investigating:1 versus:4 coupled:1 characteristics:1 duplicating:1 middle:2 skipped:1 motivated:1 technology:14 binary:22 different:35 verified:7 assure:2 alphabet:5 paz:1 same:68 poincar:4 authentication:5 pad:1 arguments:2 constructed:5 events:1 investigated:5 assigns:1 closest:1 disadvantages:1 investigates:2 delicate:2 entanglement:12 changing:1 cr:6 relies:3 traps:7 zagury:1 largely:1 minimize:1 ccs:1 vaidman:4 severe:1 without:21 solve:7 mann:1 components:4 model:2 laboratories:3 ekert:10 ccc:3 gates:17 unsolvable:1 cj:1 being:13 generally:4 ci:2 rest:3 imprint:5 relevant:15 meekhof:1 aspect:2 diffie:2 blow:1 zoller:2 grouped:2 thinking:1 photons:13 cl:1 seems:4 except:3 lets:3 interested:2 treatment:1 versa:2 complements:1 real:16 aspects:1 around:1 read:1 mor:8 unveil:6 early:2 np:8 predetermined:1 listening:5 secrecy:1 world:5 accepted:3 correcting:2 mod:4 particle:56 identifying:1 collective:58 serves:2 discarded:1 benefit:5 either:30 always:18 output:13 stationary:1 reduced:12 satisfactory:1 laflamme:2 exposed:3 e2θ:1 conditional:2 respect:1 organizing:1 generates:1 provided:8 authenticate:2 dimensions:10 confirm:1 cavity:2 memories:25 kilian:1 adleman:2 provides:40 ψabc:1 refer:7 measuring:14 destroys:1 process:25 scientific:1 power:3 seconds:1 sixth:1 equivalent:6 communicate:2 mayers:17 broken:5 symp:5 exciting:1 throw:4 comparison:2 stations:10 aˆ:1 discussed:6 develops:2 acm:3 practical:17 mutually:1 stand:4 mixed:19 invested:1 ot:26 levitin:5 communication:34 ηj:1 itotal:10 accounts:1 determine:2 parties:1 operator:10 conceptually:1 nowadays:2 log:19 prepare:5 area:1 assumed:5 strictly:1 there:42 decode:1 start:5 symbiosis:1 lot:8 assumes:2 ago:3 complete:8 smolin:8 jun:1 delayed:1 sophisticated:4 suffers:2 aµ:2 technologies:3 trying:4 irreversible:1 amplify:2 pull:1 applying:2 arranges:1 subclasses:1 agree:2 obtains:10 strongly:5 ab:13 hellman:2 ai:12 certain:6 ak:1 describe:7 general:29 kimble:1 reliability:2 au:7 aw:5 av:7 corresponding:10 again:4 rosen:1 tight:1 deviation:1 helstrom:1 separate:6 includes:3 a1:13 a3:10 important:26 bounded:5 a4:2 suited:2 studied:2 included:2 conclusive:9 building:12 quantify:1 dyer:1 decoherence:6 starting:1 original:22 represent:3 epeau:6 sci:1 consider:29 duplicates:1 caused:1 lack:2 unique:1 generalize:3 c2:46 follow:4 expressions:2 denotes:1 reasoning:1 causes:2 duplicated:5 content:2 chain:1 subjected:4 equivalence:1 tr:9 program:6 protocols:13 th:19 activities:1 worse:2 straightforward:1 very:49 induce:11 resistance:2 reordering:1 decide:2 ln:23 difference:10 condition:4 leads:2 list:3 applicable:1 large:32 small:82 ten:1 english:1 renormalized:2 past:3 rate:66 design:4 pass:1 further:15 subscripts:1 what:8 xor:10 sub:3 deeply:3 section:72 brief:5 version:6 subspaces:2 utkenhaus:1 public:16 contrast:3 full:10 modify:2 answers:1 hours:1 b2n:1 inverse:2 operating:1 b2i:4 situation:7 directions:1 strong:9 equations:2 publishes:1 sender:7 nth:1 losses:3 allows:3 prior:3 amount:13 permutation:3 options:2 uniquely:1 via:8 followed:1 requiring:1 ask:2 analyzing:7 factoring:3 establish:4 select:1 conventional:2 flaws:1 takes:2 improves:5 probabilities:22 ψp:1 contains:13 comparing:3 ψm:1 taken:7 goldenberg:4 achieving:2 minor:1 more:90 knows:13 initiated:1 vl:7 operators:9 corrected:10 surprisingly:1 particular:8 known:27 foundations:2 presumed:1 none:4 include:2 science:1 equation:22 r3:3 det:3 intercepted:2 remain:6 paragraph:1 morgan:2 learn:15 abandon:1 strategies:1 beautiful:1 ions:4 compare:8 omit:2 impacts:1 stated:3 correctness:1 suggestions:3 accept:1 states:256 contradicts:2 numbers:5 sense:3 station:2 axis:15 information:352 needs:7 goal:9 rather:9 breaking:3 dismissed:1 influences:2 acta:1 centimeters:1 ensemble:2 simplicity:4 circuit:1 wiley:1 derived:14 tries:2 develop:3 horizontal:1 geometrical:1 concentrating:4 short:7 onto:18 register:3 broadcasting:1 negligible:4 fundamental:2 pay:1 sigact:1 helv:1 help:10 ith:3 developed:3 soon:2 distortion:6 held:1 paper:6 through:21 berthiaume:1 committed:3 existence:6 suffer:3 its:22 continued:1 encoding:9 actually:12 detected:3 parts:3 systems:23 might:41 good:4 return:1 reordered:1 oxford:1 2t:2 easily:12 finite:1 2r:23 fully:14 presented:13 uρu:1 infer:1 asher:2 2c:3 found:21 2n:35 2i:3 referred:1 cθ1:2 cθ2:2 england:1 weight:2 reduce:15 idea:11 slowdown:2 deterministically:1 extended:4 connect:2 measurement:118 quantum:568 operation:11 beyond:4 event:4 really:1 try:3 biham:10 discrete:4 robert:1 since:73 induces:13 projected:7 research:5 safety:8 denoted:6 aligned:1 induced:5 issue:11 occurs:2 fiber:2 belief:1 commits:1 confidence:1 guess:4 effect:4 labs:2 difficulty:1 reason:3 members:1 put:7 ash:1 beginning:1 generate:1 thrown:3 definition:6 pairs:25 benefits:1 v1:14 computers:11 exponentially:34 threat:1 consequence:2 throws:1 arose:1 reversing:1 probability:97 upper:3 sn:6 number:28 preservation:2 instances:2 done:42 least:8 mixing:1 stage:10 differ:3 temperature:1 introduction:8 leading:12 interact:2 unexposed:1 obtainable:1 assumption:21 statement:1 compromise:1 scheme:166 store:8 2x:2 imperfect:1 passed:1 recursively:2 part:5 signaling:3 focusing:2 alphabets:1 translation:1 believe:9 convinced:1 percentage:1 king:1 kind:1 wootters:7 fuchs:4 determined:3 contrary:4 recovered:6 treated:3 motivation:2 qpa:31 bitwise:7 randomly:4 conjugate:3 cumbersome:1 ρdm:3 orders:1 lie:1 generalizes:2 built:8 depending:3 self:3 interferes:1 extracted:5 internal:3 generalized:11 analogy:2 finding:7 2d:1 unperturbed:1 play:1 added:5 serve:2 measures:14 reach:1 singlet:38 most:29 significant:3 nothing:4 measured:13 achievement:5 stands:5 loopholes:1 salvail:2 clear:14 sometimes:4 cover:1 kn:1 dimension:1 braunstein:3 optical:2 clean:2 physics:5 attacking:2 favorable:1 thomas:1 cot2:1 converge:2 registers:2 relation:3 fine:1 find:26 impact:1 henceforth:2 technologically:2 transmitting:4 subsection:2 factor:9 ieb:1 his:26 dominant:4 gains:1 notation:9 dependent:7 zurek:3 resent:1 international:1 combinations:3 during:2 him:11 enemy:1 arxiv:1 stirling:1 factorization:3 investigate:5 stored:3 common:19 wrote:1 approaching:2 redefine:1 set:12 art:1 achieved:2 throwing:5 unpublished:2 lior:1 see:27 individual:16 close:11 sem:1 theoretic:6 analog:1 project:5 permuted:1 probable:4 currently:6 halves:1 various:25 pn:3 probably:7 subscript:1 conditions:3 supposed:1 knowing:1 recently:11 creating:5 missing:6 attention:1 vanishing:4 succeed:2 distinguish:8 both:55 enables:3 improved:4 reverse:1 hint:1 sensitive:4 connection:5 intercept:1 whole:3 finds:2 experimental:2 arbitrarily:2 point:6 simple:33 address:1 corresponds:8 community:1 dimensional:28 decipher:1 simply:2 likes:1 throughout:1 expensive:2 pr:1 worthless:1 described:20 raise:1 create:11 due:38 pc:2 secret:30 describes:4 pf:5 ensured:1 pe:67 pj:15 pk:11 ph:6 pi:1 meeting:2 pl:4 lett:35 lived:1 josza:2 wheeler:1 else:6 moment:2 whatever:1 lives:2 hughston:1 demand:4 assigning:3 p2:12 p3:8 p0:6 practicality:1 look:2 exponential:4 p5:1 solid:2 reliable:4 forgetting:1 substrings:9 optimization:1 replaced:6 error:272 dominic:2 2k:27 unitary:26 approximate:1 century:2 averaging:2 von:4 probabilistically:1 obstacle:2 monroe:1 lengthy:1 bollinger:1 anymore:3 shorter:4 rules:7 randomization:11 imoto:1 emphasize:1 multiplets:1 modification:1 proved:1 higher:5 development:2 literature:4 keys:9 eavesdroppers:1 levels:2 uses:41 user:17 recent:5 lower:2 task:12 pµ:2 analysis:39 concrete:2 simmons:1 machinery:1 convenient:1 organization:1 things:1 abilities:8 calderbank:1 shape:1 questions:4 using:122 regardless:2 alternative:7 letting:1 kluwer:1 conclusions:4 surprises:1 lempel:1 guaranteed:2 shortcut:1 signals:11 source:5 theorem:14 relevance:2 input:23 solvable:3 transformation:36 build:2 adversaries:2 demands:4 showing:6 unlimited:1 suffering:1 entangled:17 sanpera:1 integer:2 bit:210 translucent:18 rabin:1 modifications:2 lost:1 follows:11 signal:5 translates:1 separately:9 communications:2 continue:1 yields:18 popular:2 experimentalists:4 reduces:8 terminology:1 mathematical:4 neumann:4 absolutely:1 deposit:1 creation:3 some:78 back:1 understood:2 strongest:5 towards:2 b0:3 examples:9 b2:1 b3:1 scale:6 describing:4 decision:3 measurements:34 proc:19 prob:2 minimal:3 bc:12 bl:1 bm:6 processing:4 bi:17 bj:4 bu:2 bv:2 bp:7 major:1 hilbert:22 integers:2 anything:4 extending:1 tracing:3 deserves:1 bloch:1 restrict:2 computational:5 unnoticed:1 into:33 within:4 qec:17 appropriate:13 proportional:1 span:1 r2493:1 few:11 probabilistic:1 question:14 lond:4 fast:2 u2:1 forward:1 analyze:6 sections:6 opens:2 opponent:1 files:5 considerably:1 arise:1 registered:1 reed:1 line:3 observation:1 directed:3 intuitive:4 circuits:2 up:20 us:42 ui:6 verification:3 uj:1 similar:16 ki:2 gisin:4 bell:19 storing:2 constant:1 defined:11 influence:4 doesn:3 single:28 chau:1 defines:1 codes:27 sˆz:7 puzzling:1 sˆx:6 dashed:1 i1m:1 application:5 priori:3 electrical:1 eiφ1:2 eiφ2:2 elements:2 users:66 calculating:8 problems:26 prepared:9 meaning:7 allowing:1 prepares:2 structure:3 swaps:1 cryptographic:21 zbinden:1 independently:3 correlated:9 implies:6 algorithm:1 vice:2 required:27 calculates:3 incomplete:3 far:7 requires:9 having:11 once:7 code:78 partial:4 results:29 existing:21 eds:1 ρjk:4 2c2:2 adjustment:1 contributions:1 centers:17 issues:1 seemed:1 simon:1 knill:1 concerned:2 deterministic:19 send:11 suits:1 intensive:3 chapt:1 helps:1 excluded:1 fatal:1 sent:25 random:12 outside:1 continues:2 electron:4 wishes:4 putting:2 bounding:2 matrices:114 severely:1 transmission:34 trb:3 tre:2 eve:197 prototypes:2 deals:2 dealt:1 smaller:17 sin2:11 theo:4 odd:23 refereed:1 index:2 optimize:1 plays:1 opaque:3 3p:2 expressed:3 networks:11 access:6 experiment:1 3n:1 3l:1 construct:1 degree:1 exchange:7 respectively:12 commercial:1 teleportation:7 gilles:3 sinn:2 desired:22 objects:1 focused:1 lev:1 others:4 consideration:2 invented:3 remark:1 trans:3 2x2:1 receive:1 involved:1 larger:9 contradiction:2 suggests:8 resulting:9 rdm:6 implement:4 makes:1 delays:1 involves:1 transformations:16 scales:1 messengers:1 outcomes:2 expect:3 boolean:1 decrease:2 summation:2 apply:5 tools:1 imaginary:1 manipulate:3 use:119 refers:2 superpositions:1 remains:2 next:11 classically:2 doubling:1 noisy:10 optimizing:3 formally:3 started:6 becomes:8 occurred:1 haroche:1 normalized:6 actual:3 iii:1 alde:1 entangle:1 majority:2 account:10 bernstein:2 ρe:7 ρi:6 when:92 ρn:1 ρp:12 obvious:3 ρy:1 fulfill:3 proof:45 control:7 calculation:18 purposes:10 high:1 assumptions:14 something:1 tal:1 wonderful:1 tan:6 mix:1 feynman:1 holds:8 instead:24 sin:61 obeys:6 blocks:26 npe:2 inst:1 recognizes:1 multiplication:2 efficiently:3 realized:1 discusses:2 computations:2 light:3 lines:3 correspond:1 redundant:1 element:4 allow:4 divided:1 torino:1 aiken:1 produces:1 altogether:2 turchette:1 2sc:1 symbols:2 pulses:9 mentioned:4 perfect:31 underwater:1 complicate:2 teleporting:2 chosen:6 lo:1 h2:8 willing:1 degrees:7 choose:13 pergamon:1 defining:3 symmetrization:1 greater:1 practice:9 landau:2 mention:1 hands:8 day:1 dirac:1 verifying:1 university:1 tran:3 identified:16 sufficiently:1 magnitude:1 transmitted:37 trap:10 identifies:1 macchiavello:2 constraints:1 subset:1 doing:6 einstein:1 programmed:1 related:4 elementary:1 m0:2 books:2 computable:1 doubled:1 measure:24 our:83 special:6 out:9 matrix:35 res:1 rev:44 mφ0:1 mφ1:1 performs:24 postpone:1 suffices:2 announced:2 interactions:3 diagonal:17 completely:11 surely:2 york:4 anyhow:1 jozsa:6 retrieves:1 interaction:5 her:49 informs:2 determining:1 could:46 feasible:2 length:26 removing:1 hence:38 diminishes:1 deviates:2 randomizes:1 succeeds:3 powerful:6 randomized:1 ψxt:1 reached:1 precisely:1 quality:2 hiding:1 fascinating:2 privacy:82 ordering:1 unknown:6 system:46 their:51 attack:109 intermediate:1 siam:1 perfectly:6 final:61 townsend:5 low:1 eavesdrop:5 explanation:2 exactly:10 rsa:2 rivest:2 environmental:1 simulate:3 herself:2 holland:1 bec:3 distinguishes:1 depends:10 limiting:1 revzen:1 india:1 providing:5 distinguished:5 result:105 exhibit:1 unchanged:3 fail:1 need:15 north:1 demonstration:1 clearly:7 intercepts:1 angle:35 rearranged:1 dallas:1 studying:1 able:18 polarization:7 instance:19 ur2:3 subject:4 accuracy:1 unless:10 collaboration:1 who:21 plugging:1 intentions:1 cipher:2 connected:1 overlapping:10 representation:1 device:6 cloned:3 class:5 delivery:2 haifa:1 neighboring:1 urn:5 stronger:1 counted:1 looked:1 proceedings:1 mechanical:1 2sin:1 χn:8 superscript:1 normally:1 fact:18 gain:20 impression:2 agreed:4 charles:4 chapters:5 chuang:1 telling:1 longer:6 trivial:5 q1:3 q0:2 satisfies:4 q2:1 based:58 knowledge:13 should:14 bases:8 candidates:4 reorganizing:1 partially:3 local:1 achieve:2 exchanged:1 move:1 handle:1 means:8 syst:2 hopefully:1 overall:2 joint:25 legitimate:22 words:17 exchanges:1 timing:2 quantifies:4 areas:1 processes:4 determinants:9 c2n:2 influenced:1 optimally:2 europhys:1 qe:5 she:109 contain:4 including:7 qk:11 qj:10 nist:1 guessing:2 requirement:3 exists:6 correlations:12 computer:9 closer:1 nuclear:2 complementary:1 written:17 difficulties:1 identification:5 bruno:2 correctly:5 progress:5 neither:3 brune:1 barenco:2 reproduced:1 superior:2 importance:6 deliver:1 efficiency:10 sθ:33 2pe:4 key:179 probing:1 useless:2 problem:45 david:1 taking:3 gilbert:1 equal:29 fulfilled:1 etc:19 harvard:1 figures:2 estimation:11 otherwise:7 detailed:1 adjusted:1 unclear:1 cn:6 conclude:2 anticorrelations:1 cf:1 cirac:2 maximize:2 cs:8 leaked:1 quan:1 quit:4 singlets:13 estimating:1 addition:15 devise:2 yao:8 phononic:2 itano:2 waste:1 define:5 field:1 determinant:2 aj:20 controlled:5 route:1 sufficient:4 coherence:3 subspace:9 θei:1 angles:8 ours:2 last:2 c1:1 repetition:6 present:23 c4:21 multi:1 unlike:8 bb84:9 value:20 will:54 supply:1 vd:9 file:7 almost:12 vi:6 vk:6 thus:75 site:3 surface:1 helped:1 vr:1 vs:3 properties:6 claimed:2 inf:3 φp:12 perhaps:1 s2k:12 began:1 s2n:2 indistinguishable:1 enumeration:1 unity:1 became:1 pauli:2 largest:2 underground:1 party:3 φj:1 gets:11 φm:2 difficult:17 ball:1 logic:1 upon:21 mutual:63 v0:2 ion:16 v2:6 v3:2 sooner:1 taste:1 frequently:4 contribution:1 identity:1 keep:19 center:89 nevertheless:1 com:1 well:27 thought:2 sets:3 position:1 usual:1 less:21 accurate:1 obtain:37 lossy:2 purified:4 web:1 disturbance:6 bibliography:2 density:119 passively:3 realize:1 reasons:5 add:5 extends:2 developments:3 crack:2 usage:2 match:1 details:14 identical:13 tests:5 increased:7 checking:2 devised:1 execute:2 increases:2 know:18 press:7 immediately:1 loss:1 necessary:1 like:14 success:8 alternatively:10 ρb:5 extremely:6 loses:1 lose:2 become:8 works:10 page:4 accessible:5 parity:121 exceed:2 because:4 qed:4 classical:134 foreseeable:2 searching:2 unpredictably:1 choosing:11 proofs:5 happens:3 informationtheoretic:1 lead:5 literally:1 avoid:3 overlap:8 manipulations:1 does:43 assuming:7 chains:1 demonstrated:1 limitations:2 noise:21 obey:1 slight:2 journal:1 complication:2 expansion:5 cθ:35 although:12 yuen:3 cγ:32 cα:6 adversary:6 simpler:8 gained:3 deriving:7 about:24 rare:1 carried:4 extension:2 freedom:7 certainty:2 introduces:5 dependence:2 surge:1 a2:15 discard:4 introduced:2 projectors:1 equally:4 own:3 letters:4 previously:20 h3:1 commitment:23 h4:1 twostate:1 weather:1 forget:1 additional:17 whom:1 transfer:10 reduction:26 noticed:2 restricts:1 quanta:1 interferometry:1 function:20 tricky:2 barnett:1 repeater:1 hr:2 but:102 subjective:2 repeated:2 construction:1 hn:4 goals:2 highest:1 illustrative:1 he:49 made:5 compute:3 society:1 whether:23 wish:8 flip:2 tan2:6 placed:1 below:1 projecting:4 limit:7 demonstrate:3 distribution:87 minutes:4 cryptosystems:6 mechanics:13 povm:16 universal:2 contribute:4 remove:2 denote:5 interchanged:2 davidovich:1 functions:3 compared:5 variety:1 detail:1 other:90 compares:1 shannon:3 conclusion:1 repeat:1 rdms:8 june:2 chance:1 previous:22 bch:3 auxiliary:3 strings:48 portion:4 4k:7 understand:2 indirectly:1
|
quant-ph9906074.txt |@word represent:1 consider:5 ron:1 rev:4 results:1 four:10 montr:2 edu:2 consists:1 contributions:1 causes:4 amplification:1 calculate:2 producing:1 subjected:1 send:3 finally:1 protocols:1 fatal:3 sent:7 case:1 advantage:4 orthogonal:1 very:3 choice:1 affect:1 al4:1 exact:1 splitter:2 solves:1 level:6 shamir:1 eve:6 leave:1 small:5 noted:1 ville:1 smaller:2 pulse:12 go:1 rate:13 further:1 implemented:1 linear:4 even:4 errors:1 plays:1 adjustable:1 section:3 while:4 expressed:1 current:2 experiment:1 localized:1 goes:2 destroyed:1 new:2 increasing:2 satisfy:1 full:1 channeled:1 respectively:2 promising:1 gilles:1 intercept:1 free:2 others:1 invented:1 imperfections:1 change:2 obtained:1 sender:1 remarks:1 study:1 losses:21 allows:2 through:2 suggests:1 resulting:3 alamos:1 usually:8 complicated:1 bob:18 changes:1 tasks:1 followed:1 secure:13 explained:1 polarizers:1 apply:2 counts:4 bangalore:1 linearly:4 use:8 identifies:1 usa:1 positive:1 hilbert:1 scenarios:1 calculation:4 bases:1 call:2 therefore:1 centre:1 denmark:1 taken:2 theoretical:4 more:15 flaw:1 successful:1 becomes:1 quant:3 emission:1 surprisingly:1 effort:1 must:1 states:26 account:3 mb:1 science:1 work:4 modified:11 attacks:4 fock:2 mq:1 believed:1 making:1 initial:2 compare:1 conf:1 give:1 process:15 bennett:4 organized:1 purposes:1 implementations:1 high:9 indicates:1 magnitudes:1 tal:1 huge:1 needs:1 notation:1 fortunately:1 discussion:2 holds:1 write:1 far:3 vital:2 parameter:10 brassard:5 description:1 information:5 insecure:4 containing:1 lab:1 hence:1 succ:1 analyse:3 revealed:1 types:1 realized:1 whenever:2 light:2 yielding:2 warburton:1 provide:2 so:6 decreasing:2 order:17 six:2 over:3 mainly:1 produced:2 experiments:3 pulses:6 directs:1 eavesdropping:1 still:1 ieee:2 its:1 before:1 perfect:11 superior:1 probability:5 la:1 energies:1 better:1 detected:2 systems:4 wales:1 might:2 into:5 overcome:1 eugene:1 count:1 downconversion:8 thereby:1 reflected:1 they:6 rotation:1 now:2 ebec:1 thankful:3 preferable:1 university:2 didn:1 crypto:1 capability:1 realistic:5 magnitude:1 mode:6 reasonable:2 each:4 references:1 universit:1 polzik:1 referred:1 schemes:6 ee:1 reduce:1 used:6 solution:1 literature:1 expect:1 measurement:9 quantum:16 our:1 beyond:1 eq:1 special:1 canada:1 biham:1 accomplish:1 space:2 restricted:1 furthermore:2 since:3 crucial:3 projected:2 denotes:1 performs:1 denoted:1 independence:2 shows:1 fiber:1 theory:1 diagonal:1 possibility:1 drives:1 california:1 york:1 generate:1 definition:1 pairs:1 interaction:2 created:2 could:1 computers:1 keep:1 creates:2 corrections:1 onto:1 south:1 first:2 already:1 forwards:1 encoding:1 number:2 qkd:20 done:4 another:3 impossible:2 precisely:2 horizontal:4 decode:1 privacy:1 introduction:2 system:3 least:1 their:1 attack:11 conservation:1 rates:2 calculations:1 scheme:3 bits:1 final:4 imperfect:2 explanation:1 exactly:1 tapster:1 optical:1 than:6 relative:2 polarized:1 impractical:1 unfortunately:2 distinguishes:1 measured:3 second:9 loudon:1 were:3 india:1 outcome:1 distinguished:1 motivation:1 correction:1 say:1 conjugate:1 need:2 seen:1 cumbersome:1 any:6 eal:2 wcp:15 strength:1 angle:2 polarization:16 ideal:1 potential:2 finding:1 negligible:1 detector:2 smolin:1 channel:12 towards:2 shall:1 jun:1 singlet:7 most:1 significant:1 preliminary:1 nothing:1 acknowledgements:1 extremely:2 ekert:1 ka:1 nonlinearity:1 salvail:1 considered:5 average:1 sometimes:2 detectors:5 principle:2 inaccuracies:1 left:1 physics:1 sum:1 fact:2 laws:1 show:4 charles:1 threshold:1 find:4 impact:4 based:7 implementation:9 explain:2 pump:2 should:2 only:8 version:1 achieve:1 do:1 above:1 cryptography:2 get:1 dependent:3 de:2 beam:3 cannot:2 combinations:1 him:1 resend:1 regarding:1 qu:2 fields:2 arxiv:1 yield:1 investigate:2 paper:3 common:1 though:1 contain:1 including:1 us:1 decides:1 achieved:1 sensitivity:1 detection:2 see:3 computer:1 result:1 recently:1 rarity:1 arm:8 inequalities:1 away:1 below:1 importance:1 state:30 various:1 between:5 probably:1 conditions:1 email:3 letting:1 emitted:1 terms:8 creating:2 vertical:5 qubits:8 she:5 attention:1 weak:7 however:5 efficiency:1 here:2 key:13 distinguish:1 problem:3 suggested:1 both:2 enables:1 many:1 taking:1 3j7:1 against:9 conference:1 receiver:1 qubit:8 pdc:22 experimental:5 otherwise:2 adjusted:1 relevant:1 bell:1 simple:2 ca:2 dimensional:1 simply:3 considering:1 broadening:1 strong:1 basis:22 addition:1 barry:2 due:4 been:1 much:8 expected:1 ph:2 choose:1 sanders:2 direction:2 controlled:1 going:2 photon:14 coherent:5 epartement:1 decreased:1 careful:1 present:2 paying:1 novel:1 laser:1 bb84:8 engineering:1 value:1 will:3 near:1 error:1 rotator:2 h3c:1 studied:1 thus:5 them:3 according:3 itself:1 dual:1 limit:1 iro:2 different:1 anymore:2 perhaps:1 suggest:2 make:1 same:3 orders:2 checking:1 potentially:3 modification:1 several:1 independent:2 attenuation:1 lie:1 numerical:1 effect:4 hand:1 levels:1 uses:2 entanglement:1 totally:3 contribution:1 modes:1 nevertheless:1 well:1 analysis:4 without:2 solve:1 boyer:1 parametric:10 nb:1 usual:1 distances:1 protocol:2 less:1 resp:2 rotated:1 obtain:3 via:1 questions:1 immediately:1 macquarie:1 momenta:1 yet:3 previous:1 blow:2 adding:1 photons:10 seems:3 source:3 unambiguously:1 advantages:1 lett:3 sydney:1 input:3 rectilinear:1 adi:1 opt:1 australia:1 around:1 easily:3 rules:1 mor:4 providing:1 spanned:1 dark:3 department:1 increases:1 entangled:1 vacuum:4 using:4 bit:7 mod:1 loss:11 rotate:1 helpful:1 success:1 signal:1 performing:2 alice:24 discarded:1 yields:2 become:1 security:11 inter:1 collective:1 because:2 classical:2 people:1 sends:2 conditional:1 calculated:1 choosing:1 escape:1 practical:2 provided:2 sufficiently:1 measurements:3 comments:1 equal:1 provides:2 assuming:1 proc:1 refer:1 measuring:3 destroys:1 power:1 equivalent:1 processing:1 how:1 step:1 graaf:1 although:1 output:4 analyses:1 adversary:1 throw:1 simpler:1 about:1 would:4 getting:1 eavesdropper:1 discussed:2 meaning:1 angeles:2 ou:1 own:1 unnoticed:1 presence:7 umontreal:1 recreate:1 ucla:1 down:1 pair:1 appropriate:2 promise:1 yuen:1 operator:1 proportional:1 uncertainties:1 van:1 her:6 assumed:5 there:3 approximate:1 dispersion:2 los:3 describes:1 mandel:1 was:4 medium:1 complete:1 form:1 adjusting:1 conclusively:4 but:9 sophisticated:1 correlated:1 role:1 true:1 he:1 directed:1 whether:1 devices:3 crystal:2 note:1 frequency:2 those:1 site:1 demonstrate:1 distribution:11 semiclass:1 clear:1 mechanics:1 later:1 povm:4 abstract:1 measure:1 proven:2 denote:1 single:6 au:1 corresponding:1 archive:1 ideally:1 no:6 whereas:1 when:10 thinks:1 field:6 other:7 electrical:1 spatial:2 test:1 picture:1 superposition:2 phoenix:1 setting:1 problems:1 generated:1 important:2 palma:1 allowing:1 prepares:1 aware:1 conclusive:5 cryptographic:2 independently:1 suffers:1 longer:1 required:2 arisen:1 useful:1 time:3 reached:1 serious:1 having:2 once:1
|
quant-ph9906075.txt |@word represent:1 consider:2 amplifier:3 results:10 four:5 quadrature:5 2r2:2 2r1:2 gr:1 inverse:1 paris:1 pˆl:1 finally:1 squeezing:13 preserved:2 pˆv:1 sent:1 case:4 confirmation:1 amplitudes:1 worse:1 orthogonal:2 very:3 choice:1 every:3 hewlett:1 experimentally:2 bringing:1 condition:1 swapping:32 level:1 did:1 knight:2 pacs:1 pˆ1:9 discrete:2 pˆ3:9 bangor:1 pˆ4:15 optics:2 challenge:1 des:1 inseparability:1 cosh:7 second:1 further:2 even:4 ˆu:1 assistance:1 near:1 new:1 contrast:1 outgoing:1 αin:4 transportation:1 degree:3 respectively:1 never:3 teleportation:30 here:2 nonunit:2 sinh:3 box:1 sending:1 receive:1 leaves:1 funded:1 resulting:1 bob:22 via:2 projection:2 achievable:4 should:1 post:1 unit:10 use:2 superpositions:1 would:2 daad:1 therefore:2 criteria:1 taken:1 more:1 teleports:2 sharing:1 successful:1 becomes:6 operators:3 normalized:1 detects:1 iii:1 must:1 entangle:1 science:1 originally:1 work:1 obvious:1 indicating:1 im:1 unconditional:6 numbers:1 compare:1 boschi:1 figure:1 give:1 bennett:1 share:3 states:46 indicates:2 performed:2 tan:8 occur:3 teleport:2 end:1 bund:1 provide:1 s2:15 s1:16 xˆ:2 write:1 criterion:3 optimal:1 parameter:1 displacements:2 information:3 demonstrates:1 after:6 confirmed:2 epsrc:1 demonstrating:1 realized:4 light:4 claire:17 representation:1 order:1 superscript:1 indeed:1 produced:8 through:1 ηc:11 fidelity:20 its:1 before:3 perfect:1 teleporting:1 chosen:2 compelling:1 systems:6 mail:1 non:3 good:1 introduce:1 they:1 now:5 2s1:2 2s2:2 finite:1 2r:11 2s:3 always:1 university:1 2e:4 inequality:1 mode:76 each:2 found:1 referred:1 another:1 displacement:5 used:1 obtains:1 combining:2 quantum:10 our:6 operation:3 emerges:1 shown:2 ηc2:1 space:2 since:1 rev:14 projected:1 denotes:1 pˆ2:8 illustrate:1 occurs:2 singlemode:1 linear:2 polkinghorne:3 labs:1 completely:1 detecting:3 r1:16 r2:15 round:1 place:2 hence:1 first:2 separable:1 already:1 manuscript:1 variables:2 xf:1 xd:1 entanglement:73 xin:1 directly:4 impossible:1 quality:2 aharonov:1 xu:3 given:3 unknown:4 eqs:4 least:1 assumption:1 realization:1 perfectly:2 gives:1 continuous:8 took:1 part:1 x2:2 x3:1 x1:4 than:1 scheme:6 fuchs:1 require:1 see:2 submitted:1 correponds:1 annihilation:1 were:1 enables:2 ann:1 say:1 violating:1 idler:2 need:3 twomode:1 any:14 subsystems:2 built:1 efficient:1 able:1 note:3 generalized:1 detector:3 heisenberg:1 electric:1 shall:1 measures:1 optimized:2 drummond:1 phase:2 appear:1 arising:1 average:2 later:1 detectors:1 looked:1 braunstein:4 optical:1 principle:1 exp:1 fact:2 minimal:1 selection:1 show:1 violation:3 random:2 sze:1 relation:1 loock:2 superimposed:1 unwrapped:1 find:2 based:4 parameters:2 operational:1 only:11 local:6 achieve:2 do:1 his:2 means:1 beat:1 samuel:1 db:4 truly:1 beam:4 cannot:1 dx:1 dv:1 him:1 dp:1 resource:1 proposes:1 arxiv:1 summary:1 reid:1 she:1 set:1 correlations:1 up:2 detection:7 namely:1 projections:1 close:1 optimum:12 pvl:1 preparation:1 inequalities:2 nondegenerate:1 subsequent:3 nature:1 ralph:3 state:28 between:2 xˆ1:2 xˆ3:4 xˆ2:4 2σx:1 2pv:4 initially:2 2σp:1 however:3 inseparable:3 efficiency:10 bose:2 suggested:1 both:7 uncertainty:1 equal:1 enabling:1 zukowski:1 σx:2 und:1 bristol:1 exceeds:2 σp:2 whole:1 experimental:1 otherwise:1 bell:1 simple:1 combines:1 pv:3 asks:1 create:1 due:1 been:13 describes:1 combined:1 certain:1 pk:1 ph:6 fig:5 wants:2 enable:2 corresponding:1 sufficient:3 photon:3 coherent:12 ours:1 rahmen:1 wales:1 those:2 p2:3 p3:1 p1:4 tanh:5 variances:1 reliable:1 kimble:2 will:4 while:1 separability:1 squeezed:34 opt:1 von:1 thus:4 them:3 couples:1 duan:2 different:1 verified:2 grant:1 perform:1 demonstration:1 same:2 quant:6 gets:2 events:1 pan:1 investigated:1 context:2 displace:1 bouwmeester:1 uses:1 infinite:1 modes:4 without:4 parametric:3 usual:1 ny:1 protocol:5 proposed:2 obtain:3 sources:6 bandwidth:1 thanks:1 polarization:4 infinitely:1 photons:3 quadratures:3 source:1 transformed:1 lett:9 easy:1 input:4 mod:1 ηa2:1 real:2 possible:3 deteriorates:1 entangled:23 vacuum:5 using:21 projects:1 apart:1 necessary:1 like:1 exploiting:1 signal:3 alice:16 detections:3 yields:3 either:4 arbitrary:2 output:10 reduced:3 exceed:1 right:1 classical:12 creation:1 some:3 choosing:1 indirect:1 ˆin:2 fopt:6 nonzero:10 provided:1 recently:1 electromagnetic:2 investigations:1 efficiencies:3 provides:2 2xu:4 demonstrated:2 displaces:1 measuring:1 who:1 ensures:1 hsp:1 although:1 become:3 described:2 imaginary:1 bz:1 comparison:1 about:1 practical:1 briegel:1 furusawa:1 introduced:1 equally:9 beamsplitter:5 ηa:10 fidelities:1 appropriate:1 operator:1 van:3 her:3 interacted:1 initial:15 vedral:2 was:3 function:1 jun:1 but:4 gain:15 encoded:1 applying:2 packard:1 maximum:3 us:7 ur:1 limit:3 verification:5 uk:2 demonstrate:1 similar:2 pin:1 defined:1 recognize:1 measurement:1 general:1 multiparticle:1 single:23 proves:1 pˆ:6 compared:1 no:1 generally:1 field:2 other:4 separate:1 describe:1 generated:2 variable:8 independently:2 assume:1 together:1 teleported:6 time:1 requires:1
|
quant-ph9906076.txt |@word precise:1 now:1 interpretation:1 words:1 just:1 violation:1 when:2 magnetic:2 able:1 results:3 interpreted:1 four:2 course:1 paper:5 mentioned:3 particularly:1 longer:1 scattering:3 its:1 fifth:1 leinaas:1 difference:1 based:2 family:1 parameters:4 interesting:1 concerned:2 technique:1 had:1 should:3 better:1 being:1 ıc:3 explicitly:1 differently:1 republic:1 hamiltonians:1 might:1 hope:1 do:1 non:3 his:1 aspects:1 depends:3 means:2 very:1 couple:3 de:1 possible:1 operator:1 wave:6 finding:1 made:1 hamilton:1 lett:4 mention:1 arriving:1 using:1 emphasized:1 highly:1 occurring:1 treating:1 naturally:1 europhys:1 imposed:2 like:1 tube:1 did:1 follows:1 da:1 differential:4 solution:1 method:1 flux:2 commute:1 common:1 though:1 science:1 study:1 works:1 noted:1 referred:2 mathematical:2 arxiv:1 directly:1 classical:1 observation:1 czech:1 prague:1 revised:1 some:3 coupled:1 consists:1 zero:1 radius:1 result:1 our:4 happen:1 out:1 happens:1 provided:1 what:4 exploited:1 give:1 illustrated:1 space:1 nuclear:1 section:4 since:1 rev:2 while:1 comments:14 work:1 symmetric:1 critical:1 graphically:1 understood:1 formula:3 boundary:7 conditions:7 plotting:1 math:2 side:2 occurs:1 recently:1 theory:2 nowadays:1 nature:1 problems:1 however:1 illustration:1 standard:2 admits:1 manuel:1 completely:1 complicated:1 possibility:1 schulz:1 analyzed:1 approach:1 quite:2 beginning:1 regular:1 ctu:1 remark:1 ˇt:3 derivation:1 anything:1 involved:2 introductory:1 monopole:1 incident:1 o:1 called:2 prior:1 admit:2 concrete:1 extensions:1 decoupled:2 ˇa:1 consequence:1 definition:1 consequently:1 functions:1 among:1 via:1 suited:1 symmetry:3 nonrelativistic:1 appeared:1 merely:1 faculty:1 number:3 three:1 dimensional:1 included:1 addressed:3 set:1 references:2 approximately:1 another:3 type:1 elementary:1 respect:1 tools:1 angular:3 aharonov:2 selfadjoint:1 long:1 karlhede:1 their:1 ruijsenaars:1 there:3 due:2 been:6 doing:1 doubt:2 too:2 way:1 basic:2 ph:1 was:6 until:1 more:5 function:1 only:2 corresponding:2 complete:2 form:1 furthermore:2 operators:1 jun:1 idealized:1 part:1 basically:1 somewhat:1 known:1 missed:1 adami:1 systematically:1 than:4 reflection:1 case:3 kind:1 rotational:3 unfortunately:1 pacs:1 wish:1 pretend:1 deduce:1 value:1 aim:1 didn:2 limit:1 momentum:3 were:3 already:1 situation:1 problem:3 providing:1 similar:1 example:4 procedure:1 history:1 point:2 va:1 compare:1 studied:1 symmetries:1 sousa:1 solved:1 grunberg:1 abstract:1 modern:1 am:1 them:1 ann:2 general:2 states:4 need:2 conserved:1 itself:1 claimed:1 seem:1 hamiltonian:2 apparently:1 relatively:1 different:1 nk:1 angle:2 us:2 depending:1 rather:1 make:3 sending:1 moroz:6 cross:4 same:5 note:2 far:1 other:3 quant:1 papers:1 department:1 mathematics:1 several:2 parameter:1 tool:1 revision:1 even:1 dependence:1 see:2 trivially:1 may:2 tarrach:1 preceding:1 numerical:1 derived:1 effect:3 hand:1 plane:1 bounded:4 purpose:1 letter:3 formulae:1 remarks:4 choice:1 concerning:1 both:2 recent:3 short:1 attempt:1 coupling:1 sectors:1 practically:1 nevertheless:1 slightly:1 clear:1 no:3 analysis:2 notion:1 bohm:2 graphs:1 so:1 machinery:1 time:3 teta:1 first:1 essential:1 discussion:1 fact:2 applied:2
|
quant-ph9906077.txt |@word consider:1 rev:5 results:3 computation:1 remarkably:1 paris:1 tr:2 critical:1 νil:2 outside:1 very:1 wave:2 impinged:1 νnk:2 figs:1 experimentally:1 splitter:3 squares:1 large:1 small:2 eigenvalues:1 optics:2 fakir:1 measuring:1 horn:1 feasibility:2 rate:5 cost:1 traveling:2 greenberger:1 dynamics:1 chair:1 approached:1 apparatus:1 sum:5 selected:3 expressed:1 version:1 obvious:2 increasing:1 method:2 construct:1 respectively:1 component:1 teleportation:1 here:1 diagonal:2 desired:1 smearing:1 inversion:1 active:1 ley:1 equations:1 obtained:5 incoming:1 shift:5 allows:3 exiting:4 stressed:1 suitable:1 plotted:1 composed:2 via:1 eiφ:1 private:1 electromagnetically:1 analyzing:1 total:1 unit:1 plot:5 conventional:1 superpositions:7 would:2 next:1 depicted:2 therefore:1 type:1 theoretical:2 more:1 ψout:3 lowering:3 successful:6 becomes:2 operators:1 labelled:1 varying:2 must:2 states:31 characterize:2 setup:9 modified:1 fock:23 values:5 transparency:2 following:2 example:2 figure:8 transmissivity:6 high:6 fulfillment:1 νn:3 νk:2 νj:1 information:1 needs:1 varied:1 provide:2 how:3 pure:1 optimal:1 ordinary:3 parameter:2 ensemble:1 ψin:3 huge:1 modulation:2 after:2 applications:4 produce:2 data:1 effective:2 ss:1 so:6 fundamental:1 media:1 order:7 paper:1 through:9 affect:2 volta:1 its:2 before:2 group:1 chosen:1 decreases:1 actually:2 absence:1 production:6 fig:7 pavia:3 decreased:1 schmidt:2 non:3 good:1 propose:1 outlined:1 noticing:1 modification:1 now:5 developments:1 easily:1 term:1 radiant:2 traced:1 kerr:24 imamoglu:2 sufficiently:2 mode:34 each:2 found:1 universit:1 decreasing:1 domain:1 ei:1 generation:4 reduce:1 frequency:1 obtains:1 measurement:6 quantum:20 our:2 eq:6 out:6 shown:6 matrix:7 factors:2 since:1 crucial:1 research:1 increase:1 may:5 formula:1 induced:2 shows:1 linear:2 fisica:1 approaches:3 ask:1 generate:2 interaction:1 created:2 could:3 bassi:1 motion:1 exponentially:1 dipartimento:1 first:1 probability:4 enhances:1 number:16 channels:1 synthesize:1 least:1 ring:6 quality:5 given:8 needed:2 introduction:1 unknown:1 eqs:2 relations:1 indicate:2 scheme:6 final:1 mandel:1 imperfect:1 relative:1 optical:7 shifter:5 than:1 coefficients:3 distance:1 see:2 tunable:1 ranging:1 preparation:10 future:1 2kπ:2 amplitude:1 modern:1 bs1:5 bs2:5 medium:7 qualitatively:1 seen:1 seem:1 kelley:2 their:2 relatively:1 multipartite:1 zero:1 efficient:1 lim:3 click:1 k2:1 k1:1 detector:9 νkl:1 modulus:2 heisenberg:3 play:1 loudon:1 though:1 measures:1 paid:1 device:10 χt:12 nonlinearity:2 clear:1 detectors:1 kl:5 principle:3 exp:2 fact:2 quantity:1 drastically:1 spaced:1 show:3 probe:1 chuang:1 d2:19 availability:1 d1:17 giant:1 photodetector:5 based:3 knowledge:1 parameters:3 state:50 should:2 only:4 experiment:2 achieve:1 do:1 di:3 impinging:1 overall:2 ϕs:27 beam:6 ϕn:1 opatrn:1 reconstruct:1 evolution:1 contributes:1 numerous:1 arxiv:1 imposed:2 bad:1 photodetectors:3 behroozi:1 ignored:1 undergoes:1 detection:2 alessandro:1 arg:1 limiting:1 reconstructing:1 exploited:1 capacity:1 probable:1 currently:1 tend:1 pump:7 determined:1 αe:2 between:3 conditions:1 available:3 notice:6 terms:2 creating:1 nature:1 importance:1 however:1 residual:1 jl:2 efficiency:12 both:1 many:2 conclusions:1 contribution:1 finds:1 experimental:12 ck:2 splitters:3 filtering:9 fields:1 simple:1 homodyne:1 whatever:1 pon:6 exploit:1 pom:1 simply:1 moreover:1 described:2 tuning:2 cavities:2 basis:4 due:1 been:1 reduction:2 kronecker:1 ph:1 ariano:2 generating:1 controlled:3 photon:17 zeilinger:1 coherent:6 external:1 c3:7 c2:6 c1:6 case:4 novel:1 exponential:1 value:2 hau:1 will:5 while:3 maccone:2 procedure:1 opt:3 coupled:3 thus:1 conditioned:1 couples:1 quantize:1 reads:1 vs:1 technology:4 different:4 italy:1 generic:1 suggest:1 radiation:5 cross:4 same:4 any:2 shifts:3 drawback:1 quant:1 units:1 higher:1 used:8 peaks:1 upon:1 effect:3 harris:1 entanglement:2 normalization:1 recent:2 relies:1 lower:2 off:5 modes:18 displacing:1 components:2 position:1 model:1 left:4 deltas:1 ρbd:1 proposed:7 less:2 obtain:2 ozawa:1 using:6 yamamoto:1 yet:1 monitored:1 density:7 iϕ:2 source:1 lett:4 input:20 excited:1 identical:2 tests:1 explained:1 susceptibility:2 possible:3 predetermined:2 entangled:6 vacuum:2 integer:1 advanced:1 mod:1 necessary:1 identifying:1 alternatively:1 signal:12 δs:2 serves:1 specific:1 steps:1 arbitrary:2 setups:1 output:22 works:2 reduces:2 sketch:1 right:4 classical:1 truncated:1 affects:2 creation:4 b1:12 b2:11 nonzero:1 cavity:29 electromagnetic:1 per:2 kleiner:2 does:3 expressing:1 tends:2 cnm:2 welsch:1 bd:5 eiϕ:4 use:1 bs:2 plots:1 sacchi:1 actual:1 working:1 tracing:1 capable:2 dependence:1 o:1 dutton:1 equally:1 presence:1 communication:2 into:2 photodetection:11 obtaining:2 phase:17 references:1 yuen:1 operator:1 proportional:1 span:1 additional:1 prepare:1 synthesized:3 there:1 low:5 analyze:1 synthesis:3 function:4 conditional:2 elsewhere:1 enough:1 χk1:1 jun:1 but:1 delta:1 convergence:1 proposal:1 sitions:1 infm:1 inside:1 devices:1 limit:2 spectroscopy:1 pumped:1 distribution:6 mechanics:1 constant:1 choosing:1 certain:1 abstract:1 measure:1 denote:1 single:1 reliability:1 laboratory:1 tomography:1 crystals:3 regime:1 functions:1 no:1 nonlinearities:4 whereas:2 field:6 other:3 role:1 details:1 conclusion:1 picture:2 elements:1 superposition:6 a1:12 generated:2 a2:9 pumps:2 peak:1 included:1 structure:1 feasible:1 coupling:2 resolution:1 time:1 starting:3
|
quant-ph9906078.txt |@word represent:1 concept:12 arrives:4 consider:7 squared:2 brownian:11 results:1 illustrated:2 consists:2 row:1 whose:1 γx:4 calculate:3 editors:1 passage:2 nπ:9 ℜe:1 ny:10 preserved:1 under:2 stochastic:7 analogous:3 attenuated:1 sent:2 applied:1 returned:1 orthogonal:1 far:3 rise:1 springer:3 wave:61 electron:15 replaces:1 putting:2 condition:6 entire:3 school:1 lalo:1 presented:1 die:1 t2:11 solution:8 leave:3 vector:2 discounting:3 small:1 diu:1 setup:3 application:3 smaller:2 tel:5 consistent:2 measurable:7 outcomes:1 zero:10 traveling:1 reznik:1 dynamics:1 qmd:3 machines:1 linear:1 even:1 reproduce:2 what:3 appear:1 rate:2 incompatible:2 section:2 brief:1 expressed:2 symmetric:1 current:35 experiment:15 above:9 lifshitz:1 new:2 net:1 rd:1 ever:1 method:2 contrast:2 notions:3 reflecting:2 never:2 component:3 separation:1 others:1 directions:2 path:2 along:3 quite:1 observing:1 appears:3 catastrophe:1 obtained:10 hibbs:1 schuss:7 leaves:3 completely:1 commonly:1 ignoring:2 prior:12 resulting:3 permit:1 real:1 proportionality:1 adopting:2 devices:1 makes:1 der:1 quotient:2 regardless:1 f1:4 plenum:1 replace:1 first:6 unattenuated:1 pp:1 apply:2 total:3 planck:5 unit:5 use:1 additive:2 takes:1 probabilities:2 stated:2 definition:6 next:2 process:12 sample:3 call:1 therefore:8 m2:12 ψb:36 σy:1 mckean:1 ψf:10 theoretical:1 more:2 israel:2 relevant:1 brings:1 apparent:1 odinger:13 berlin:1 doob:1 normalized:1 particular:1 known:1 foundations:1 hole:5 detects:1 iii:1 potential:2 must:1 evolves:4 account:1 valued:3 recovering:1 integrating:1 decay:1 equation:18 accumulated:1 theories:1 4x2:2 obvious:1 concepts:1 following:6 making:2 collapsing:1 define:6 tau:2 compare:1 identifies:1 do:1 calculation:3 neglected:1 modes:1 states:1 slit:18 assumptions:1 suffers:1 sense:5 sharp:1 looser:1 axis:7 information:3 end:5 rather:3 discussion:3 spreads:1 feature:1 machine:9 till:1 methodology:1 instead:1 verlag:1 sin:6 circular:1 description:7 algebra:2 may:3 after:5 applications:1 produce:2 drastic:2 mqm:12 fixed:1 parallel:3 diffusion:2 flux:2 imply:3 light:1 simple:1 reflects:3 negligible:1 sect:1 fundamental:3 years:1 order:1 interpretation:5 developed:1 over:7 move:1 interpreted:3 produced:1 held:1 wiener:9 paper:1 including:1 cuts:3 mentioned:2 y0:9 y2:1 its:17 before:1 find:3 write:2 outer:1 surviving:4 directional:4 lateral:1 coordinates:1 actually:7 aviv:5 absence:5 complex:1 systems:1 mail:2 setting:1 outside:1 eventually:1 them:1 allcock:1 views:1 propose:1 processes:4 introduce:2 number:1 differential:1 records:2 walls:4 they:1 half:2 now:4 transparent:3 bigger:1 represents:7 brightness:1 always:1 university:4 hamiltonian:4 statement:1 realistic:1 fτ:1 each:3 found:2 went:1 traces:2 side:4 mean:2 different:7 domain:4 square:2 series:1 gaussian:6 used:4 flow:1 x20:3 decays:1 measurement:32 quantum:45 our:7 approximated:1 avoided:1 eq:16 event:2 out:4 large:1 shown:7 dsx:13 space:7 gradient:1 furthermore:3 since:2 interference:4 particles:29 contained:1 denoted:1 surprise:1 evaluation:1 occurs:1 math:2 benjamin:1 wiley:4 theory:22 interactions:1 gardiner:1 discontinuity:1 free:4 standard:3 approaches:1 included:1 detecting:3 universally:1 σy2:2 interaction:1 derivation:1 language:1 r3:1 geometry:1 could:1 βy:4 times:12 motion:2 turn:1 length:1 plane:8 place:1 due:3 cos:5 hence:2 arrived:1 assign:2 first:2 origin:6 there:17 xn:1 probability:79 wilder:1 requirement:1 reaches:4 done:1 long:3 another:4 impossible:2 dissertation:1 aharonov:1 size:2 y02:3 passes:1 given:31 allgemeinen:1 likely:1 introduction:3 data:1 eqs:4 histograms:2 mcgrawhill:1 system:3 adopted:1 unruh:1 their:5 assumption:1 observations:2 difference:4 normalization:1 postulate:6 recovered:2 gives:8 collapse:29 relative:2 continuous:7 eliminates:2 direct:1 released:2 part:3 values:1 x2:1 absorbs:2 x0:33 x1:1 photographic:11 than:4 population:1 begins:1 detection:6 filtered:1 edition:2 double:2 measured:4 second:1 limiting:1 future:1 contrary:1 grigolini:1 amplitude:3 tion:1 adopts:1 depresses:1 irreversibly:1 rewrite:1 cohen:1 measure:6 argument:1 already:1 say:3 manner:2 need:1 seen:3 seem:1 element:1 any:7 irreversibility:1 forced:1 angle:1 schell:1 lim:1 latter:1 mechanism:1 definite:1 note:1 instance:1 ideal:4 without:2 absorbed:18 generalized:2 so:8 detector:50 modulus:4 evaluated:1 begin:2 trace:3 opposite:3 denoting:1 measures:2 reach:2 most:1 detect:1 propagate:4 ht:14 occurred:1 device:19 segment:1 give:1 observation:5 considered:1 calculated:4 adopt:3 detectors:3 spend:1 feynman:37 points:7 electrons:3 principle:2 exp:25 mechanical:3 velocity:3 physics:4 notion:6 fact:1 intensity:2 show:1 absorbing:55 agreed:2 random:9 contemporary:1 relation:1 inconsistent:1 suffices:1 wigner:1 uniform:1 paradoxes:1 postulates:10 o:1 based:5 popescu:1 dividing:1 distributed:2 behind:3 should:3 terminal:1 only:4 princeton:2 ambiguity:1 factor:1 hamiltonians:1 continuity:1 plate:18 predict:1 hit:2 means:7 dependent:1 differs:1 expectation:1 methods:1 joint:5 cannot:8 dz:5 nearly:1 dx:10 dy:6 symmetrically:1 influence:1 neither:2 scientific:1 evolution:2 resolve:2 densities:2 upper:1 approach:6 arxiv:1 summary:2 2πi:7 difficulties:1 common:1 though:1 contain:1 release:1 through:4 qm:30 view:6 preserve:1 traverse:1 set:6 constructing:1 observer:1 observes:1 physically:1 packet:17 gottfried:1 observed:15 argued:1 namely:1 result:3 ignores:1 2σx:4 modifies:1 subject:1 closer:1 said:1 diffraction:1 pattern:10 review:1 siam:1 boundaries:9 state:1 determined:3 various:4 example:4 propagated:1 boundary:24 conditions:5 across:2 arrival:35 effect:3 ends:1 infinite:3 terms:5 sections:2 confusion:1 screen:39 emitted:2 however:5 jr:1 interfere:1 distribution:11 infinity:1 concentrated:3 both:1 interpretations:1 last:1 freely:2 uncertainty:8 equal:2 against:1 etc:1 connection:1 manifestations:1 context:1 recordings:2 uni:4 expression:3 experimental:1 otherwise:1 configuration:1 among:2 ch:4 point:34 wall:40 whatever:1 dimensional:10 written:1 respect:1 pr:24 better:1 σx2:17 described:10 basis:1 addition:2 trajectory:22 detected:4 been:8 hitting:1 mπ:23 basic:1 expected:1 αx:7 ph:5 ann:1 location:5 direction:8 arises:1 mind:1 undefined:2 countably:2 assert:2 observe:1 oppenheim:1 bayesian:1 fokker:5 those:2 case:4 multi:2 screens:1 value:3 will:3 while:3 replaced:5 error:1 situation:3 endpoints:2 enclosed:1 procedure:2 computed:1 resolved:1 planar:1 vol:2 von:3 thus:24 non:1 surface:5 according:22 sudden:1 im:7 il:2 vx:3 limit:2 vanish:2 interacts:1 currents:2 propagation:1 cumulative:1 discounted:5 same:11 influences:2 shorter:1 parts:2 quant:4 pauli:1 plates:2 several:1 events:4 higher:4 independent:3 literature:1 assigns:6 see:3 paths:3 assignment:1 trajectories:52 upon:2 counterparts:1 hand:3 moment:4 moving:3 purpose:3 pdf:1 discriminate:1 invariance:1 landau:1 tighter:3 schr:13 center:2 σx:4 disappears:1 modeled:2 well:7 analysis:1 obviously:4 patterns:1 contact:1 sets:3 coordinate:16 position:4 model:6 dimension:4 usual:5 distances:1 velocities:3 proposed:6 being:1 nd:1 rotated:1 obtain:1 vanishes:7 shape:1 intervals:2 predicts:2 world:1 facts:1 followed:1 momenta:1 converges:1 ψb1:2 λm:4 grounded:1 density:56 absorption:21 bell:1 had:1 mathematically:2 source:4 spread:3 nor:2 practise:1 transformation:1 identical:6 aspects:1 around:2 loss:1 survival:3 possible:3 possibly:1 press:1 using:1 modifying:1 apart:1 brought:1 rotate:2 necessary:1 semi:1 particle:75 δy:2 follows:6 performing:1 holes:3 arrivals:1 flux:1 either:4 integrals:5 multiplicative:1 stationary:1 essential:1 mathematical:10 because:5 often:1 classical:3 truncated:1 ignored:1 conditional:3 some:1 experiments:3 understood:2 examples:1 images:1 finite:5 confusing:1 happens:1 describing:1 tracked:1 lead:2 demonstrates:1 measurements:12 integration:1 per:3 instantaneous:6 does:9 exit:1 salecker:1 propagating:2 proc:1 refer:1 measuring:17 object:1 inescapable:1 equivalent:1 perpendicular:2 although:3 renders:1 between:5 about:7 actual:1 extension:1 instantaneously:7 certainty:1 finding:2 discussed:1 impermeable:2 reduced:1 compatible:1 diffusion:8 unidirectional:12 constraints:3 considerations:1 equally:1 rev:1 letters:1 presence:6 ψf1:5 pergamon:1 into:10 within:4 integral:24 ensue:1 occurring:1 lies:1 references:1 determine:1 approximately:1 proportional:2 neumann:3 terminated:1 statistics:3 additional:1 area:2 assumed:1 initial:15 available:2 spots:1 start:3 describes:1 handbook:2 fraction:1 was:9 function:77 suffer:1 complete:1 form:2 jun:1 but:6 histogram:14 repeated:3 construction:2 repeatedly:2 survived:1 delta:2 line:3 irreversible:1 collapses:4 singapore:1 made:1 applying:1 whether:2 characteristic:1 inside:2 up:3 us:1 placed:4 below:4 off:2 planes:5 continuously:4 problem:6 geiger:1 similar:1 called:1 distance:1 mechanics:17 ac:2 later:1 constant:2 fokkerplanck:1 stronger:2 abstract:1 describe:2 moved:1 single:2 exist:1 formulation:8 watched:3 formalism:2 constructed:4 functions:4 beyond:1 paradox:1 no:9 way:2 whereas:3 when:8 defined:12 started:2 other:8 dt:23 normal:4 spatial:2 department:1 mathematics:1 defines:2 borne:1 concerning:1 revision:1 equations:1 conditioned:4 separate:1 preceding:1 reached:8 prepared:1 bounded:2 variable:4 astronomy:1 dimensions:3 implies:5 longer:1 assume:4 requires:2 interval:17 packets:2 satisfies:2 2mπ:3 mass:2 time:99 appl:1 n2:3 4a:2 resolution:1 itˆo:1 once:1
|
quant-ph9906079.txt |@word represent:2 consider:1 rev:3 global:1 results:2 four:1 consists:1 indefinite:1 layers:2 whose:1 alamos:3 hump:1 quasi:2 elliptic:3 stable:3 stochastic:5 quasienergy:3 division:1 supported:2 springer:1 wave:15 resonant:1 husimi:22 exact:6 condition:2 leads:1 hamiltonian:9 proc:1 solution:1 leave:1 vector:1 small:3 round:1 upper:3 oscillation:1 approximation:6 zero:4 dynamics:2 situated:1 theory:2 even:1 index:1 nonlinear:1 sum:4 expressed:2 cell:12 suppose:1 net:3 acknowledgments:1 gµ:7 respectively:1 mei:1 separation:2 along:1 extrema:2 appears:1 extreme:6 study:2 studied:1 allows:1 reason:1 periodic:3 action:2 resonance:18 studies:1 useful:1 projection:1 substitution:1 analyzing:1 univ:1 planck:1 use:5 ψq:1 hilbert:2 chaotic:3 ψn:5 ψm:1 theoretical:1 more:2 separated:1 th:1 becomes:1 operators:1 under:3 odinger:1 particular:1 known:1 account:1 quantized:1 effectively:1 equation:2 work:2 oscillator:13 values:1 thin:1 example:5 compare:1 states:19 indicates:1 numbers:1 degenerate:3 absolute:1 lamb:1 soc:1 eng:1 travel:1 regions:1 parameter:5 sin:1 chernikov:1 symmetric:1 factored:1 plane:2 cylindric:1 cambridge:2 quasiclassical:6 effective:1 lines:3 thin1:1 element:1 used:2 fundamental:1 representation:1 order:3 neglect:1 move:1 perturbed:1 stability:1 paper:2 through:1 looks:1 differs:1 existence:1 its:2 write:1 symmetry:12 interesting:2 coordinates:2 fig:9 mail:1 h0:18 correspondence:1 them:2 motivated:1 ya:5 half:1 now:2 term:3 kamenev:5 tonian:1 james:2 university:2 trap:1 each:8 2m:1 2n:1 side:2 characterized:2 significantly:1 series:1 energy:2 gaussian:1 related:3 frequency:4 quantum:30 laboratory:2 eq:18 large:1 shown:6 matrix:1 space:27 since:1 sagdeev:1 chaos:4 research:1 particles:1 re:12 gov:1 ref:7 math:1 foundation:1 numerical:1 linear:1 radons:1 mω:4 given:1 completely:1 york:1 interaction:1 r0:1 motion:2 exponentially:2 top:1 first:2 probability:2 opez:1 variables:2 number:5 differ:1 perturbation:6 rewritten:1 los:3 nizhny:4 eqs:3 system:17 construct:1 zaslavsky:1 calculations:1 floquet:4 2ae:2 zeroth:1 took:1 j2:4 x2:1 than:2 coefficients:2 iωt:1 sections:1 namely:1 amplitude:1 were:3 russia:2 decompose:1 symmetries:1 derivative:1 rewrite:2 rh0:5 dynamically:1 spectrum:2 correspond:1 separatrices:2 separatrix:1 st:2 partly:2 convenient:5 agency:1 h20:1 build:1 εk:1 finding:2 so:4 formulas:1 populate:1 regular:3 connected:1 phase:27 analytically:1 eigenfunctions:1 sums:1 considered:3 coincides:1 exp:25 kx:3 spaced:1 show:2 jµ:4 labels:1 relation:1 threshold:1 cnls:2 find:3 ground:9 µm:3 ratio:1 parameters:3 ieq:1 only:3 factor:1 quantph:1 beams:1 simplest:1 new:1 dr:2 prime:1 covering:1 arxiv:1 summary:1 investigate:2 qe:26 double:1 analytical:1 cells:11 monochromatic:5 set:3 national:3 packet:5 ωt:1 relative:1 see:6 individual:4 radius:3 result:1 discussions:1 close:2 contour:1 interacting:3 definite:2 2πs:5 boundaries:1 state:10 closed:1 between:3 approach:1 terms:4 initially:1 weak:3 however:2 both:2 cos:5 region:2 uncertainty:1 equal:3 contract:1 called:1 expression:2 arbitrarily:1 minima:1 presumably:1 ch:1 cn:3 cm:3 point:6 corresponds:3 2ne:5 grants:1 constant:1 crystalline:2 described:4 second:1 basis:1 due:2 been:1 detuning:1 basic:1 pk:1 ph:1 systems:2 corresponding:3 argument:1 coherent:2 covered:1 2n0:1 present:2 case:6 hughes:1 laser:1 value:5 will:1 near:2 harmonic:13 behavior:1 eik:2 eim:1 ein:1 jpn:1 almost:1 ip:2 refs:2 thus:4 non:1 around:1 φq:2 cross:1 same:5 quant:1 φe:4 dimensionless:5 defines:1 independent:3 investigated:1 i0:1 trajectories:2 hand:2 ion:2 levels:4 doolen:1 symmetrical:1 infinite:3 normalization:1 lower:3 weakly:1 schr:1 center:5 eimϕ:2 patterns:1 coordinate:2 position:1 ae:5 possesses:2 maxima:7 novgorod:2 detail:2 differentiation:1 eigenstates:2 web:4 dicke:1 arctg:1 valid:1 lett:2 versa:1 transformation:3 momentum:2 eigenfunction:1 breaks:1 unlimited:1 period:1 schematically:1 increases:1 press:1 using:4 like:1 particle:6 follows:1 δn:1 decrease:1 security:1 stationary:1 therein:1 right:2 classical:16 some:2 respect:3 oscillations:1 throughout:1 cnq:4 critical:1 tends:1 bessel:1 demonstrated:2 agreement:2 expansion:1 found:1 plots:1 properties:2 lieberman:1 equally:1 own:1 into:3 numerically:2 thankful:1 luna:2 references:1 proportional:3 iπm:1 vˆ:2 assumed:1 there:5 width:6 analyze:2 was:7 function:30 complete:2 form:5 forming:1 m2:1 jun:1 hk:1 gain:1 russian:1 inside:1 uq:5 maximum:8 placed:1 below:2 limit:2 similar:1 agree:1 regimes:1 zeroes:1 lanl:1 associated:1 up:1 defined:5 contribute:1 influence:1 general:3 single:1 pˆ:2 our:2 controlled:1 regime:1 functions:10 compared:1 nm:2 no:3 dashed:1 when:7 ne:20 field:1 other:2 department:1 prange:1 berman:2 acosta:2 in2:1 structure:8 lichtenberg:1 vice:1 bottom:1 mass:1 time:3 n0:6 n2:2
|
quant-ph9906080.txt |@word represent:3 epeau:1 partial:2 consider:10 rev:7 results:3 tripartite:2 entropy:5 computation:1 consists:9 reasoning:1 viceversa:1 increase:1 dimensionality:1 calculate:2 equivalence:1 thapliyal:1 finally:1 those:1 under:3 include:1 applied:2 provides:1 advantage:1 orthogonal:1 very:1 choice:1 every:1 redefinition:1 difference:1 matrices:6 categories:1 dim:1 level:3 did:1 suffices:1 list:1 large:10 small:4 eigenvalues:1 proof:1 upper:4 smaller:1 deutsch:1 dealing:1 likely:1 incidentally:1 qualitatively:1 bernstein:1 even:1 established:1 what:2 abc:5 sub:6 advantageous:1 section:5 above:12 deal:1 shared:8 increasing:2 consisting:7 ρt:1 teleportation:11 here:1 desired:2 plenio:1 them:4 compressed:5 groups:2 making:3 consideration:1 obtained:5 search:1 broken:1 popescu:4 larger:4 allows:2 later:1 p2:12 amount:4 resulting:2 schumacher:1 symmetrical:1 bob:5 suitable:1 makes:1 composed:2 named:1 extra:1 problematic:1 julia:1 flexibility:1 unitary:3 pp:1 achievable:1 apply:6 total:4 use:5 asymptotic:3 would:12 prove:2 helvetica:1 coordena:1 distributing:2 classically:2 partite:28 call:1 therefore:3 taken:2 exhaustive:1 stage:1 theoretical:1 decomposable:6 more:11 teleports:1 optimizing:2 clever:1 buhrman:2 composite:2 becomes:1 naive:1 reversibly:1 correspondingly:1 basically:1 particular:4 known:4 cases:2 must:3 worst:1 states:65 keeping:1 ρb:1 erratum:1 recall:1 work:2 cat:1 prompts:1 obvious:1 achieve:1 following:3 ρx:10 bipartite:15 example:10 attain:1 locc:12 ao1:1 figure:1 process:2 december:1 bennett:8 india:1 involve:3 minimum:1 performed:1 employs:1 sense:1 teleport:8 respective:1 ef:12 goal:1 s3:2 s2:6 discussion:2 holds:2 rippin:1 write:4 how:3 pure:10 optimal:17 parameter:1 ensemble:1 brassard:2 map:1 product:8 may:15 ancilla:5 after:1 different:6 collection:1 applications:2 deviates:1 end:1 data:6 shortcomings:1 short:1 elusive:1 imply:1 slightly:1 ghz:34 provide:1 complexity:1 negligible:1 fundamental:1 sb:2 sa:3 operate:2 s1:7 sd:2 operations:5 horne:1 help:1 numbers:1 developed:1 over:4 choose:3 lanl:6 through:3 argued:1 fidelity:1 still:3 ieee:1 its:5 before:1 superior:1 teleporting:5 unitaries:1 exact:4 actually:1 better:1 systems:13 constitutes:1 coordinated:2 schmidt:5 teleportations:14 inefficiency:2 correspondence:1 non:4 recreate:1 greater:1 dam:1 motivates:1 ernesto:1 they:3 instead:3 oxford:2 now:8 easily:2 february:1 products:1 2k:1 university:1 presented:1 labeling:1 orthonormal:1 inequality:2 each:32 found:2 2n:1 macchiavello:1 mean:1 subsystem:14 successively:1 directly:4 doing:1 series:8 einstein:1 idea:2 constitute:1 society:1 unprimed:1 used:9 measure:2 multiparticle:4 our:7 operation:2 eq:1 shown:2 matrix:3 space:8 since:5 rx:1 rz:1 particles:1 conclusions:1 ra:2 rb:1 print:6 formula:1 issue:1 math:1 shows:2 log2:1 written:2 differ:1 undo:1 ascending:1 clarify:1 formation:6 term:1 van:1 jozsa:2 generate:1 definition:1 pairs:40 recovering:1 created:2 turn:1 resembling:1 due:1 routes:2 generalizations:5 support:1 first:10 separable:1 initial:2 vedral:1 possessing:1 coding:1 number:24 done:2 relations:1 another:3 knight:1 open:1 take:4 given:2 rewritten:1 similarly:2 introduction:4 system:20 least:2 their:4 wootters:1 final:1 imperfect:1 inefficient:5 exactly:2 sx:5 manipulation:3 copy:7 than:9 coefficients:1 showed:1 wiesner:1 require:1 depends:1 preparation:1 matter:2 appealing:1 classes:5 were:1 identical:1 hz:2 galv:1 sab:2 argument:1 needs:1 1r1:2 1r2:2 need:7 seen:4 weinfurter:1 any:10 multipartite:6 subsystems:20 built:3 min:1 efficient:7 convenient:1 agency:1 r3:1 parks:1 note:3 high:1 generalized:2 satisfactory:1 finding:2 so:2 adopted:1 nivel:1 continuous:2 multiple:1 allow:1 trace:1 shall:1 track:1 compress:2 most:9 but:4 successive:1 pair:5 coin:1 especially:1 considered:3 clear:2 partition:1 physica:1 order:6 proceedings:1 part:1 physics:2 fact:3 quantity:3 particularly:1 show:1 authors:1 simon:1 spaces:3 dimension:2 trivial:4 find:4 capes:1 ensembles:1 dividing:1 true:1 original:1 distributed:4 ox1:1 only:6 unable:1 acknowledge:1 minimally:1 distributes:1 local:7 hope:2 continuity:1 do:1 establishes:1 cryptography:1 means:4 de:3 cannot:5 preparing:1 closely:1 international:1 during:1 prime:9 well:4 regarding:1 resource:1 podolsky:1 arxiv:1 public:1 twice:1 investigate:1 view:1 set:7 ancillae:5 tossing:1 up:1 see:9 actively:1 sec:1 result:5 enhanced:1 close:2 best:2 said:1 tensor:8 ways:3 sites:1 label:1 state:63 future:1 invokes:1 closed:1 between:14 progress:1 approach:2 hence:2 creating:7 qubits:12 combining:1 however:3 equals:1 incommensurate:5 efficiency:3 key:3 1a1:1 both:4 last:1 many:7 taking:1 1a2:1 according:1 improves:1 interesting:2 qubit:7 argue:1 arbitrarily:3 among:4 characterization:2 simple:5 royal:1 ca:1 asymptotically:7 corresponds:2 cd:1 dimensional:7 simply:2 pessoal:1 sequences:3 cr:1 writing:1 application:1 considering:1 0a1:1 0a2:1 described:1 transformations:6 basis:2 create:5 locally:1 three:6 been:5 ai:2 much:2 interest:2 basic:2 ph:7 fig:3 enable:1 corresponding:7 zeilinger:3 optimality:3 decompressed:2 demand:1 c2:3 c1:3 maximally:4 protocols:1 case:12 p3:10 p1:37 p4:2 harder:1 say:1 evaluated:1 choices:2 will:22 suppose:1 error:1 property:3 procedure:4 ix:1 vectors:1 von:4 chau:1 thus:5 site:2 equal:3 itself:1 ic:1 ib:1 1c2:1 containing:1 perhaps:1 perform:2 lett:5 same:5 clearly:1 quant:7 inseparable:1 units:2 party:28 couple:1 higher:2 extended:1 trivially:1 generalizes:1 possible:8 uses:1 entanglement:21 a2i:2 identity:1 recent:1 lower:2 scenario:1 charlie:4 epr:48 analysis:1 obviously:1 sets:2 kempe:5 possesses:1 know:1 protocol:50 just:1 less:1 being:4 when:3 distribute:6 obtain:3 rest:1 ρa:1 identify:2 thanks:1 yet:2 adding:2 signal:1 density:8 passively:1 seems:2 other:7 transformed:2 location:9 easy:1 theorem:4 save:1 transformation:2 build:7 real:1 acta:1 definitive:1 represents:2 evaluate:1 showing:1 decomposed:1 3pu:1 spanned:1 additivity:2 ancillary:2 zukowski:1 entangled:5 distillable:2 sanpera:1 subparts:1 using:18 bit:1 necessary:3 like:3 identifying:1 reduces:1 performing:1 alice:5 specific:1 steps:4 either:4 arbitrary:7 reduced:4 grouping:1 lucien:1 neumann:4 classical:2 sequence:1 creation:1 some:13 unnecessary:1 donald:1 examples:2 b2:2 dimensions:1 centre:1 per:6 economical:4 conference:1 obey:1 equivalent:2 processing:1 consuming:1 mayers:1 clarendon:1 step:3 2m:1 bangalore:1 hilbert:6 takes:2 comparison:1 actual:1 theorems:1 discussed:4 meaning:1 o:1 constituting:1 practical:1 ox:2 mixed:3 discard:1 glasses:1 denote:1 road:1 subset:3 communication:3 into:7 within:1 bound:6 copies:18 references:1 parties:19 proportional:1 methods:1 rely:2 computer:1 compression:7 prepare:1 few:1 spending:1 strictly:2 there:8 question:1 transform:1 custom:1 start:3 way:9 brazilian:1 analyze:1 was:2 irreversibly:1 building:3 hard:2 irreversibility:1 form:3 smolin:1 regard:1 1b2:1 jul:1 hb:2 hc:1 ha:8 irreversible:1 themselves:2 observation:1 made:2 applying:1 builds:2 consist:3 whether:2 wish:1 bounds:8 us:17 below:1 converted:1 limit:3 uk:2 distribution:2 define:1 similar:2 called:1 entropies:6 b1:2 ac:2 ab:2 proved:3 introducing:1 defined:2 certain:2 abstract:1 describe:5 general:8 peres:1 quantum:11 single:9 laboratory:2 physical:1 again:2 functions:2 assessing:1 lo:2 want:3 no:6 amounts:2 ekert:1 rosen:1 grouped:1 interested:1 sizes:1 superdense:1 briefly:1 kinds:2 primed:2 prepared:2 a1:1 cleve:2 generated:1 a2:1 bounded:2 allowing:1 cryptographic:1 1b1:1 independently:1 implies:1 values:1 proposed:1 factors:3 1c1:1 depth:1 teleported:2 bacciagaluppi:1 far:1 n2:6 requires:1 having:1
|
quant-ph9906081.txt |@word miyazaki:1 consider:2 rev:8 controversial:1 consists:1 clarified:1 denotes:1 inverse:1 subjected:1 young:1 finally:1 th:1 under:2 γb:2 γa:3 include:1 tyutin:4 ǫab:2 supported:1 very:1 choice:1 introduction:1 difference:1 condition:1 annihilated:1 level:3 did:1 notes:5 integrating:1 applicable:1 adjust:1 minimal:1 eigenvalues:3 falck:1 ga:1 consistent:4 rouet:1 fradkin:5 ωab:1 second:7 remarkably:1 canonical:8 g24:1 developed:1 bb:1 iterating:1 brackets:2 batalin:5 version:1 above:2 lifshitz:1 new:4 method:10 fujiwara:1 satisfy:4 lee:1 degree:1 respectively:1 here:7 desired:3 address:3 path:1 equations:2 obtained:10 institute:1 shift:1 studied:1 reason:1 adopt:1 p2:1 poisson:4 action:1 relation:2 uniquely:2 adjustable:2 b341:1 apply:1 unit:2 standing:1 derivatives:2 charge:1 γi:1 next:3 nucl:4 going:1 a56:1 type:1 introducing:2 operators:3 jai:1 known:1 fermionic:1 tae:2 henneaux:1 science:1 work:1 det:4 modified:2 theories:1 values:1 following:4 meet:1 yeshiva:1 give:1 recover:1 states:3 sphere:9 b180:1 hydrogen:1 shuffled:1 pp:1 how:1 pair:1 instead:1 parameter:8 seoul:1 algebra:6 relates:1 after:4 demanding:1 aop:1 representations:1 law:3 ambiguous:2 effective:5 whenever:1 sw:3 correspond:1 su:3 cannot:3 so:3 fundamental:1 order:6 exponentiating:1 neto:3 indeed:1 over:2 soon:1 htot:2 including:3 omitting:1 converting:1 its:1 caω:1 group:1 la:1 chosen:1 interesting:1 fix:1 coordinates:3 hm:4 systems:1 bω2:1 eur:1 correspondence:1 symmetrization:1 non:1 sogang:5 introduce:2 number:2 framework:2 skyrme:1 effects:1 they:1 nov:1 now:7 b279:1 discuss:1 easily:1 february:1 several:1 dirac:18 university:3 hamiltonian:15 d48:1 2c:1 found:2 2n:2 d46:1 constraints:16 weyl:5 ei:2 series:2 energy:16 ef:1 idea:1 extended:2 measure:1 quantum:8 our:2 ghosts:2 homma:1 eq:3 special:1 out:1 shown:1 space:8 furthermore:2 since:1 lagrangian:10 dπi:2 research:2 re:1 formula:2 ref:1 correct:1 math:3 ogawa:1 theory:2 free:13 standard:2 clarify:1 approaches:1 york:3 approach:1 generate:2 qj:17 ministry:1 could:2 motion:2 πj:5 fleck:1 obscure:1 δij:5 b456:1 first:32 symmetry:3 variables:1 primary:1 relations:2 directly:1 electronic:3 angular:1 igarashi:1 given:7 cartesian:1 rewritten:1 similarly:1 ordering:5 πi:25 πn:5 system:3 construct:3 their:1 returns:1 fermions:1 1i:1 stora:1 scheme:10 a32:1 exactly:3 park:11 b336:1 authors:1 spacings:1 representing:1 last:1 dtl:2 iteration:1 shabanov:2 project:1 determined:1 witt:2 generality:2 explicit:1 correction:3 spectrum:17 generalization:1 analysis:1 vilenkin:1 conjugate:2 curved:1 unaffected:1 any:4 symmetrized:1 χa:1 note:3 oliveira:2 take:1 lectures:1 bk21:1 consistency:1 algebraic:1 wess:1 gauss:3 letter:1 phase:3 class:37 g23:1 consequences:1 later:1 physica:1 kr:3 bracket:6 exp:2 mechanical:1 physics:2 fact:1 marinov:1 show:3 senjanovic:1 delta:1 gauge:10 keywords:1 q2:1 d59:1 commutators:2 should:1 only:1 explicitly:1 generators:2 bfv:2 ambiguity:6 bft:16 local:1 achieve:1 abelian:4 cheng:1 dekker:1 de:2 dc:1 ones:2 report:1 dt:5 subscript:1 evolution:1 podolsky:1 fields:16 arxiv:1 yield:7 summary:1 involutive:3 qi:46 through:1 qk:44 fixed:6 requirement:1 imposing:1 respect:1 see:1 radius:1 result:8 corre:1 recently:2 brst:6 satisfying:1 mechanically:1 lef:3 partition:4 symmetric:1 case:3 state:1 won:1 various:1 between:3 invariant:7 boundary:1 conditions:2 choose:1 korea:1 terms:6 reproduced:1 however:3 yoon:2 configuration:1 suppressed:1 a232:1 improved:3 b511:1 quantization:8 context:1 contribution:1 mechanics:3 point:1 cc:1 dimensional:8 grants:1 simply:1 constant:1 rep:2 unusual:1 amer:1 described:1 transformations:1 due:4 laplacian:1 int:4 describes:1 basic:1 harwood:1 ph:3 ann:2 define:2 box:1 determinant:1 corresponding:7 θb:1 subspace:2 observe:1 c2:2 present:2 applied:2 novel:1 pacs:1 103a:1 value:1 transformation:4 will:7 bop:1 rotator:1 situation:1 property:1 procedure:3 redefinitions:1 unitary:1 surface:2 δqi:2 quantize:1 converts:1 kuhn:1 ready:1 hong:3 constrained:1 perform:2 acknowledgments:1 same:2 φa:10 φb:2 quant:3 widely:1 physical:11 zumino:1 used:2 sym:1 hand:3 kubo:1 moving:2 kim:14 frequently:1 landau:1 kleinert:1 recent:1 well:4 ccs:3 without:2 sets:1 firstly:1 model:6 left:1 just:1 being:1 skyrmion:2 obtain:13 girotti:2 λb:1 identify:1 klauder:1 momenta:5 previous:1 infinitely:1 nilpotent:1 education:1 lett:7 mod:7 dqi:3 momentum:1 generalized:3 rules:1 term:3 b55:1 unification:1 using:5 occurring:1 loss:2 phenomena:1 replacing:1 particle:12 identifying:2 systematically:2 follows:4 performing:2 δp:2 δq:2 abdalla:1 yields:3 arbitrary:3 anti:2 δb:7 λqi:2 δa:2 because:1 classical:1 some:2 b1:2 b2:2 moreover:1 proper:1 2qk:2 2qi:2 describing:1 affects:1 avoid:1 integration:2 providence:1 does:2 prog:1 restoring:1 faddeev:2 ba:2 power:2 bc:1 equivalent:1 agreement:1 d42:1 super:2 hilbert:2 constraint:8 o:4 nonvanishing:1 act:1 introduced:2 2cc:1 soc:1 ηb:1 ηa:2 pergamon:1 into:5 functional:2 three:2 nothing:1 right:1 references:1 been:4 operator:4 proportional:1 additional:2 there:1 long:1 start:1 restricts:1 way:2 was:1 naturally:3 function:6 banerjee:2 form:5 unsettled:1 but:1 formalisms:2 hn:2 atom:1 c60:1 foerster:1 embedded:1 fulfilling:1 variations:1 us:2 limit:2 iterated:1 ωa:5 problem:3 ωb:2 called:1 strongly:3 ac:3 ab:8 ordered:1 defined:2 abstract:1 describe:1 general:1 fujii:1 δba:1 vilkovisky:2 formalism:9 constructed:1 functions:1 no:2 fixing:4 when:1 field:2 other:3 sponding:1 department:1 theor:2 a15:1 a14:2 suppl:1 generates:1 a13:1 a12:1 models:1 polynomials:1 commutator:1 a6:1 g21:1 structure:2 ghost:2 auxiliary:8 together:1 mass:1 time:1 observables:1 starting:1 original:4
|
quant-ph9906082.txt |@word sector:1 measurements:2 partial:2 results:1 integration:2 leads:1 entropy:1 aachen:1 localized:3 whose:1 const:1 calculate:1 concerned:1 deterministic:2 quasi:1 does:1 under:3 ontological:1 must:1 straightforward:1 far:1 amorphous:1 wave:2 lyapunov:1 corollary:1 affect:2 condition:2 randomness:1 routledge:1 presented:2 turns:2 solution:1 t0:3 large:4 vector:1 small:2 originally:1 prevent:1 smaller:2 force:10 organized:1 prediction:1 further:2 dynamics:8 estimated:1 will:7 what:1 fine:1 sum:2 localization:1 analogously:1 expressed:2 causes:1 reconstruction:2 values:1 increasing:1 consisting:4 contrast:2 body:3 q1:1 full:1 christian:1 degree:1 exchange:1 here:5 atoms:2 behaviour:4 evident:1 objects:8 alone:1 equations:4 deduced:1 appraisal:1 example:1 der:2 via:2 although:1 scales:1 replace:1 summation:1 total:4 derivatives:1 conventional:4 would:1 remains:1 contains:1 aus:1 classically:1 ψi:2 ψn:1 therefore:3 ψl:2 type:3 more:3 introducing:1 becomes:5 odinger:3 glass:1 appendix:2 particular:1 foundations:1 circumstances:1 obeying:1 tunnel:1 avoiding:1 equation:13 averaged:1 mi:3 obvious:1 universe:1 following:5 averages:2 mx:1 proof:1 figure:1 ohne:1 process:2 permutations:2 neglected:1 xcm:7 states:1 dxn:2 assumptions:3 performed:1 exclude:1 subsystem:4 cushing:1 verlag:1 hoc:1 undivided:1 feature:1 regions:1 located:1 significance:1 instead:1 ordinary:1 absolute:1 fq:2 quantenmechanik:2 after:3 derived:4 containing:2 dx1:2 hence:1 physik:4 law:4 short:2 natural:1 phases:1 si:1 so:2 fundamental:1 representation:1 order:5 interpretation:7 dx:5 over:2 insight:2 paper:1 statistical:4 helm:3 its:2 probability:2 masses:1 coordinates:8 absence:1 microscopic:7 systems:7 jacobi:3 hidden:2 main:2 defining:1 affected:1 thereby:6 largest:1 introduce:1 framework:3 hamilton:3 effects:2 multidimensional:1 now:1 transparent:1 nor:1 represents:1 february:1 goldstein:3 university:1 level:1 sufficiently:1 magnitude:1 each:3 2m:11 universit:1 characterized:1 mean:1 heavy:1 differential:1 directly:1 energy:1 manifests:1 used:1 obtains:3 geiger:4 quantum:63 our:1 beyond:1 out:7 shown:4 space:2 restricted:1 rev:2 chaos:4 denotes:1 particles:5 attracted:1 contained:1 suggesting:1 formula:1 rn:3 issue:1 shows:1 theory:9 interactions:1 clarify:1 completely:1 definition:2 interaction:2 derivation:1 transition:2 keep:1 motion:17 appearing:1 american:1 consequence:1 first:1 origin:1 initial:1 xn:26 features:4 symmetry:1 variables:3 number:7 system:17 intuitively:1 simplified:1 approximately:1 another:1 precisely:1 given:6 introduction:3 condensate:1 equ:15 theoretische:1 least:1 assumption:5 statement:1 exponents:1 unbroken:1 collapse:1 explanation:1 albert:1 part:1 x2:15 x3:1 x1:38 representing:1 than:3 regensburg:5 distance:2 kind:1 holland:1 characterizations:1 submitted:2 determined:7 motivation:1 generality:1 topics:1 mind:1 argument:1 inequivalent:1 elsevier:1 recover:2 any:1 symmetrized:1 subsystems:16 built:1 convenient:1 note:2 potential:8 harald:1 forces:5 xi:38 modulus:4 investigations:1 object:3 realism:1 clearer:1 most:1 germany:1 phase:3 homogeneous:1 measured:2 why:2 fji:1 dordrecht:1 average:2 ks:1 ext:3 urr:2 mechanical:16 maxima:1 physics:3 fact:2 superfluidity:1 mainz:1 selection:1 show:1 characterisation:2 relation:1 trivial:1 help:1 postulates:2 state:3 only:5 explicitly:2 coefficients:1 employed:1 equilibrium:2 continuity:1 his:1 above:1 viewpoint:1 means:2 de:3 expectation:1 cannot:1 words:1 during:2 dt:4 du:1 neither:1 processes:1 consist:1 arxiv:1 factorization:4 summary:1 contain:1 qi:1 qn:1 thesis:1 publishers:1 correlations:2 relative:1 depends:1 radius:1 result:2 terms:2 rmi:1 ergodicity:1 disjunct:2 mechanically:1 review:1 sites:1 written:1 various:1 between:4 justified:1 rm2:1 rm3:1 rm1:1 recently:1 nature:3 vanishing:3 key:1 bose:2 configuration:2 suppressed:1 distribution:1 suggested:1 both:1 x2i:1 many:3 region:1 according:1 fulfilled:1 und:1 uni:3 contribution:1 experimental:1 ch:2 cm:4 point:3 simple:2 ca:1 cf:3 dimensional:1 cancel:1 respect:1 addition:4 trajectory:3 due:6 been:5 much:2 interest:1 ph:2 fig:2 ergodic:1 corresponding:1 restrictions:1 concerning:1 coherence:1 fij:3 coherent:1 bohmian:20 understand:1 external:1 last:1 worked:1 irrelevant:2 case:7 pacs:1 single:2 value:3 aim:1 while:3 error:1 averaging:1 ii:3 itself:1 motivated:1 vanish:1 different:5 squareintegrable:1 journal:2 indistinguishable:1 same:2 parts:1 quant:1 wavepacket:1 schematic:1 mixtures:1 regime:1 acceleration:1 calculation:2 investigated:1 effect:4 levels:1 potentials:2 infinite:1 schr:3 center:23 onedimensional:1 locality:2 bohm:5 academic:1 solids:2 without:2 coordinate:4 position:6 usual:2 proposed:1 less:2 being:4 newton:4 reviewed:1 press:1 faisal:1 underlying:1 alternative:2 macroscopic:18 preprint:2 kluwer:1 conclusions:1 had:1 exclusively:1 discuss:1 pinball:1 internal:1 lett:4 momentum:1 identical:2 gustav:1 around:4 easily:2 possible:2 corresponds:1 schematically:1 dewdney:1 hiley:2 confined:1 using:2 ruled:1 loss:1 necessary:2 like:7 particle:21 follows:1 collective:4 essential:4 wavepackets:1 classical:37 sequence:1 some:1 calculated:1 accelerate:1 proofs:1 affects:1 normal:1 fluids:1 overlap:3 behave:2 eliminate:1 provides:3 minimal:2 scientific:1 equivalent:2 step:1 cν:3 bz:1 simpler:1 freedom:1 o:1 range:1 r1:1 continous:2 consequently:1 subset:1 cambridge:2 presence:1 into:1 within:3 integral:1 device:1 appropriate:3 references:1 einstein:2 elementary:2 conceptually:1 institut:1 additional:6 assumed:1 support:3 there:3 gases:1 noting:1 way:2 was:1 function:4 gaseous:1 form:2 phenomena:2 jun:1 but:6 uncertainity:3 correlated:1 atom:2 elimination:1 true:2 made:1 intuitive:4 up:1 ur:1 limit:6 malik:1 problem:1 similar:1 called:2 clear:1 mechanics:17 ad:1 defined:1 certain:3 abstract:1 measurement:9 proven:1 general:1 substantially:1 chap:3 formulation:4 distributions:2 physical:3 functions:1 compared:1 no:4 index:1 wavefunction:19 vanishes:2 other:4 zanghi:2 sufficient:2 picture:2 briefly:1 superconductivity:1 leaving:1 meaning:2 important:2 independently:1 condensation:1 assume:1 governed:1 factorizes:1 mass:28 decoherence:4 having:1
|
quant-ph9906083.txt |@word deγ:1 sci:3 consider:5 chinese:1 rev:14 magnetic:1 trigonometric:2 four:2 jˆ3:2 grateful:1 parameterization:2 oldest:1 gj:12 conveniently:1 devoted:3 looking:1 inverse:4 ver:1 eigenbasis:5 alamos:1 equivalence:2 tr:6 ts:1 γj:31 dereli:2 those:7 th:1 under:4 analogous:1 norm:1 carried:1 applied:3 charles:1 g3:3 mainstream:1 g1:1 g0:3 iτ2:2 zachos:3 results:3 ankara:1 gazi:1 probability:4 ical:1 specific:5 nieto:5 exact:1 condition:2 entire:7 induced:1 variable:3 hamiltonian:19 irreducible:14 mb:1 t2:6 solution:3 t1:7 admissible:9 convenience:1 vector:7 l135:1 eigenvalues:2 optics:6 bo:1 zd:20 det:1 among:1 direct:4 cosh:3 elegant:2 second:4 perspective:7 bilkent:2 further:2 dynamics:1 odd:2 eigenspaces:2 canonical:75 even:2 established:5 ˆr:4 plays:1 sub:4 toledo:1 diag:1 section:13 lawrence:1 brief:3 expressed:3 find:5 current:1 laurence:1 version:2 above:4 fractional:3 new:2 ˆj:3 apply:1 method:1 satisfy:2 full:3 simultaneously:3 degree:6 arik:1 respectively:4 realizations:7 here:13 heitler:1 met:1 them:2 sinh:4 represented:4 luis:2 strong:1 equations:3 balian:1 change:1 obtained:5 search:3 divisor:1 technical:1 shift:1 leaves:1 vectors:7 los:1 suggests:1 professor:2 action:32 xvi:1 adopting:1 fourier:15 glu:2 uniquely:1 examining:1 via:1 followed:1 family:1 marginal:3 floratos:2 treatment:1 maths:1 rπ:3 tana:1 summation:1 redefining:1 establish:2 unit:6 readily:1 seligman:2 use:5 takes:1 remains:1 positive:2 negative:6 hilbert:10 distinct:1 theme:1 linear:7 m1:25 mandel:1 m3:2 m2:18 eϕ:1 scope:1 compactly:1 type:3 theoretical:1 reflects:1 more:14 admitting:1 pˆ2:2 formally:4 duality:4 becomes:5 operators:14 ellinas:1 berlin:2 appendix:3 particular:8 known:4 cases:2 iii:3 eγ:1 must:1 springer:1 rotational:1 integrating:1 deformed:2 equation:6 work:8 oscillator:30 centrifugal:1 london:3 iα2:3 reviews:1 suggestive:1 infinitesimal:3 values:1 gˆ3:2 following:5 making:1 kogan:1 example:2 stimulating:1 wang:2 processing:1 brown:1 calculation:4 dτ2:1 outline:1 preserving:2 states:2 indicates:3 sinθ:1 assumptions:1 numbers:1 sense:6 dj:3 g2:1 motion:7 provide:2 s2:6 s1:6 acts:1 xˆ:1 eigenenergies:1 sˆt:2 pair:14 pure:7 ralph:1 opt:1 ignore:1 parameter:4 divides:1 product:6 express:1 landmark:1 algebra:14 overall:2 ζj:4 earlier:1 derived:3 mapping:1 dc:3 wellbehaved:1 applications:1 inst:2 representations:40 iτ1:2 constants:1 realized:2 short:2 advocated:1 dynamical:18 resentation:1 explicit:3 correspond:3 parameterized:3 element:11 diffeomorphism:1 perhaps:1 switch:1 cannot:2 so:3 fundamental:1 sl:18 representation:22 kurt:2 order:5 typical:1 alper:1 holds:1 wigner:30 over:2 mainly:1 satisfied:2 produced:1 through:3 mentioned:1 existence:6 satisfies:1 still:1 ieee:1 its:8 before:2 revived:1 derive:1 group:38 manuscript:1 chosen:1 matrices:2 sα:1 glogower:2 gen:3 drawback:1 degrees:3 systems:6 derivative:1 main:2 defining:2 deformation:1 correspondence:13 qq:1 non:6 ikθ:1 return:2 than:2 material:1 evolution:6 investigated:1 ηj:14 pegg:4 they:4 focus:1 oxford:1 formulating:1 rotation:1 now:8 transparent:2 2s2:1 2t:1 represents:1 term:1 dirac:3 2s:1 fully:1 university:5 level:4 identified:2 labeling:1 sin:5 orthonormal:1 sufficiently:1 modd:3 toroidal:2 each:13 found:12 soc:2 characterized:2 referred:1 homogeneous:2 weyl:4 ei:6 formulate:1 barnett:4 principles:1 used:1 applicable:1 literature:1 static:1 yield:1 begun:1 measure:2 quantum:80 our:9 operation:1 beyond:1 eq:128 special:3 shown:10 matrix:5 discrete:41 furthermore:1 since:7 crucial:4 gˆj:11 gˆ:48 investigation:1 reader:2 denoted:2 gˆa:1 ref:11 correct:2 math:7 xxxv:1 foundation:1 particularize:1 theory:7 associate:2 diagonal:12 standard:6 completely:3 base:2 york:2 dirk:1 earliest:1 remainder:1 e3:1 publication:1 definition:1 created:1 gˆ2:2 inspection:2 route:1 transition:1 days:2 counterpart:1 introduction:3 place:1 hence:11 facilitate:1 neglect:1 first:5 sanchez:2 already:2 zak:1 symmetry:17 variables:8 number:4 walter:1 autonomous:1 done:2 long:1 directly:1 superposition:1 angular:1 min:1 given:25 interesting:1 glauber:3 paves:1 leading:4 system:10 relations:6 their:12 calculations:1 realization:10 subgroups:3 recovered:1 discussion:1 shifted:2 asymmetric:1 continuous:33 optical:1 jordan:2 norms:2 natural:1 translation:1 sign:1 dt:7 sˆ:7 cosθ:1 john:1 automorphic:1 cyclic:19 sections:4 summary:1 imply:5 dtd:1 determined:1 fˆ:28 wiley:1 treated:1 result:1 seminal:1 motivation:1 generality:3 respecting:1 acknowledged:1 topics:1 argument:1 conference:1 say:2 2t1:1 su:1 close:1 qps:2 seek:1 any:3 relatively:1 dη3:1 strength:1 angle:33 zero:1 depending:2 lim:2 latter:1 aside:1 k3:2 instance:4 k1:1 nonalgebraic:1 square:1 generalized:39 analogy:6 paris:1 finding:1 victor:1 greatest:1 heisenberg:3 δn:1 added:1 entanglement:1 sm:1 trace:2 index:1 gλ:1 soto:1 algebraic:19 attempt:1 visa:1 connected:5 gauss:1 automorphism:6 phase:78 class:1 manifested:2 eigenfunctions:1 considered:2 kj:1 torus:2 adopt:1 implications:2 physica:1 proceedings:1 bracket:1 verlag:1 principle:1 exp:1 mechanical:1 dηj:1 camb:1 physics:3 sum:1 fact:3 dover:1 sector:1 called:1 emerging:1 particularly:6 yeh:1 eigenspectrum:3 lewis:2 labels:4 contemporary:1 x2:2 multiplicities:1 relation:1 fletcher:1 d2:1 indicate:1 principal:1 partners:2 based:8 knowledge:1 extending:1 eigenspace:3 eigenenergy:2 written:1 should:2 only:6 explicitly:1 generators:17 factor:3 integrable:1 circle:3 hamiltonians:1 local:1 dτ1:1 do:1 normalizations:2 notation:3 dependent:3 simplest:5 db:1 carruthers:5 da:1 aim:1 ones:4 rocca:2 progress:1 dv:2 hermitian:6 dr:1 subscript:1 prime:4 regarding:2 continuum:4 g0d:1 approach:12 arxiv:1 factorization:1 sˆα:4 europhys:1 common:1 frequency:1 fixed:3 valid:1 view:1 hκ:2 set:3 constructing:2 exists:2 achieved:1 1960s:1 cin:1 connections:1 namely:4 gunnar:1 projections:1 piza:1 discussions:2 terms:12 analog:1 appear:1 phases:1 satisfying:4 commutation:4 review:2 definite:1 dγ3:2 symmetric:3 iγj:2 state:15 projecting:1 correctly:1 between:16 conceptual:1 invariant:7 neither:1 conditions:4 choose:1 recently:4 historical:2 extend:2 nature:2 importance:1 weak:2 attention:2 wk:4 however:2 moyal:4 continuously:2 comm:1 miranowicz:1 eˆn:3 wp:2 article:2 problem:22 both:4 cos:5 limits:1 desired:1 iγ3:3 iγ1:1 iγ0:12 quantization:1 mathematical:1 connection:8 became:1 dγj:1 context:2 casimir:1 vourdas:5 expression:2 hχ:41 boyer:3 mechanics:7 ci:1 relevant:2 groups:2 point:2 simple:1 cb:1 ca:1 complies:1 harmonic:7 nˆ:1 dimensional:24 werner:1 spans:3 respect:4 ct:27 turkey:1 sine:3 described:3 transformations:18 spanned:2 basis:29 associativity:2 three:5 been:7 int:2 axis:3 eigenstate:1 interest:2 expected:2 aldrovandi:1 ph:2 algebras:1 ann:2 qho:12 define:6 direction:1 arises:1 corresponding:9 observable:1 itzykson:1 sufficient:1 coherence:1 spectrum:9 translationally:2 coherent:1 observe:1 univ:1 covered:1 c3:1 c2:1 c1:1 presented:2 irrelevant:1 former:1 present:1 case:16 k2:1 multi:1 east:1 laser:1 look:1 single:1 arnold:3 choices:2 will:27 eigenproblem:2 symbolically:1 applies:1 exist:1 property:2 study:1 procedure:1 dλ:1 identical:1 detailed:1 unitary:64 vogel:1 endowed:1 speech:1 thus:1 iλ:5 iv:6 ii:8 characterize:1 ik:1 examined:10 equality:1 tχ:6 dual:4 seen:2 partner:17 wisely:1 barker:1 spaces:1 different:6 ing:1 because:1 author:1 generic:2 suggest:1 make:1 belong:1 radiation:2 admit:2 same:5 acoustic:1 parts:2 quant:2 split:3 finite:13 natl:2 entitled:1 development:2 independent:2 extended:3 infinity:3 lie:2 welsh:1 counterparts:2 hand:3 v1:6 v2:6 harris:1 purpose:5 infinite:2 completeness:3 uˆ:17 t23:1 normalization:7 recent:1 eigenvectors:7 supports:2 scenario:6 nevertheless:1 valued:2 well:9 phil:1 academic:2 de:1 without:3 experimental:1 convenient:1 coordinate:1 dimension:6 subgroup:9 unified:1 construct:1 manifold:2 cj:1 being:4 sˆr:1 modular:1 labeled:1 obtain:3 detail:2 press:4 orthonormality:2 using:18 alternative:2 rotates:1 previous:1 note:1 preprint:1 generator:8 application:1 workers:1 characterization:1 guaranteed:1 discuss:1 lattice:2 sˆm:29 nor:1 versa:1 theorem:1 constant:1 extensive:1 formal:3 transformation:18 momentum:2 take:2 real:9 fairlie:2 lct:10 unify:1 bernardo:2 depends:1 eigenvalue:1 louisell:1 possible:1 iη:1 corresponds:3 early:2 quest:1 similarly:3 confined:1 integer:1 unique:2 moshinsky:3 mod:6 generated:1 loss:3 necessary:3 reduces:1 isomorphism:1 δr:1 manifest:3 separately:1 δm:2 yields:6 either:1 integrals:1 arbitrary:13 hung:1 jˆ:4 works:2 signal:1 therein:1 parity:3 drop:1 methods:1 classical:13 sequence:2 shen:1 some:9 born:2 acad:3 evaluated:2 b2:1 moreover:1 wwm:6 establishing:1 conventionally:1 provided:1 fock:9 describing:7 dimensions:1 eiζ:2 electromagnetic:1 does:1 decomposition:2 pei:1 provides:2 steps:1 proc:4 demonstrated:2 refer:2 inserting:1 considering:1 equivalent:4 radial:2 ωc:2 although:2 few:1 properties:14 after:1 simpler:2 integers:3 conclusions:1 detr:1 central:1 oj:1 extension:1 most:1 column:1 freedom:7 aˆ:21 dependence:2 o:73 covariant:1 important:1 wolf:3 act:2 mixed:1 importantly:1 illuminating:1 introduced:2 other:7 vi:1 em:3 primitive:1 cambridge:1 letters:1 chu:1 presence:1 into:4 within:10 rotations:1 isomorphic:1 soo:1 lies:1 appropriate:6 right:1 references:1 determine:1 operator:79 chang:1 next:1 additional:1 vˆ:16 area:2 there:6 nucl:1 specifically:2 noticed:1 start:6 joseph:1 inner:4 way:1 call:1 was:13 naturally:3 function:25 ago:1 complete:3 form:6 ψm:8 jun:1 but:3 formalisms:2 taken:1 construction:1 larger:1 tracial:1 hd:5 made:2 middle:1 2πd:1 uq:1 up:2 us:4 wψ:13 international:1 ωj:2 limit:18 ωo:1 ωn:1 ωa:1 gilmore:1 distribution:3 ωb:1 similar:6 ωd:1 eigenvector:1 examples:1 aa:20 sometimes:1 associated:1 defined:20 certain:2 abstract:1 describe:2 general:8 proper:1 examine:10 pˆ:3 periods:1 dθ:3 formulation:8 dζ:1 dη:2 formalism:12 distributions:4 dγ:5 physical:4 again:2 functions:6 susskind:4 whereas:3 attacked:1 when:10 sˆs:2 schwinger:21 field:1 interested:4 role:1 b425:1 department:1 nr:1 confine:1 acknowledgments:1 conclude:1 picture:2 elements:18 generates:1 separate:1 symbol:4 problems:1 polynomials:2 includes:1 kirkwood:5 a2:1 allowing:1 studied:5 included:1 sides:1 building:1 implies:7 nµ:2 assume:2 requires:1 dτ:1 space:46 sˆ0:1 equivalently:2 implied:4 4k:3 time:12 n1:4 n2:6 n3:2 starting:2 lett:7
|
quant-ph9906084.txt |@word secondly:1 partial:9 consider:3 squared:1 dynamic:12 results:3 founded:1 proposition:6 computation:24 go:1 query:27 devoted:1 whose:4 preserves:3 inverse:1 depend:1 finally:4 tm:3 marks:1 norm:4 case:8 string:1 orthogonal:1 reversibility:1 p0:5 focus:2 corollary:2 wishes:1 every:8 entries:1 24th:1 condition:4 four:2 solves:1 forth:2 quintuple:2 leave:1 convenience:4 vector:1 science:3 12t:1 round:5 configurations:3 says:1 occurrence:1 consists:2 zero:1 street:1 design:2 further:1 machines:10 even:1 what:2 stands:1 section:10 find:1 cell:16 version:1 above:5 designing:1 international:1 movement:2 satisfy:1 degree:1 respectively:2 never:1 modify:2 equals:1 here:4 ranges:1 desired:5 1m:1 address:1 directions:2 path:7 along:3 change:4 obtained:1 search:1 increments:2 tapes:29 rests:1 study:1 vectors:2 allows:1 leaving:1 procedure:2 makes:7 uniquely:1 useful:1 extra:4 marked:1 replace:1 1st:2 marker:1 apply:4 counts:1 tools:2 tomoyuki:1 unit:3 use:2 prove:2 distinct:4 next:1 calculation:1 program:1 call:3 therefore:2 m2:9 encode:1 means:1 theoretical:1 reflects:1 more:3 formally:2 initiated:1 becomes:1 operators:1 reversible:1 particular:2 known:3 foundations:1 hold:2 iii:1 must:3 valued:1 word:4 quartic:1 bits:1 recall:2 work:1 modified:1 mt:1 ij:1 halts:20 following:8 making:1 proof:13 control:4 transition:10 process:2 expanding:1 bennett:1 accept:1 states:7 effectively:1 sense:1 information:2 needs:3 requirements:1 goal:1 verify:1 discussion:1 holds:1 feature:1 orthogonality:1 machine:5 how:2 instead:4 brassard:1 prohibits:1 product:2 may:3 turing:11 after:4 formedness:9 cf0:4 produce:3 end:5 natural:1 remember:1 whenever:2 lemmas:6 counter:7 correspond:1 complexity:5 maintain:1 so:6 fundamental:1 enter:1 definitions:2 m1:12 unsolved:1 executed:1 help:2 ith:4 produces:2 september:1 over:1 move:13 symbols:7 course:1 paper:3 including:1 existence:1 satisfies:7 still:5 ieee:1 its:19 before:1 write:8 τm:1 τj:2 qkm:1 maps:1 interesting:1 writing:1 squaring:1 pad:2 main:1 easier:1 non:1 return:1 halt:1 weakness:1 runs:3 introduce:3 primary:1 reaches:5 they:1 symposium:2 own:2 now:2 handy:1 2t:7 several:1 university:1 identified:1 2d:1 iff:2 magnitude:1 l2:4 each:14 disregard:1 found:1 polynomially:1 mean:2 subset:2 significantly:1 simplicity:1 ed:7 reduce:2 idea:1 slowdown:8 fraction:1 combining:2 quantum:25 our:3 special:1 shown:1 matrix:1 space:1 since:14 interference:1 denotes:2 content:5 fellowship:2 reader:4 current:2 suffices:1 foundation:3 theory:3 associate:1 qf:30 differ:1 mapping:1 vazirani:4 completely:2 y01:1 beginning:1 8t:1 additional:1 definition:6 starts:1 computers:1 programming:3 introduction:1 length:10 place:1 circuit:1 hence:1 uses:2 onto:1 first:10 reversing:1 initial:4 suffix:2 probability:13 xm:2 u1:14 number:9 oracles:5 another:1 blank:4 force:3 clarity:1 given:15 1r:4 heads:11 1t:30 thirdly:1 unitarity:1 behaves:1 construct:2 their:3 returns:1 brevity:1 tighter:1 statement:1 zeros:1 siam:2 behaved:3 final:32 scans:4 terminates:1 mostly:1 tuple:6 reversed:2 exactly:10 regards:2 simulate:4 x2:2 alphabets:3 x1:2 than:4 updating:1 princeton:2 structured:2 counters:1 idle:2 determined:3 amplitude:3 enables:1 distinguished:2 pre:3 fashion:1 comput:2 qpm:1 unchanged:1 qˆ0:1 argument:1 already:2 say:4 7t:1 need:1 any:40 complete:1 paths:3 strength:1 note:10 internal:2 build:2 forces:1 indexed:6 qtms:5 allow:1 normal:19 who:1 reach:2 most:1 significant:1 preliminary:1 pair:4 accepting:3 grateful:1 qp1:1 class:1 appear:1 constructed:1 considered:1 partition:1 proceedings:1 notion:2 show:12 supported:1 synchronous:15 rth:2 halting:1 spaces:1 postdoctoral:1 stepping:4 d2:3 agrees:1 d0:8 d1:3 completion:9 q0:21 copy:1 simulating:1 much:1 representation:2 written:3 separability:2 lemma:39 only:9 tape:118 subsection:2 bernstein:4 local:1 achieve:1 do:2 notation:1 di:3 ones:1 reversal:1 new:4 timing:4 during:1 qp:3 evolution:2 µa:3 arxiv:1 qa:2 34th:1 queries:3 shi:1 fixed:3 cǫ:7 scanning:1 set:10 constructing:1 exists:12 10t:1 see:4 computer:4 result:4 y0:1 qtm:111 subject:1 said:1 αx:3 familiarity:2 qf1:3 qf2:3 µm:16 state:33 invokes:1 between:1 consecutive:2 boundary:1 conditions:3 µb:2 gives:2 ends:2 recently:1 extend:2 initially:2 however:1 interfere:1 configuration:17 τk:1 σk:17 σj:1 σi:6 toward:1 last:2 rightward:1 many:1 τi:1 nserc:1 merging:1 qfi:3 0i:1 finds:1 otherwise:3 arbitrarily:1 words:2 simple:1 cf:4 deposits:1 qpi:1 simply:1 invariant:1 polynomial:10 moreover:2 cq:3 throughout:1 second:1 ensures:1 leads:1 basis:4 union:1 create:2 acceptance:8 three:6 mark:1 ai:5 yao:3 describes:1 treat:1 pj:1 pk:1 ph:1 empty:10 define:10 direction:4 partly:1 formed:51 requires:1 observe:1 understand:1 general:6 present:2 reverse:1 p2:7 multi:16 p1:7 unlike:1 propositions:1 ǫi:3 expanded:1 harder:1 will:9 proves:1 suppose:1 ǫv:4 hdi:1 concurrently:3 unitary:4 cont:5 thus:5 them:1 ii:2 middle:1 itself:1 dimacs:1 ignoring:2 01t:1 binary:6 different:2 author:1 alphabet:4 make:3 same:6 clearly:1 quant:1 copying:2 qam:1 finite:2 qai:1 difficult:1 status:1 independent:1 arrives:2 dǫ:2 cubic:1 running:10 moving:5 purpose:1 infinite:1 changing:2 expand:3 simulates:9 qa1:1 undefined:1 qa2:1 well:66 solve:1 log:13 simulated:3 firstly:1 position:2 model:4 olden:1 left:2 less:2 being:1 obtain:1 rest:1 leftward:1 unary:3 previous:1 adding:2 enters:7 5t:1 except:2 discuss:1 add:2 easy:3 theorem:6 input:42 take:1 identical:3 read:1 possible:3 using:10 bit:5 2nd:1 formal:2 like:1 excluding:1 follows:6 collect:1 steps:24 δk:1 output:1 works:1 stationary:12 essential:1 terminology:1 stretched:1 mathematical:1 exceed:1 because:3 classical:4 ignored:1 some:2 back:6 16t:2 erase:1 conventionally:1 orthonormal:3 conservative:6 does:5 proc:1 minimal:1 equivalent:1 pp:1 expansion:1 restrictive:3 step:6 although:2 2m:1 hadamard:1 post:2 includes:2 central:1 extension:2 accepts:1 o:7 simulation:24 mutually:1 unidirectional:13 2k:15 slightly:1 freeing:1 timeevolution:1 keeps:1 into:10 within:1 bound:2 copies:1 modifying:2 phase:4 right:5 references:1 operator:2 reducing:1 rounds:1 acknowledgements:1 span:1 deal:1 area:6 there:14 question:1 transform:5 decode:1 start:11 quadratic:8 inner:1 way:2 series:2 overhead:2 sections:2 function:9 head:26 elsewhere:8 form:23 fundamentals:1 adjusting:2 criteria:1 jun:1 but:1 bǫ:3 construction:1 hd:7 he:1 made:1 applying:1 andy:1 wish:2 cells:6 variations:1 up:1 us:1 record:2 below:2 demonstrate:1 problem:5 similar:3 called:2 associated:3 computing:1 defined:8 certain:3 abstract:1 contribute:1 denote:8 single:26 scanned:1 exist:4 rule:3 corresponding:1 moves:1 check:1 defines:1 nj:1 completeness:1 no:2 when:14 detail:2 application:1 interested:1 outputs:2 department:1 forcing:1 2di:1 reverses:4 briefly:1 elements:1 superposition:10 provided:1 symbol:16 update:2 polynomials:1 stay:5 concurrent:6 important:2 allowing:1 implies:3 assume:9 starting:3 4t:2 4r:5 together:3 qp2:1 time:47 oracle:20 expands:1 incrementing:2
|
quant-ph9906085.txt |@word consider:6 priori:1 helstrom:1 results:4 illustrated:2 roy:1 entropy:40 broader:1 invariably:1 expressions:1 reasoning:1 disposal:2 equivalence:3 behaviours:1 th:2 under:2 meister:1 characterised:1 worth:2 ingredient:1 applied:4 belonging:1 amplitudes:1 advantage:2 orthogonal:2 institute:1 than:2 rise:4 springer:1 wave:2 difference:1 matrices:1 strand:1 hamiltonian:1 solution:1 large:1 insights:1 vector:2 demonstrated:1 fortiori:1 der:1 upper:1 consistent:2 literature:1 further:1 linear:4 even:1 what:1 nonlinear:1 selected:1 foregoing:2 expressed:3 find:1 reminiscent:1 above:1 sup:1 new:2 method:1 coefficient:1 justification:1 led:1 here:8 diagonal:2 behaviour:1 desired:1 pursuit:1 others:1 represented:6 implicit:1 obtained:2 technical:2 study:2 allows:1 contradiction:1 resulting:1 stimulating:1 poisson:3 hospitality:1 suitable:1 involves:1 composed:1 projection:3 family:2 extra:1 outcomes:1 apply:1 select:1 readily:1 conventional:2 takes:1 commun:2 remains:3 positive:1 calt:1 properties:5 therefore:4 totality:1 taken:3 type:1 von:13 reflects:2 more:5 duality:1 relax:1 operators:2 odinger:2 berlin:1 particular:2 known:2 projective:1 must:1 nutku:1 account:1 hessian:3 equation:1 work:2 obvious:2 cam:1 example:6 unconditional:1 performed:1 compare:2 give:2 calculation:1 expanding:1 states:10 weighting:1 minimum:2 numbers:1 sense:2 times:1 conversely:1 2ls:1 verlag:1 information:28 rays:1 turn:1 beyer:1 discussion:2 holds:1 write:1 how:2 methodology:1 numerous:1 pure:15 significance:1 instead:1 ordinary:5 parameter:1 ensemble:3 ft:1 quantenmechanik:1 algebra:1 thermodynamic:1 after:1 constraint:3 hence:1 choice:1 natural:3 dynamical:1 explicit:1 departure:1 st:1 perhaps:1 counterbalances:1 allow:1 correlation:1 subsequently:1 acknowledges:1 order:2 typical:1 fα:1 interpretation:1 mielnik:2 indeed:4 over:1 choose:1 thermal:1 xi:10 london:3 statistical:5 differs:2 kibble:2 its:2 superior:1 derive:1 acknowledge:1 ln:13 solving:1 translation:1 expectations:1 estimating:1 concavity:1 systems:2 mail:2 main:1 rockafellar:1 thereby:1 fig:2 introduce:2 emphasised:1 sρ:16 now:1 silver:1 represents:2 february:1 finite:1 university:2 brody:5 concave:2 appropriate:1 accommodates:1 displacements:1 realistic:1 each:3 side:1 lifted:1 weighted:2 financial:1 series:1 principles:2 deficiency:1 used:3 measurement:8 quantum:43 our:8 beyond:1 shannon:6 out:2 category:1 shown:2 matrix:20 space:17 since:2 rev:4 holevo:1 denotes:4 content:1 combinatorial:1 contained:1 formula:4 suffices:1 correct:1 math:4 shows:2 regards:1 theory:11 differ:1 free:3 standard:4 admits:2 york:1 eigenvalues:4 care:1 derivation:1 geometry:1 transition:2 nonnegative:1 fβα:4 consequence:2 onto:1 think:1 first:1 origin:1 initial:2 probability:8 number:1 another:1 precisely:1 electronic:2 illustrate:1 equating:1 given:24 bracket:2 indicate:1 unknown:1 system:12 least:1 their:1 assumption:3 hypothetical:1 scheme:1 gives:4 part:1 authors:1 x0:3 representing:1 peculiar:1 coefficients:1 king:1 determines:1 holland:1 princeton:4 require:2 summary:1 depends:1 determined:4 contrary:1 amplitude:1 were:1 outcome:2 solely:1 ingenious:1 function:20 rao:1 ann:1 modern:1 argument:2 curves:2 say:1 qualitatively:1 concentration:1 element:1 clearly:2 viewed:3 ray:1 affairs:1 studying:1 hyperplanes:1 note:1 instance:1 take:1 analogy:2 canonical:2 trace:8 shall:5 underpinnings:1 measures:1 reach:1 involving:1 wc2r:1 formulae:1 phase:3 probabilistic:3 class:4 treats:1 consequences:1 clear:1 traditional:1 braunstein:1 points:1 exp:5 typically:1 fact:4 quantity:1 show:1 able:1 relation:1 subtle:1 agrees:1 based:1 knowledge:2 situations:1 should:3 moments:2 only:7 explicitly:3 factor:1 constant:1 hope:1 do:1 his:2 legendre:1 goes:1 means:1 familiar:1 express:1 expectation:6 dv:8 evolution:1 conditions:2 arxiv:1 consisting:1 investigate:1 though:1 contain:2 through:2 implication:1 view:2 riemannian:2 satisfy:1 set:2 computed:1 exists:2 up:3 detection:1 see:2 college:1 result:4 eliminating:1 theoretic:4 subject:2 satisfying:1 capacity:1 nondegenerate:1 positivity:1 definite:1 below:1 symmetric:1 state:35 between:3 caves:2 approach:4 available:3 terms:4 statistically:1 missing:2 initially:2 parameterising:1 however:5 wi:13 eλ1:1 multiplier:3 article:1 understanding:1 distribution:11 concentrated:2 observable:9 limits:1 tractable:1 many:2 equal:1 symplectic:5 context:4 variance:1 argue:1 expression:5 reside:1 ch:1 point:5 address:1 cf:2 dimensional:1 lagrange:3 respect:2 gratitude:1 basis:2 trajectory:1 copies:1 been:1 interest:1 ph:2 define:1 generating:5 arises:1 corresponding:7 commutes:1 gas:1 covariance:1 dimensionalities:1 hughston:5 derivative:2 c2:1 denote:1 present:2 case:6 look:1 pacs:1 expanded:1 examine:1 value:1 transformation:2 will:1 fubini:2 suppose:3 grundlagen:1 property:1 procedure:1 identical:2 endowed:1 metric:4 damtp:2 thus:4 according:2 itself:2 dual:1 different:1 generic:2 suggest:1 make:2 belong:1 same:4 any:3 unity:1 complex:1 quant:2 arguments:1 defines:1 independent:4 weinberg:2 trajectories:1 upon:1 hand:1 moment:2 idea:1 totally:1 prescribed:1 lower:2 estimation:2 schr:2 nevertheless:3 com:1 well:1 analysis:3 academic:1 mathematische:1 english:1 possesses:1 spherical:1 manifold:3 popescu:1 being:1 0ds:1 guided:1 obtain:5 relevant:1 eigenstates:4 preprint:1 generator:1 density:30 conclude:1 character:1 exclusively:2 thermodynamics:1 belongs:1 combine:1 lett:3 eigenstate:1 pparc:1 real:1 aspects:3 eigenvalue:1 showing:1 term:1 know:1 press:3 unique:2 mod:1 like:1 follows:10 qualitative:1 informative:1 alternatively:1 resolved:1 terminology:2 because:8 neumann:13 classical:3 conditional:1 some:3 remarking:1 convex:4 recognition:1 provided:3 footing:1 integration:3 does:2 decomposition:1 assuming:2 proc:1 minimal:2 refer:1 who:1 slight:1 equivalent:1 arbitrary:1 dcb:1 use:2 expansion:1 although:1 plots:2 normalisation:1 hilbert:4 bz:1 proceed:1 gained:1 about:2 carried:1 commutator:1 dependence:1 compatible:1 distinct:3 preskill:1 introduced:4 soc:1 cambridge:1 communication:1 into:4 integral:1 bound:1 twostate:1 hermitian:1 right:2 operator:2 amsterdam:1 utility:1 gursey:1 normalised:1 support:1 there:4 question:1 specifically:2 intention:1 was:2 strict:1 lowest:1 north:1 complete:1 form:6 offer:1 regard:1 jun:1 drummond:1 gaussian:2 volume:1 heat:1 satisfactorily:1 delta:2 encoded:1 line:1 proposal:1 surprising:1 evident:1 wish:1 smooth:1 maximum:2 us:5 liouville:1 owing:1 uk:3 demonstrate:2 problem:5 similar:2 agree:1 entropies:2 recalling:2 mechanics:8 ac:1 associated:7 defined:1 inadequate:1 condition:1 general:10 single:1 exist:1 dλ:2 formulation:1 distributions:2 physical:1 illustration:1 functions:4 istanbul:1 no:2 whereas:1 when:3 field:1 other:5 special:1 department:1 mathematics:1 elements:1 yahoo:1 cb3:1 fisher:2 structure:6 svn:6 lane:2 implies:3 physics:1 required:1 curve:2 governed:1 implied:1 weights:2 observables:5
|
quant-ph9906086.txt |@word four:1 entropy:4 consists:3 calculate:3 characterises:2 under:6 characterised:7 worth:1 rise:4 mania:1 solution:4 vector:23 indices:2 degeneracy:1 direct:3 ωab:13 second:2 street:1 even:5 established:1 incompatible:1 specification:8 selected:1 above:3 new:5 ever:1 consisting:5 notions:1 here:12 represented:10 path:3 obtained:6 substance:2 study:18 loop:3 suitable:3 appropriately:1 tu:2 projection:1 classification:1 highly:1 brought:1 eastwood:2 total:8 schilling:2 bra:6 would:2 negative:1 call:2 therefore:4 type:4 relax:1 composite:1 brings:1 odinger:28 berlin:3 physically:3 hurd:3 springer:2 join:5 quartic:1 work:1 root:2 example:14 indicated:4 give:1 weinberg:9 reviewing:1 degenerate:5 end:1 verify:1 feature:4 how:5 methodology:2 ordinary:1 description:1 earlier:3 symmetrisation:1 attempt:1 effective:1 greek:1 acknowledges:1 order:4 operations:2 origin:4 interpretation:5 over:7 vary:2 satisfied:3 london:9 satisfies:2 recognised:1 writing:1 distinguishing:1 compelling:1 condition:5 maximal:3 eventually:1 them:1 combination:1 they:2 silver:1 represents:9 toroidal:1 each:15 side:1 lifted:1 financial:1 independent:10 series:1 principles:1 used:1 poincare:4 laboratory:1 gradient:7 particles:14 linear:13 standard:6 admits:2 proportionality:1 estimate:1 9ew:1 r3:7 ds2:1 corrections:1 features:5 clear:1 spinning:1 another:6 illustrate:2 toy:1 twisted:11 observations:1 ashtekar:2 collapse:1 speakable:1 uhlmann:2 distance:22 showed:1 princeton:1 collinear:1 kth:1 solely:1 modern:1 mind:1 manner:1 seen:2 ray:3 τab:6 latter:1 responsible:1 degenerates:1 quadric:21 shall:6 foliate:1 boltzmann:1 nonlinear:18 phase:35 observation:1 calculated:1 partition:1 flow:3 βej:3 bracket:2 principle:2 notion:2 labels:2 attempts:1 solutions:1 keywords:1 analogue:4 d3:1 touches:2 situations:2 rich:1 oct:1 do:3 establishes:2 preferred:5 dx:8 despite:1 dt:3 ds:5 fields:6 twice:1 riemannian:2 observed:1 depends:3 result:10 discussions:1 best:1 subject:1 tensor:3 symmetric:6 µk:2 simplest:3 conceptual:1 drawn:1 µa:1 µb:1 preserve:1 triplet:6 terms:9 positron:8 however:5 extent:1 topology:2 cos:3 uncertainty:13 variance:4 argue:1 adapted:1 connection:2 2nd:3 applicability:1 gratitude:1 basis:2 union:1 simplification:1 three:16 been:3 much:1 interest:3 basic:1 expected:1 quantities:1 lift:4 maximally:11 spin:85 applied:2 transformation:1 euclidean:2 neat:1 applies:3 property:5 elaborate:1 procedure:3 equator:2 ib:1 containing:3 suggest:1 make:1 clearly:3 complex:39 quant:4 several:1 isometries:1 evolve:1 trajectories:9 hand:8 workings:1 weakly:1 whereby:1 epr:1 greatest:3 studying:1 possesses:1 popescu:2 newton:1 assigned:2 eigenstates:16 previous:1 regarded:3 had:2 belongs:3 iθ:3 advances:1 possible:8 possibly:1 unique:11 apart:2 specific:5 arbitrary:5 right:1 truncates:1 rψ:1 subclass:1 kobayashi:2 particular:6 illustration:1 substitution:2 properties:9 proceed:1 stokes:1 metrical:5 accepts:1 o:2 constituting:1 nonvanishing:2 probabilities:5 raised:1 disentangled:21 bound:2 bath:2 down:5 lies:9 hermitian:8 refined:1 methods:1 support:1 initial:9 physicists:2 way:6 was:5 lowest:1 form:23 taken:1 heat:2 flavour:1 nonlinearity:1 maximum:5 examples:5 evidence:1 peres:3 exist:1 distributions:3 regime:1 no:7 whereas:3 generally:2 setting:2 role:2 superfluous:1 eternity:1 picture:1 superposition:5 describe:1 variable:3 ξa:2 ξb:2 longer:2 dψ:3 assume:2 governed:1 time:9 characterising:1 concept:1 remarkable:1 global:1 leads:3 roy:4 foundations:2 ward:1 inverse:2 depend:1 technique:1 reverting:2 finally:1 meister:1 analogous:2 must:1 advantage:1 orthogonal:8 frequencies:4 geometrical:9 level:5 discrete:1 round:1 dealing:1 axes:2 uniform:1 current:1 commensurate:1 paradoxical:1 satisfy:1 understanding:1 tangent:17 cos2:2 qαγ:1 qαβ:21 alone:1 along:4 xα:2 change:3 shift:1 studied:3 spheres:4 maximising:1 poisson:3 useful:1 merely:1 planck:1 additive:1 covariant:1 positive:2 gibbons:7 selects:2 apparent:1 validity:1 rigid:3 virtue:1 cases:1 insights:2 rotational:1 sheds:1 modified:3 values:1 believed:1 trans:27 unconditional:2 heslot:2 heart:1 figure:18 arise:3 topic:1 weighting:1 performed:1 spanning:2 conversely:6 dxb:4 2ls:1 verlag:2 rays:1 s2:1 write:6 pure:17 parameter:4 map:8 product:6 irrational:1 may:3 applications:2 produce:1 compatibility:1 sz:11 natural:12 dynamical:9 explicit:1 ordinarily:1 so:11 representation:1 exclusive:1 maximisation:1 aforementioned:1 schwartz:1 indeed:5 pointed:1 soc:32 entity:1 statistical:11 argued:1 still:1 group:3 interesting:4 nontrivial:1 coordinates:17 offers:1 constitutes:1 main:2 decades:1 texas:1 correspondence:6 introduce:4 touching:1 half:1 now:6 discuss:2 term:2 brody:27 advent:1 spinor:10 weighted:2 ei:3 ej:4 ed:5 conventions:1 owing:1 emerges:2 shown:2 space:96 furthermore:1 squared:1 contained:2 investigation:1 rational:2 formula:2 after:1 theory:25 possibility:2 advantages:1 e1:4 inevitable:1 e2:4 language:1 transition:7 turn:1 βa:1 βb:1 βh:2 think:2 first:8 xj:2 symmetry:5 striking:1 omitted:1 variables:4 u3:2 directly:4 carry:1 open:1 angular:10 constructing:1 wilczek:2 given:81 necessarily:5 unitarity:1 indicate:2 structures:1 gives:8 cup:1 anandan:4 representing:4 than:1 intrinsically:1 royal:2 third:3 require:3 were:1 merits:1 outcome:3 ann:2 argument:3 say:5 any:29 subsystems:2 note:8 potential:4 take:2 objective:1 coincide:1 begin:1 opposite:1 arguing:1 algebraic:4 printed:1 automorphism:1 pair:15 surprising:1 considered:2 average:2 phil:25 drive:1 harvey:1 abraham:1 laws:1 show:3 osculating:1 spaces:4 fibre:2 ratio:7 state:142 only:7 ratiu:2 get:1 dekker:1 expectation:11 aα:1 aξ:1 sum:2 imposing:1 tu2:2 relative:4 elected:1 namely:4 college:2 surfaces:5 satisfying:5 eigenfunctions:1 subsequent:2 review:1 definite:1 αa:8 outside:1 αb:3 jth:1 between:15 geometric:39 twistor:2 originated:1 killing:12 multiplier:1 article:2 come:1 concentrated:6 many:6 region:1 according:4 called:7 enabling:1 berry:4 embedding:3 huggett:1 expression:5 lagrange:1 associated:15 skew:2 springerverlag:1 foliated:2 combined:4 direction:4 implied:1 irrelevant:2 those:3 case:30 hdt:3 arnold:3 intimately:1 situation:8 orientation:1 endowed:4 metric:9 marcel:1 supremum:1 different:4 verified:1 coexisting:1 hψ:1 same:4 constructed:1 status:1 extended:1 closest:2 singapore:1 hγβ:1 entanglement:12 estimation:2 parameterised:2 peculiarities:1 without:3 solve:1 components:3 model:1 dimension:4 isometry:1 muon:2 manifold:14 being:4 when:12 touch:2 speed:3 multiples:1 generator:4 thinking:1 except:1 lett:10 pitman:1 eigenstate:4 momentum:3 real:9 antisymmetrisation:1 aspects:3 eigenvalue:2 rules:1 harmonic:2 confined:1 using:1 cd:9 ruled:1 acquainted:1 particle:16 reduces:2 miracle:1 stationary:2 beltrami:1 conditional:1 specified:3 dimensions:7 eiθ:3 eiλ:1 footing:1 decomposition:1 provides:2 moderate:1 ψabc:2 ωij:1 scientific:1 equivalent:3 notable:1 meets:1 ratios:2 central:1 acd:1 discussed:1 generated:3 mutually:1 act:2 mixed:7 purported:1 cambridge:2 communication:1 image:1 references:1 determine:5 einstein:3 elementary:1 spinors:7 normalised:1 there:26 start:1 shapere:2 regard:2 aµ:1 downstairs:1 adler:2 marsden:3 liouville:4 strongly:1 ac:1 ab:44 af:1 certain:2 measurement:18 general:25 britain:1 together:2 hβα:5 field:12 valid:2 spatial:1 mathematics:1 polar:24 briefly:3 includes:1 cb3:1 important:1 observables:14 curve:12 mass:2 starting:2 original:2 represent:4 since:8 consider:24 expressions:1 polarity:3 preserves:1 equivalence:1 tn:1 program:3 belonging:1 returning:1 very:2 induce:2 print:2 strand:1 generalised:1 hamiltonian:22 t2:5 t3:2 t1:1 segre:2 ga:2 tex:1 intricate:1 zero:1 perspective:1 further:9 canonical:6 what:5 abc:18 sub:1 brackets:2 section:1 intersect:3 contrast:2 dimensionality:1 directions:1 antisymmetric:3 allows:2 action:2 via:3 family:6 select:1 takes:1 distinct:5 codify:1 contains:4 nucl:1 characteristics:1 ψb:11 ψc:2 ψa:5 more:14 linden:2 initiated:1 operators:2 problem:3 varying:1 known:3 projective:34 evolves:2 none:1 recall:2 equation:27 det:1 sweeps:1 remain:1 canonically:1 beautiful:1 states:67 sphere:7 minimum:1 numbers:2 hyperplane:6 sense:13 axis:23 information:2 respective:1 goal:1 polchinski:3 rather:3 acts:1 acta:1 ensemble:3 simplicity:1 suppose:9 wiley:1 orbits:1 plane:29 develop:1 horizontal:4 choice:15 fundamental:2 helv:1 ith:1 developed:2 thermal:1 paper:2 through:14 existence:1 kibble:13 its:11 roots:1 pirani:1 energies:1 solving:2 conjugation:6 actually:1 microscopic:1 systems:10 differed:1 might:5 propose:1 number:4 framework:3 oxford:2 conic:22 iff:1 inequality:7 2m:2 2n:8 2j:1 referred:1 disentanglement:2 energy:22 reduce:1 idea:5 sketched:1 quantum:120 operation:3 beyond:2 really:1 involutory:1 induces:4 sustain:1 denoted:1 induced:2 reason:2 base:1 ask:1 generate:2 definition:1 pairs:5 omit:1 circuit:1 consequence:4 exhibited:1 major:1 probability:18 geodesic:3 least:1 temperature:1 introduction:4 leading:1 construct:1 expand:1 recovered:1 relationship:2 authors:3 schr:28 king:1 kind:1 determines:13 cyclic:3 double:1 determined:8 contrary:1 treated:1 ψab:2 affirmative:1 conjugate:32 null:2 paths:1 constructions:1 randjbar:1 self:7 hyperplanes:6 pparc:1 play:1 towards:2 measures:2 singlet:7 most:1 plan:1 undertaken:1 nothing:1 measured:1 equatorial:3 torus:3 antipodal:2 exp:6 kt:1 physics:4 joining:2 phenomenon:1 relation:15 find:3 generators:4 factor:2 circle:3 his:1 hit:1 notation:8 dependent:2 zurek:2 express:1 closely:1 arxiv:1 doublet:1 set:7 achieved:1 unpublished:1 see:8 individual:2 close:2 uξ:1 probable:1 currently:1 various:2 lowered:1 pictured:1 available:1 initially:2 complement:1 attention:1 δab:1 interface:1 both:6 reverse:1 desired:1 sudbery:1 roman:1 symplectic:9 context:3 point:80 simple:2 corresponds:10 dimensional:8 bη:1 indefinite:1 ensures:1 described:4 transformations:3 quantisation:7 px:1 due:1 reduction:1 ph:27 addison:1 tangents:1 wheeler:2 understand:2 hughston:35 gac:1 gab:14 ǫc:1 look:1 expanded:1 empirical:1 while:2 sw7:1 unitary:4 vol:1 itself:6 modification:1 higher:1 development:3 literature:1 lie:3 flows:1 subvariety:1 moment:4 levels:1 moving:1 eigenvectors:1 lower:2 analysis:1 comprise:1 distances:1 chord:2 λb:1 λa:2 world:4 conclusions:1 φab:8 theorem:1 relevance:1 remaining:1 nonphysical:1 entangled:23 rotate:1 tangentially:2 systematically:1 follows:26 essential:1 mathematical:3 often:1 some:16 serves:1 scale:10 measurements:2 integration:1 lαβ:8 proc:5 ba:2 bc:1 jumps:1 relating:1 hilbert:22 constraint:2 range:1 involving:1 extensions:1 into:4 integral:6 locus:7 1999a:3 1999c:2 1999b:2 few:1 probabilistic:1 question:1 lond:27 specifically:2 u2:2 sections:2 b410:1 line:30 gravitating:1 characteristic:6 up:14 us:16 gratifying:1 maximises:2 uk:3 planes:2 similar:1 laplace:1 blackett:1 gisin:3 bell:2 constant:6 defined:5 likewise:1 influence:1 globally:1 single:2 associates:1 defines:3 paradox:1 streater:1 points:45 department:1 confine:1 realisable:1 generates:1 problems:1 develops:1 allowing:1 structure:17 ago:1 furthest:1 lane:1 implies:7 required:4 orbit:1 neighbouring:1 weights:1 far:1 requires:1 having:1 once:4 illustrates:1 illustrated:1 eds:3 gb:5 ψcd:2 go:1 issues:3 compact:1 simon:2 concerned:1 include:1 ingredient:1 ǫac:4 ǫab:14 presently:1 wave:10 electron:16 rigourous:1 notes:1 eigenvalues:7 refer:1 deleting:1 noted:1 jump:1 fold:1 incidentally:2 dynamics:13 index:6 plays:1 invertible:1 expressed:3 poles:3 degree:4 respectively:3 following:4 explore:2 objects:1 consideration:6 great:2 contradiction:1 suggests:2 preferentially:1 resulting:6 stimulating:1 opinion:1 makes:1 involves:1 formulated:3 nearest:3 outcomes:4 summation:1 apply:1 use:10 superpositions:2 commun:3 remains:1 classically:1 cirelli:2 account:1 infinitesimal:1 obvious:1 process:1 purposes:2 holds:2 lepton:2 dxa:2 instead:1 superluminal:1 1998b:1 1998c:2 1998a:2 physical:8 light:1 lines:6 correspond:4 element:2 extremal:1 allow:1 subsequently:3 saturated:1 mielnik:1 envisage:1 ln:1 semple:2 derivative:1 horwitz:3 richness:1 operator:10 rotation:2 dirac:2 profound:1 university:4 identified:2 magnitude:1 enigmatic:1 doing:1 related:4 constitute:1 society:2 frequency:3 interplay:2 measure:10 our:2 special:9 out:4 category:1 respects:1 matrix:10 rep:2 rev:10 woodhouse:2 geom:1 lecture:1 suffices:2 math:9 york:3 geometry:33 could:1 keep:1 ahler:2 length:2 explored:1 hence:3 austin:1 sinθ:1 tributed:1 aharonov:4 unknown:1 system:40 relations:7 their:5 doomed:1 foliation:2 penrose:3 distinguishes:1 submitted:2 punctured:1 providing:2 symmetries:1 unchanged:1 need:1 apparently:1 intersecting:1 viewed:4 angle:4 minimally:1 pursued:2 mechanism:1 instance:1 heisenberg:3 who:2 petrov:1 gravitation:1 orthogonally:1 wc2r:1 intrinsic:1 class:2 consequences:1 repeated:2 χd:7 mechanical:10 fact:12 characterisation:4 agrees:1 principal:4 based:1 2bz:1 should:3 equilibrium:3 means:1 overall:3 bear:1 words:3 evolution:13 qr:1 approach:2 differential:2 grav:1 contain:1 fixed:6 view:4 requirement:1 modulo:1 computed:1 exists:4 hβ:1 edition:1 geometrically:1 phases:3 extend:1 nondegenerate:5 tend:1 written:3 identification:1 closed:3 invariant:9 tensorial:1 key:2 ǫcr:1 ket:6 percival:2 observable:20 hits:1 equal:1 chosen:2 admit:1 hω:1 hρ:1 grounds:1 unitarily:1 detailed:1 relevant:3 cb:2 cf:6 daemi:2 respect:11 cp:73 trajectory:15 degrees:3 define:6 arises:7 corresponding:38 sufficient:2 subspace:2 essentially:1 angles:1 present:5 multi:1 examine:1 value:2 will:2 damtp:1 thus:16 surface:16 dual:4 quantization:1 generic:11 cross:6 φa:1 φb:2 gibbs:1 finite:8 difficult:2 cubic:11 upon:1 qβ:1 infinite:3 spinorial:1 identity:3 4πmp:1 off:3 geroch:2 nevertheless:1 well:3 position:5 arising:2 drawing:1 usual:3 spherical:1 linked:1 moments:3 rosen:1 obtain:4 underlying:2 distant:2 macroscopic:2 preprint:2 1989a:3 1989b:1 density:17 nonrelativistic:1 resolved:1 checking:1 lanl:2 vη:1 press:3 intersection:5 geometers:1 necessary:1 like:1 alternatively:1 fubini:16 δj:2 become:3 δb:1 because:4 nomizu:2 classical:8 ǫba:2 ǫbd:3 proper:4 lead:1 does:3 demonstrated:1 disentangle:1 ωbc:1 dcb:1 analysed:1 wesley:1 about:3 carried:1 freedom:5 interlinked:1 compatible:2 introduced:2 homogeneous:11 equally:1 previously:1 functional:1 twostate:1 additional:3 imperial:1 inasmuch:2 quadratic:2 inner:2 naturally:2 function:29 but:9 reminds:1 neutral:1 construction:4 goals:1 nonplanar:1 made:2 compute:2 evident:1 whether:6 wish:3 gravitational:3 fαβ:1 demonstrate:2 distribution:7 mechanics:48 intersects:8 denote:4 functions:5 compared:1 variety:2 detail:3 other:15 details:2 kinds:1 ultimately:1 bundle:2 anticommutator:1 unspeakable:1
|
quant-ph9906087.txt |@word represent:1 echos:2 similarity:1 caused:1 magnetic:5 global:1 rod:1 results:1 indicates:3 maxima:2 sci:1 heller:1 terms:1 graph:1 technique:1 quasi:1 program:1 present:1 stable:10 analogous:2 include:1 amplitudes:1 returning:1 very:2 frequencies:1 rise:1 wave:3 lyapunov:1 electron:4 every:2 hewlett:1 resonant:1 experimentally:4 presented:2 transmission:16 supports:1 itamp:1 large:4 fourier:1 small:3 massachusetts:2 setup:1 related:1 smaller:1 tem:1 periodicity:2 pulse:1 zero:2 further:1 dynamics:2 theory:6 even:2 appear:1 fine:1 ticks:1 labeled:13 experiment:2 above:1 new:1 tips:5 coefficient:2 outgoing:1 wavefunctions:8 escaping:1 arb:1 respectively:2 component:1 here:2 cylindrical:1 separation:6 directions:2 slater:2 along:8 strong:2 knowledge:1 arc:3 shift:8 larger:1 leaving:1 periodic:9 resonance:11 narrow:1 studies:1 involves:1 plotted:1 via:1 regardless:1 family:2 claim:1 explained:1 private:1 tracking:1 visible:1 buildup:1 linearly:1 bent:1 gaas:2 plot:2 indicated:5 would:4 distinct:1 positive:2 give:1 negative:4 next:1 classically:1 call:1 therefore:3 aperture:1 resonator:24 theoretical:3 more:3 separated:1 becomes:3 marks:1 odinger:2 curvature:5 instrumental:1 transient:1 diffracted:1 particular:1 nodes:2 high:2 account:1 quantized:4 sphere:4 mm:1 equation:3 work:1 foci:1 remain:1 determining:3 f1:7 f2:1 reflector:36 figure:4 mirrors:1 calculation:2 discussed:1 sense:1 states:1 effectively:1 numbers:4 degenerate:1 allowed:1 sharp:2 times:2 simple:2 axis:10 influenced:1 rays:5 varied:5 provide:1 regions:3 located:2 significance:1 instead:3 2deg:1 parameter:1 our:3 broad:1 hersch:1 orbits:28 reflect:1 explored:1 inst:1 designed:1 waves:2 horizontal:16 geometrical:1 parallel:3 types:1 curve:1 short:3 dynamical:1 computations:1 spectra:2 lines:1 correspond:2 ghz:2 element:1 rather:1 so:1 allow:2 lined:1 demonstrates:1 wavelengths:2 electromagnetic:2 insight:1 meter:1 stability:1 experiments:3 through:3 thesis:1 existence:2 its:3 scale:1 lf:1 rapidly:1 symmetry:7 fit:1 how:1 energies:1 exhibits:1 absence:1 fig:23 might:1 h0:1 emphasize:1 versus:2 non:1 return:11 thereby:2 prevented:1 number:3 band:1 billiard:6 they:4 half:4 now:1 discuss:1 represents:1 james:1 university:4 level:1 did:1 mode:4 each:7 crossing:1 found:3 side:1 characterized:1 square:1 ockmann:2 series:1 energy:1 reduce:1 used:4 conductance:5 attenuation:1 expect:1 changed:1 quantum:10 wavelength:6 operation:1 avoided:1 eq:1 out:2 leave:1 shown:8 converted:1 funding:1 network:2 resonators:1 since:1 interference:2 contained:1 mediated:1 cause:1 occurs:2 shows:3 trajectories:1 approached:1 little:1 governing:1 reason:1 subtended:1 included:1 beginning:1 e0:1 r0:1 geometry:2 widths:1 could:1 transition:4 noted:1 motion:1 turn:1 length:3 specular:1 willemsen:1 st:2 undergo:2 first:1 copper:2 major:2 twodimensional:1 probability:2 striking:1 reflected:1 transform:1 katine:4 thick:1 open:7 angular:3 given:3 perturbation:1 publication:1 bears:1 system:2 approximately:2 their:6 returns:1 intermediate:1 calculations:1 1m:1 gives:1 fraction:1 ratio:1 accurately:1 transverse:1 part:1 simulate:1 off:12 than:2 modes:5 distance:2 unfortunately:1 showed:2 split:1 intensity:3 determined:2 amplitude:5 were:7 impinge:1 geometrically:1 qpc:18 ram:1 spectrum:9 seen:1 unaffected:1 any:3 ray:1 paths:2 absorber:3 angle:5 partly:1 studying:1 separate:1 billiards:1 predominantly:1 note:3 edge:1 unperturbed:1 play:2 towards:1 multiple:1 electric:6 normal:2 caustics:1 impurities:1 measured:8 class:1 diffractive:21 forever:1 especially:1 considered:1 calculated:1 maier:2 stronger:2 inferred:1 points:1 electrons:1 consisted:2 physics:2 fact:1 show:2 text:1 supported:6 scattered:2 solutions:1 d2:2 d1:9 slow:1 resemblance:1 simulating:1 conduction:1 only:11 factor:1 local:1 plate:2 hit:3 dependent:1 de:1 db:1 cannot:1 secondary:1 processes:1 resolve:1 aluminum:1 fields:1 arxiv:1 summary:1 investigate:1 paper:2 predicted:1 mapped:1 including:1 fixed:3 bars:5 multiplying:1 maximum:1 see:2 decided:1 radius:3 result:1 close:2 contour:1 analog:1 subject:1 surfaces:1 phases:1 exponent:1 pattern:1 away:3 aberration:1 state:1 future:2 various:1 closed:4 between:8 geometric:2 pictured:1 available:1 emitted:1 recently:1 vertical:9 opening:4 importance:2 spacing:2 attention:1 focus:2 however:5 analyzer:2 harvard:4 group:1 come:1 remaining:1 thank:2 suggested:1 both:5 essentially:1 many:2 region:4 escape:2 chosen:1 context:1 contribution:1 experimental:5 cm:8 point:4 wall:23 perot:9 loan:1 coexistence:1 walk:1 semiclassical:6 haggerty:1 wider:1 cu:2 second:1 addition:1 diffracting:1 three:1 been:1 much:3 ph:2 systems:2 sical:1 direction:1 corresponding:2 moved:1 formed:2 gas:1 hits:1 coherently:1 angles:1 repetition:1 those:3 case:2 diffract:1 rectangular:1 will:5 near:2 behavior:2 westervelt:1 tunneling:1 layer:1 studied:5 coupled:1 thus:3 them:1 itself:1 curved:1 disappear:1 stein:2 grant:1 lengths:3 silvered:1 make:1 cross:1 clearly:3 shorter:2 shifts:4 complex:2 quant:1 dotted:3 schematic:2 units:1 plates:4 higher:1 independent:1 literature:1 peaks:23 numerical:3 running:2 edges:1 moving:1 appreciable:1 heterostructure:2 shortens:1 simulates:1 weakly:1 schr:2 reflection:5 contact:1 thoroughly:1 position:9 chemistry:1 drawing:1 left:5 spherical:1 edwards:2 manifold:1 proposed:1 tip:3 proximity:1 underlying:1 voltage:1 scattering:1 adding:1 seems:1 except:1 source:2 setting:1 combine:1 lett:3 excited:1 identical:1 around:2 rev:4 repetitions:1 emanating:1 dark:1 increases:1 grid:2 marked:3 using:1 apart:1 dimensional:3 shaped:1 sizes:1 e02:1 unstable:21 become:2 because:7 often:1 classical:10 sridhar:1 some:2 back:2 bounce:2 understood:1 broglie:1 specified:1 unless:1 pronounced:1 slice:1 primary:2 lead:1 cavity:2 resonances:9 measurements:2 microwave:10 does:2 demonstrated:1 measuring:2 s11:3 radial:2 constructive:1 corp:1 although:1 plots:1 properties:2 takes:1 comparison:1 about:1 anomalous:1 dependence:1 o:1 remains:1 range:2 repulsion:1 insufficient:1 slightly:2 fabry:9 experienced:1 cambridge:2 presence:1 previously:1 communication:1 into:3 splitting:2 nsf:1 due:2 nonperiodic:1 right:6 proportional:2 theoretically:1 computer:1 additional:1 few:1 inserted:1 support:1 there:8 approximate:2 long:2 appl:1 low:1 way:1 mesoscopic:3 was:16 launching:1 function:2 form:1 jun:1 but:4 gain:1 line:4 longer:1 packard:1 type:5 smooth:1 up:1 placed:1 below:2 frequency:10 demonstrate:1 problem:1 similar:1 called:1 strongly:1 later:2 associated:1 certain:2 mirror:4 influence:2 evidence:2 dashed:2 single:1 simulations:1 lifetime:2 moves:1 regime:17 compared:1 antenna:7 no:3 corporation:1 whereas:3 wavefunction:4 when:4 sampled:1 field:11 other:4 role:2 details:1 department:1 picture:1 stat:1 semiclassically:1 center:4 important:2 peak:6 dissipation:1 sides:1 matrix:1 algaas:2 coupling:2 abscissa:1 resolution:1 diffraction:13 orbit:26 departments:1 time:4 decoherence:2 starting:1 once:1
|
quant-ph9906088.txt |@word concept:1 consider:5 illustrates:2 rev:21 magnetic:4 varying:1 amplifier:2 results:4 four:6 gf:1 scalar:1 ga:9 consists:1 compares:1 contributions:1 gj:2 gi:2 amplification:1 violate:3 interactions:1 tn:1 quasi:2 program:1 squeezing:2 preserved:1 under:3 include:1 tc:2 indicating:1 case:12 supported:1 g2:1 advantage:2 g0:2 far:2 modes:16 none:1 wave:26 mixing:11 ultracold:1 difference:1 condition:2 treating:1 leads:3 quartic:1 hamiltonian:11 transmission:1 turns:1 proposals:1 t1:1 large:4 solved:1 vector:1 small:1 optics:17 equation:1 inserting:1 holography:8 lewenstein:1 kavoulakis:1 hk0:1 d3:1 approximation:4 second:6 equal:4 further:1 dynamics:7 rectangular:1 eik0:1 even:2 reproduce:1 nonlinear:12 wavenumbers:1 dr1:1 defocussing:1 section:5 dr2:1 near:1 find:1 reminiscent:2 ballagh:1 reconstruction:2 new:2 ever:1 consisting:1 contrast:4 body:4 morgan:1 degree:1 exchange:1 respectively:1 realizations:1 component:1 here:6 atoms:30 met:1 objects:1 expansion:1 others:2 along:1 strong:4 obtained:1 incoming:1 naval:1 suitably:1 involved:1 study:2 allows:1 monoenergetic:1 ignoring:1 amount:2 describing:1 resulting:1 action:1 resonance:1 studies:2 involves:2 via:2 followed:3 4a1:1 clark:1 merely:1 ls:1 highly:1 condensates:4 total:3 research:2 manipulate:2 use:1 manufacturing:2 commun:1 distinct:1 positive:1 played:2 finally:2 periodically:1 few:2 ψi:4 ψm:1 taken:2 theoretical:2 reflects:1 more:3 sort:1 collinear:1 populations:2 successful:1 solitons:1 operators:5 apparent:1 odinger:1 berlin:1 short:1 diffracted:1 particular:3 known:2 actual:2 cases:1 iii:2 sample:2 k02:1 mf:9 locked:2 quantized:3 effectively:1 science:3 setup:1 work:3 reviews:3 ij:1 obvious:1 thin:1 transparency:1 burnett:1 spontaneous:2 example:4 performed:2 control:5 f1:2 f2:2 weaker:1 chosen:1 process:1 neglected:2 states:6 collision:1 numbers:1 degenerate:3 allowed:1 conversely:1 species:1 verlag:1 influenced:1 varied:1 describes:2 discussion:1 zhang:1 off:4 chemical:1 how:2 impinging:1 pair:1 fourth:1 beams:2 instead:1 axis:3 modulations:2 βa:1 profile:2 recording:1 product:1 rise:1 information:6 modulation:2 demonstrates:1 office:2 after:2 2g2:1 applications:5 produce:1 inst:1 spectacularly:1 waves:12 fi:1 law:1 response:1 introduced:3 occurence:1 dynamical:1 effective:3 joint:1 prerequisites:1 light:4 grant:1 lines:1 correspond:3 neglect:1 monochromaticity:1 so:3 specifying:1 allow:1 correlation:9 representation:1 order:2 help:1 schwartz:4 gω0:1 a02:9 indeed:4 over:1 a01:9 primitive:1 years:3 resonant:2 thermal:1 paper:2 including:3 lasers:2 reconstruct:1 japan:1 satisfies:1 still:1 its:2 group:5 located:1 energies:1 interesting:1 conjugation:3 writing:2 absence:1 offers:1 microscopic:1 systems:2 rabi:1 h0:2 them:3 good:1 reemitted:1 thereby:1 material:3 molecule:1 processes:2 mention:1 walls:1 a0i:1 effects:1 they:3 half:1 front:1 feature:2 now:6 discuss:2 nor:1 matched:1 kozuma:1 term:4 holographic:1 lies:1 goldstein:6 fully:1 university:1 level:1 kerr:1 microstructures:1 possibilities:1 inequality:7 mode:23 reasonable:1 2m:7 soc:1 side:8 characterized:2 mean:4 schemes:1 directly:1 populated:3 generation:1 energy:1 availability:1 idea:2 challenges:1 inhomogeneous:1 frequency:4 see:1 interplay:2 measure:1 quantum:23 our:6 lithography:1 transitions:1 eq:3 brings:1 out:1 ketterle:2 shown:3 jackson:1 machida:1 quantify:1 furthermore:2 since:1 interference:1 denotes:1 collisions:7 maximized:1 perturbed:1 induced:1 ref:7 occurs:1 shows:3 foundation:1 arizona:1 linear:1 written:1 microfabrication:1 possibility:3 formation:1 element:1 approach:3 remainder:1 generate:2 milburn:1 temperature:1 hc2:1 hc0:1 interaction:4 r1:5 r2:5 created:3 determining:1 could:1 transition:2 moment:1 times:1 counterpart:1 turn:1 length:3 explored:1 place:1 wright:3 δij:2 k0:2 repeats:1 onto:3 interact:2 canceled:1 first:9 monochromatic:1 initial:5 kuang:1 upper:3 2ωr:1 thereafter:1 number:6 restrict:1 intuitively:2 done:1 long:1 another:1 ring:2 precisely:1 electronic:2 angular:1 illustrate:1 given:4 iω0:2 revival:1 similarly:1 introduction:1 leading:1 condensate:27 πn:1 system:10 least:2 their:2 intermediate:1 consistent:3 realization:1 free:1 molecular:1 final:2 gives:1 interests:1 originating:1 collapse:1 distribution:1 exactly:1 grosspitaevskii:1 drψ:2 optical:34 permanent:1 manipulation:2 injected:2 shortly:2 sublevels:1 photographic:1 than:1 population:6 begins:1 distance:1 scheme:1 third:1 device:1 kuklov:1 transferred:1 preparation:1 matter:21 silicon:1 future:2 intensities:1 were:2 sec:1 tion:2 hologram:8 raman:1 accomplished:1 dynamically:1 mind:1 lin:1 replicated:1 need:1 seen:1 constrained:1 demonstration:2 any:3 complete:1 deng:1 strength:2 angle:2 triggered:1 zero:2 self:1 governs:1 ideas:1 phillips:2 internal:2 absorbed:1 build:2 analogy:2 shining:1 mit:1 channel:1 hyperfine:8 annihilation:6 acquire:1 fundamental:2 trace:1 investigations:1 mlynek:1 object:9 reach:1 falls:1 involving:6 significant:1 phase:12 counterpropagating:3 observation:1 surprising:1 considered:1 into:6 steady:2 reflecting:1 ohmi:1 principle:1 exp:4 subsequent:1 velocity:3 physics:4 thomas:2 particularly:1 show:3 violation:4 probe:16 scattered:1 multicomponent:2 elimination:2 pethick:1 crosssection:1 substituting:1 eliminated:2 ground:2 impact:1 partners:1 specifically:2 based:1 proposed:2 implementation:1 situations:2 pump:9 should:1 entities:1 only:5 explicitly:1 employed:1 hamiltonians:1 local:1 achieve:1 do:1 dominant:1 cryptography:1 dependent:1 familiar:1 membrane:1 2a:1 beam:16 ones:1 closely:1 during:1 dr:1 adiabatically:1 evolution:3 exhibiting:2 continuum:1 fields:19 arxiv:1 method:1 experiments:4 mewes:1 reinhardt:1 valid:1 nist:1 pitaevskii:1 behroozi:1 satisfy:1 requirement:1 ik0:2 res:1 reference:4 undergoes:1 violated:1 correlations:9 lett:9 maximum:3 intensity:7 individual:2 bare:1 result:3 eliminating:1 close:2 kinetic:1 analog:2 closer:1 instance:1 phases:1 satisfying:2 mechanically:1 commutation:1 hagley:1 scattering:4 dipole:4 label:1 state:15 determined:2 various:2 between:22 limit:7 neither:1 reading:10 numerous:1 esslinger:1 terms:8 ability:1 useful:1 nature:2 initially:2 weak:2 however:4 vanishing:1 concentrate:1 extent:1 vrd:2 bose:2 remaining:1 both:8 last:2 limits:2 reported:1 many:1 taking:1 density:6 hence:2 contract:1 recoilless:1 etc:1 involve:1 context:1 0j:1 contribution:1 hφ:1 finds:1 experimental:3 ck:2 mechanics:3 sodium:1 prepared:1 point:3 coexistence:1 dimensional:1 exhibits:1 army:1 constant:2 cw:1 considers:1 considering:1 described:5 dum:1 geometries:1 aˆ:8 addition:3 computing:1 three:8 been:7 ansch:2 yasuda:1 detuning:2 cauchy:4 slowly:1 combined:2 superradiance:1 expected:3 ph:1 pl:2 fig:4 field:20 relations:1 corresponding:1 sufficient:1 coherence:3 gas:1 coherent:3 confinement:1 external:4 func:1 c2:4 c0:5 spin:6 present:4 p2:4 intriguing:1 novel:1 laser:4 eit:1 diffract:1 excited:1 will:1 while:4 replaced:1 behavior:2 shift:3 situation:2 property:1 region:1 coupled:2 conjugate:1 thus:3 non:4 iv:2 ii:4 bigelow:1 reads:1 itself:1 confining:1 reports:1 ia:1 lenz:2 conserve:1 binary:2 different:1 nanofabrication:1 develop:2 propagation:1 perform:1 acknowledgments:1 reconstructed:3 quadratic:2 cross:11 same:2 shifts:1 stimulated:2 quant:2 emphasize:1 coworkers:3 dimensionless:1 several:2 nitride:1 independent:2 used:4 closest:1 somewhere:1 effect:1 driven:1 running:2 harris:1 moving:1 unpublished:1 potentials:1 entanglement:6 changing:1 normalization:2 recent:4 weakly:3 schr:1 traps:1 largely:1 expression:1 well:4 analysis:1 thought:1 services:1 greatest:1 very:3 echoes:1 paradigm:2 parametric:3 drawing:1 undepleted:1 kash:1 arbitrarily:1 just:7 inouye:1 being:3 kishimoto:1 accurate:1 detail:1 press:2 stored:3 atomic:30 aspect:1 immediately:2 spatially:1 momenta:1 macroscopic:2 rapid:1 zoller:1 sciences:1 absorption:2 mask:3 haf:1 mathematically:1 passive:1 lattice:1 potential:12 attractive:1 versa:1 giorgini:1 mod:1 hau:2 momentum:11 real:2 reconstructing:1 increased:1 spectacular:1 advances:2 spatial:1 possible:2 corresponds:1 entangled:1 background:1 vacuum:3 confined:1 using:2 part:1 adams:1 insert:1 theor:1 appearing:1 like:1 particle:1 shaped:1 signal:1 plane:1 δq:1 specific:1 yields:4 either:1 become:1 works:1 reduces:1 methods:1 classical:14 stringari:1 creation:4 some:4 back:2 buildup:1 growth:2 loses:1 matching:1 provided:1 recently:2 lead:2 cavity:4 electromagnetic:3 replicas:1 recorded:1 extensively:1 2c2:3 instantaneous:1 depletion:1 critical:1 provides:1 assuming:1 pattern:2 demonstrated:2 trap:5 limitations:1 noise:2 manufactured:1 equivalent:1 processing:1 illustration:2 step:3 found:1 concreteness:1 exciting:2 properties:1 about:5 central:5 carried:1 gratings:1 o:4 practical:1 dutton:1 stand:1 discusses:1 bloch:1 outlook:2 contains:1 h2:1 kasevich:3 within:1 negative:1 revivals:2 neglects:1 national:1 einstein:2 operator:3 pairs:2 bosonic:2 iµt:1 rely:1 statistics:1 prepare:1 classically:1 assumed:1 springer:1 there:3 gases:1 width:1 anderson:1 much:2 way:5 was:5 gij:2 opens:1 treat:1 function:5 medium:2 illuminated:1 form:8 enough:1 jun:1 but:2 volume:1 aperture:1 correlated:1 recoil:2 ho:1 atom:21 convergence:1 encoded:1 collapses:1 especially:1 made:1 vtrap:2 understood:1 characteristic:1 inside:1 ωr:3 up:2 placed:1 tucson:1 those:1 continuously:1 fluctuations:3 problem:1 similar:1 strongly:1 storing:1 associated:1 moore:4 af:1 defined:3 certain:1 contribute:1 influence:1 zeng:1 general:1 single:2 replica:3 accounting:1 az:1 film:1 regime:2 dalfovo:1 functions:5 compared:1 no:2 na:1 whereas:1 when:3 cˆ:18 virtual:2 reality:1 application:2 other:2 role:2 nat:1 becomes:3 department:1 proposal:1 shimizu:1 optically:1 briefly:1 elements:1 may:1 superposition:2 photon:8 center:4 describe:1 emission:2 a1:13 important:2 technol:1 allowing:1 mechanical:2 fermi:2 n2:3 ago:1 independently:1 condensation:1 coupling:4 vice:1 assume:2 typically:1 diffraction:3 approxima:1 original:5 nath:1 mass:5 image:6 time:4 n1:3 meystre:12 once:1 starting:1 having:1 4a:1
|
quant-ph9906089.txt |@word secondly:1 consider:3 pointing:1 ede:1 global:5 focus:1 leads:1 generalize:2 whose:2 preserves:1 depend:2 equivalence:1 tr:7 monotonically:2 tj:18 tf:53 norm:2 applied:1 advantage:1 δw:7 very:1 results:4 figs:2 decide:1 matrices:1 condition:2 four:7 vibrational:4 presented:1 solution:3 t0:56 admissible:1 differential:2 demonstrated:1 small:2 eigenvalues:3 equation:3 upper:2 measurable:1 pulse:5 approximation:1 second:5 dynamics:1 chem:5 employ:1 morse:7 version:1 above:2 increasing:1 method:2 satisfy:2 edited:1 respectively:1 discrete:1 here:1 inversion:2 represented:5 extrema:1 equations:4 balian:1 great:1 generalizing:1 splitting:1 institute:2 involved:1 studied:2 allows:1 approaches:1 trial:1 resulting:1 published:1 usually:1 der:1 divide:1 bounds:4 vii:1 highly:1 inequality:1 1st:1 total:4 bra:1 use:1 would:3 sake:1 positive:1 give:2 ψv:35 properties:1 ψk:3 noting:1 ψn:15 therefore:1 criteria:1 iteratively:1 rabitz:8 theoretical:5 more:1 populations:11 started:1 iu:1 operators:4 odinger:1 oregon:6 appendix:4 controlling:1 normalized:2 particular:2 cases:1 iii:1 harnessing:1 must:2 valued:1 word:1 integrating:1 science:4 setup:1 work:8 oscillator:7 eigenkets:1 values:1 ρv:26 following:2 arrive:1 example:1 proof:5 control:22 f1:1 f2:1 solved:1 suggestions:1 states:2 attain:1 sense:1 guarantee:1 needs:1 goal:2 chemical:1 df:1 pure:5 optimal:8 dipole:1 ensemble:5 simplicity:1 product:3 fs:8 after:1 applications:1 law:1 fm:4 dynamical:1 effective:2 computations:3 representation:1 order:5 feedback:1 developed:1 satisfied:1 produced:1 thermal:3 paper:5 through:2 statistical:3 during:1 mentioned:1 satisfies:2 its:4 controllable:1 τj:14 thank:1 subinterval:1 lm:1 forms:1 systems:8 main:1 eugene:3 correspondence:1 non:2 combination:1 propose:1 processes:1 bound:4 they:2 eigenvalue:2 february:1 finite:3 university:3 hamiltonian:4 orthonormal:1 sufficiently:2 2f:2 magnitude:2 l0:11 l1:32 found:1 bond:2 en:4 independent:1 energy:12 reduce:1 related:1 inverted:1 quantum:14 our:7 approximated:1 out:2 shown:1 matrix:1 driving:1 space:8 furthermore:4 since:5 rev:5 chaos:1 denotes:1 acting:3 denoted:1 shows:4 linear:2 tian:1 nth:1 completely:1 e4:4 remainder:1 steering:1 e3:2 e2:2 interaction:1 transition:1 iterative:2 quantummechanical:1 length:1 hence:5 quadratically:2 assign:1 first:1 separable:1 initial:5 number:1 approximate:1 done:2 reached:1 precisely:1 given:4 e1:4 introduction:1 eqs:3 system:21 their:1 molecular:2 final:2 gives:1 exactly:3 favorable:1 authors:1 population:6 variational:2 unfortunately:1 iteration:3 arb:4 suzuki:1 claim:1 determined:1 treated:1 fig:12 dynamically:1 generalization:1 randomly:2 close:1 need:1 elsevier:1 any:4 efficient:4 convenient:1 converges:1 polarization:1 objective:3 unperturbed:1 towards:1 multiple:1 shall:3 molecule:1 most:3 significant:1 acknowledgements:1 χv:9 average:4 traditional:1 exp:6 kt:5 usual:1 physics:3 differentiate:1 iterations:1 show:4 converge:1 relation:1 agrees:2 ground:2 highest:3 knowledge:1 implementation:2 hf:1 written:1 controls:2 should:1 lemma:3 only:4 indeed:2 attained:4 equilibrium:3 dn:1 do:3 his:1 establishes:1 dependent:2 de:1 expectation:7 ones:1 nearly:2 closely:1 compute:1 dt:25 target:5 girardeau:4 evolution:11 fields:1 arxiv:1 imposed:1 subintervals:1 fixed:2 guessing:1 requirement:1 set:3 computed:1 exists:1 sep:1 up:2 depends:2 w4:1 w3:8 w2:9 w1:10 terms:3 institutes:1 subject:1 tl0:1 definite:1 functionals:1 symmetric:2 importance:1 state:19 il1:1 boundary:2 approach:1 recently:2 initially:3 wn:2 wk:5 however:5 rapidly:2 ket:2 distribution:1 both:2 essentially:1 many:3 according:4 etc:2 connection:2 otherwise:2 minima:1 solving:1 point:1 simple:1 gaspard:1 simply:1 yamaguti:1 maximize:4 lagrange:2 constant:2 ensures:1 described:4 aˆ:10 observing:1 due:1 been:1 much:1 ph:1 choose:4 field:5 referee:1 corresponding:7 observable:10 quantities:1 sufficient:1 subspace:1 observe:3 external:2 those:1 case:5 laser:3 exponential:1 value:9 will:4 while:1 viii:1 unitary:3 vi:1 av:14 thus:9 iv:1 ii:1 ih:7 itself:1 il:9 dual:2 ia:1 verified:1 φv:10 realizing:1 same:1 complex:2 quant:1 split:1 units:6 physical:1 development:1 evolve:1 used:2 numerical:2 driven:1 levels:4 kim:1 koch:1 normalization:1 lower:2 schr:1 maximizing:2 possibly:1 yan:1 well:1 converged:1 solve:1 diatomic:1 lim:4 exponentials:3 model:1 arising:1 maxima:1 being:2 accurate:1 obtain:2 eigenstates:2 previous:3 note:1 density:2 setting:7 lett:1 theorem:1 formal:1 euler:2 b13:1 real:3 easily:1 iα:1 decomposed:1 possible:2 finding:1 mathematics:2 using:6 decomposes:1 helpful:1 schirmer:3 necessary:2 like:3 follows:3 serves:1 schwarz:1 arbitrary:3 δf:24 mathematical:1 methods:1 sequence:4 pals:1 some:2 b4:1 b5:1 b6:1 b7:1 b1:1 b2:1 b3:1 unless:1 b8:2 b9:1 energetic:2 does:1 decomposition:2 minimal:1 refer:1 bf:2 reasonable:1 equivalent:1 each:3 perpendicular:1 illustration:1 step:2 hilbert:3 constrains:1 about:2 kinematical:4 actual:1 concretely:1 constraint:1 discussed:1 remains:1 mixed:5 ρˆv:3 constraints:1 consequently:1 letters:1 within:1 numerically:3 functional:3 hermitian:2 operator:8 van:2 additional:1 vˆ:3 few:1 there:3 u1:1 u0:1 smit:1 start:1 ohtsuki:1 cauchy:1 inner:2 propagator:1 assumes:1 function:3 complete:3 form:1 restrictions:1 denoting:1 convergence:2 attainable:1 level:10 dissipative:1 illustrative:1 zhu:7 wish:1 maximum:6 us:2 achieving:1 liouville:12 limit:1 problem:2 define:5 called:1 mechanics:3 fluence:1 controllability:2 ordered:2 defined:3 certain:2 convergent:1 formulation:1 formalism:1 ina:1 defines:1 again:1 functions:4 no:1 wavefunction:1 nf:12 application:1 conditions:2 b12:1 details:2 b10:1 b11:1 department:3 nonincreasing:1 conclusion:1 leahy:2 uniformly:4 variation:1 a1:1 bolzmann:1 generated:2 important:1 bounded:6 dissipation:2 independently:1 implies:1 algorithm:16 assume:3 starting:1 dτ:1 interval:2 rule:1 weights:1 time:20 n0:1 observables:2 requires:1 once:1
|
quant-ph9906090.txt |@word consider:1 leads:2 commute:2 entropy:8 grateful:1 go:1 graph:2 tr:29 finally:2 under:2 te:1 far:1 springer:2 geometrical:2 corollary:2 putting:3 decide:1 convexity:1 dim:1 school:1 large:3 convenience:1 differential:1 small:3 noted:1 uec:2 sign:2 second:4 linear:1 spectral:1 sun:1 section:2 version:3 goes:2 sup:5 new:4 increasing:2 method:3 simultaneously:1 respectively:2 here:5 represented:4 strong:8 observing:1 obtained:1 suggestion:1 changes:1 golden:1 namely:1 pythagorean:2 establish:1 kobayashi:6 asymptotic:2 commun:3 probabilities:2 positive:1 quasi:1 call:1 therefore:3 type:1 more:1 operators:2 attained:2 appendix:2 cases:1 account:2 valued:1 tokyo:1 equation:1 following:4 trans:2 def:19 proof:5 figure:2 states:1 contradicts:1 minimum:3 information:4 end:1 bhatia:1 holds:6 maps:1 optimal:2 simplicity:1 max:8 derived:4 applications:1 inform:2 so:3 fundamental:4 representation:2 order:1 wigner:1 hiroshi:1 paper:1 japan:1 satisfies:3 ieee:2 its:2 sλ:1 derive:1 monotonicity:2 thank:1 interesting:1 systems:2 mail:1 into:2 versus:1 practice:1 attains:1 they:4 now:4 discuss:3 represents:1 equality:3 university:1 sufficiently:2 inequality:7 enλ:12 en:9 principles:1 measurement:1 quantum:23 ep:6 shown:3 acknowledgment:1 space:1 rep:1 since:4 helstrom:1 formula:1 math:4 theory:6 monotone:2 divergence:2 completely:1 york:3 put:3 indicates:1 qj:4 times:1 exponentially:1 hence:8 βn:33 first:4 xn:9 probability:10 number:2 open:1 given:3 rewritten:1 introduction:1 system:1 assumption:1 continuous:1 authors:2 uhlmann:1 sˆ:2 detection:1 kind:8 showed:2 zero:1 treated:1 seen:1 null:2 any:7 min:7 lim:10 converges:1 note:4 sequel:1 most:1 remarks:1 nagaoka:2 inequalities:1 clear:1 stronger:1 exp:1 quantity:1 show:10 relation:6 keywords:1 nϕ:9 aσ:3 should:1 lemma:9 only:3 thompson:1 dn:8 his:2 legendre:1 means:1 words:1 pearson:1 arxiv:1 nλ:2 petz:6 qn:7 set:3 exists:4 argmax:1 testing:17 relative:6 see:13 result:3 satisfying:1 exponent:6 µn:6 between:4 αn:33 weak:1 jp:2 however:1 hypothesis:22 multiplier:1 problem:4 region:1 readers:1 leibler:1 exceeds:1 estimation:1 arbitrarily:1 corresponds:6 concluding:1 lagrange:1 polynomial:1 moreover:2 ogawa:2 hiai:6 pp:6 acceptance:4 been:2 treat:1 interest:1 pj:3 ph:1 pn:9 fig:3 addison:1 concerning:2 observe:1 case:1 p1:5 exponential:1 blahut:5 will:5 suppose:6 behavior:1 error:8 situation:2 property:2 taking:4 procedure:1 vol:6 thus:5 im:2 binary:1 verified:2 make:1 same:1 concavity:1 quant:1 finite:2 interpolation:1 used:4 hand:1 analysis:1 academic:1 firstly:2 parametrically:2 left:1 λs:4 obtain:4 immediately:1 alternative:2 han:7 density:1 tomohiro:1 theorem:8 complements:2 transformation:1 real:2 psn:2 stein:6 easily:1 possible:1 amari:1 press:1 using:3 helpful:1 follows:3 yields:4 either:1 arbitrary:3 mathematical:1 methods:1 classical:6 convex:2 proper:1 decision:1 comments:1 does:1 decomposition:1 eliminate:1 tends:1 prof:2 power:5 wesley:1 although:2 hilbert:1 takes:1 constraint:2 acn:1 extensions:1 lieb:1 dyson:1 bound:6 nothing:1 references:1 operator:1 statistics:1 log:46 there:4 neyman:1 asymptotics:1 function:3 yanase:1 form:1 converse:10 jun:1 but:1 hn:1 epˆ:4 lindblad:1 true:2 applying:1 whether:1 wish:1 maximum:3 distribution:4 define:4 max0:1 entropies:1 ac:2 proved:7 abstract:1 condition:1 examine:2 pˆ:3 inf:4 distributions:2 physical:1 when:6 graduate:1 other:3 test:8 nr:5 kullback:1 important:1 massachusetts:1 matrix:1 assume:1 remarked:1 n0:3 once:1
|
quant-ph9906091.txt |@word dynamic:1 tenuous:1 sch:1 whose:7 const:7 calculate:1 aug:1 under:7 cm2:16 rise:1 experimentally:4 σth:8 solution:4 vector:11 enclosing:1 hora:2 consistent:1 direct:1 pulse:25 approximation:11 surrounding:4 second:5 manus:3 estimated:1 even:1 aymar:1 above:14 new:11 net:1 coefficient:2 simultaneously:4 notions:2 equals:2 here:7 atoms:39 ionization:45 asymmetry:1 represented:2 path:1 interpret:1 obtained:5 substance:1 study:6 changed:2 reports:1 procedure:1 stressed:1 advantages:1 stipulated:1 changes:3 criticism:2 golden:2 explained:1 plenum:2 highly:3 txu:1 total:6 unit:4 plot:3 would:4 axioms:1 discrepancies:2 kinematics:2 therefore:7 m2:1 until:1 separated:1 nauka:8 odinger:4 berlin:1 excellent:1 must:5 me:1 springer:2 tb:1 work:11 theories:1 ere:2 mv:1 concepts:7 akin:1 petersen:1 example:1 relativistic:4 indicates:2 times:2 absolute:3 hoc:1 turn:2 verify:1 feature:1 photoelectrons:3 very:5 methodology:9 ordinary:1 description:5 oscillators:1 after:2 confirmed:1 lax:1 law:1 types:1 attempt:2 effective:24 recombination:4 hypotheses:1 delone:4 correlation:1 operate:1 order:3 interpretation:4 allegrini:1 over:4 satisfied:1 zel:2 besenbacher:1 japan:1 satisfies:2 before:2 inerton:21 fiz:1 hidden:4 overcome:1 versus:5 them:2 elementary:4 effects:5 they:2 represents:1 accompanying:1 davydov:4 reasonable:1 each:4 acoustic:1 side:1 mean:3 successively:1 bradshaw:1 series:5 principles:2 semiclassical:1 extract:1 mv0:1 restricted:1 crucial:1 particles:4 conjectured:2 got:1 newly:1 forth:1 disagreements:1 turning:1 linear:7 free:14 standard:3 admits:1 nth:12 proportionality:1 corrects:1 estimate:1 enormous:1 created:2 starts:2 ati:4 incorporated:1 1970s:1 already:1 primary:1 restrict:1 kelley:1 another:1 electronic:2 researched:1 rewritten:1 eqs:1 engagement:1 approximately:2 needed:1 perturbations:1 too:1 hypothetical:1 keldysh:2 somewhat:1 begins:2 iωt:1 ultrastrong:1 showed:1 approximations:1 likely:1 tunable:1 normalizing:2 matter:11 classes:1 aether:2 okuda:5 enables:1 mind:1 spectrum:2 manner:1 seen:4 seem:2 convenient:1 latter:1 absorbed:10 forces:1 ˆp:1 broglie:6 shall:4 object:2 involving:1 vinogradova:1 inconsistency:1 metal:32 points:3 principle:3 dot:1 vigier:2 random:1 infrared:1 gauge:1 substituting:5 availability:1 finally:1 just:4 explain:5 topological:2 tries:1 do:2 de:12 agostini:13 photoelectric:31 dt:2 dr:2 runs:1 volkov:1 fields:3 volodymyr:1 berezinskii:1 pitaevskii:1 1960s:2 observed:2 depends:4 radius:3 result:3 exponent:1 µm:6 cooperation:1 conceptual:1 approach:6 accord:1 terms:4 nonresonant:1 nature:3 wn:1 however:8 bose:2 suggested:3 essentially:3 uncertainty:1 against:4 distinction:1 com:1 appeared:1 wider:1 testable:1 broadening:2 basis:3 been:4 much:4 expected:2 entered:1 concerning:1 excite:1 coherent:7 confinement:1 spin:1 applied:6 launches:1 originate:1 heidelberg:1 aim:1 contemp:1 aid:1 balance:1 characterizing:1 raychaudhuri:2 phenomenological:2 ip:13 iv:1 ii:1 im:6 interacts:1 containing:1 perform:1 things:1 make:1 intersecting:1 quant:7 several:7 entitled:1 hand:1 suitable:2 materials:1 left:1 unified:1 proposed:1 overcoming:1 identify:1 facts:2 scattering:4 previous:4 irradiated:8 regarded:2 had:3 iω:1 spread:1 transformed:1 fedorov:1 gave:1 opt:1 possible:1 unification:1 rahman:1 background:2 vapors:2 advanced:3 www:1 right:2 deal:1 successfully:2 born:1 debye:1 indirect:1 eiqr:1 proceeding:1 electromagnetic:24 normal:2 romanov:1 yields:1 super:1 properties:3 anomalous:14 o:2 natom:2 islands:1 soc:2 presence:3 bound:2 thankful:2 acad:1 often:1 initial:6 subdivide:1 why:3 physicists:1 way:2 call:1 was:28 polaron:1 medium:1 form:10 forming:1 heat:3 true:1 responding:1 maximum:2 crystal:2 fermi:8 ln:2 abstract:1 evidence:1 distributions:1 archive:2 constructed:4 ni:17 radically:1 nm:8 no:4 na:8 generally:1 ne:3 setting:2 role:1 papers:8 test:1 models:4 fabre:3 preceding:1 variable:1 dω:2 assume:2 dτ:6 interval:3 hofmann:1 together:1 time:28 concept:21 rom:1 remarkable:1 switched:1 supplement:1 devoted:1 bremsstrahlung:2 ıv:1 quasi:1 frequencies:1 untenable:1 friction:1 emphasized:1 europhys:1 clouds:4 presented:1 did:2 leave:1 der:1 unexpected:1 occurrence:1 farkas:2 prediction:5 substitute:1 spectral:1 adds:1 appear:2 current:2 lifshitz:1 satisfy:1 supporting:2 understanding:1 knocked:1 cos2:1 along:5 superconductor:1 box:1 institute:1 studied:6 simultaneous:3 usually:1 studies:2 problematic:1 merely:1 marked:1 matsuoka:1 flexibility:1 planck:3 positive:1 predictions:1 films:1 theoretical:5 today:1 introducing:1 ua:1 cases:2 effort:1 modified:1 reviews:2 believed:1 modifies:2 performed:4 hydrogen:3 verlag:2 discussion:2 write:2 till:1 pure:2 parameter:4 substructure:3 information:1 may:13 diva:1 convincingly:1 data:3 outline:1 correlate:1 explicit:3 cascade:2 accelerated:2 so:7 sn:1 representation:1 increase:2 typical:2 noyes:1 indeed:3 pointed:4 experiments:17 still:1 ieee:1 tendency:1 group:1 thank:1 interesting:1 hot:1 forms:1 suspicion:1 main:4 thereby:1 views:1 thebault:2 processes:4 introduce:1 scaling:1 now:3 discuss:1 term:1 possibilities:1 el:4 en:1 ei:9 significantly:1 ej:1 eg:4 ef:4 ea:2 ec:2 owing:3 ez:1 wavelength:6 honig:1 ev:3 eq:3 adduced:1 shown:3 space:17 looking:2 investigation:2 formula:9 correct:5 shows:1 theory:61 possibility:2 quark:1 complicated:1 besides:6 org:4 e0:2 card:1 e2:2 derivation:1 language:2 transition:4 fb:1 motion:3 thing:1 place:1 first:11 origin:1 papoular:4 reveals:1 variables:2 xe:1 long:2 directly:2 impossible:1 angular:1 size:1 given:2 checked:1 gives:2 kohler:1 moscow:10 released:3 absorbs:1 eliminated:1 than:16 coefficients:1 population:1 wide:2 unfortunately:2 accordance:2 transferred:1 future:1 were:6 prospect:1 register:1 rend:1 sukhorukov:1 ann:2 generalization:1 allen:2 any:4 105a:1 ideas:1 note:8 sciences:1 potential:19 take:4 objective:1 formulas:3 altered:1 opposite:5 neutrinos:1 paid:1 falls:2 ordinates:1 inserted:1 eigenfunctions:1 vapor:1 considered:6 mrs:1 phonons:1 quantity:1 slope:3 show:2 supposition:2 spaces:1 threshold:18 ground:1 proportion:1 written:1 only:11 explicitly:1 quantph:1 get:2 designated:1 ionized:7 reveal:1 scientist:1 predicted:3 ignored:1 connections:1 cim:2 ignores:1 surfaces:2 inequalities:6 rado:1 review:4 behind:2 radiated:1 between:17 complications:1 notice:2 jobs:1 concentrate:1 article:1 jetp:3 come:1 σn:1 many:2 region:2 according:1 voronov:2 propagation:1 expression:26 among:1 mittleman:1 moreover:1 fruitful:1 considering:1 unusual:1 wiel:1 absence:1 formed:1 photon:57 dramatic:1 external:1 ruby:2 those:7 case:18 cast:1 blokhintsev:3 metric:1 cluster:1 superconducting:3 property:1 pfree:5 different:4 develop:3 multiphoton:33 etc:2 media:1 same:18 physical:5 events:1 breakdown:12 noble:2 extended:3 eth:1 roughly:1 launched:1 model:10 researchers:1 charged:1 muon:1 being:2 when:13 rudenko:1 speed:2 photons:42 improvement:1 wavevector:1 lett:8 extensive:1 momentum:4 real:3 aspects:1 around:5 eigenvalue:1 raizer:2 specimen:3 picosecond:1 vacuum:3 amp:2 accepted:1 ruled:1 particle:20 isosceles:1 characterizes:1 ie:5 stationary:1 reduced:1 specifies:3 βni:2 belotsky:1 brito:4 images:1 provided:2 depletion:1 critical:1 provides:1 refer:1 power:3 combines:1 broken:1 anisimov:1 ratios:1 2m:3 comparison:1 island:1 theorems:1 discussed:1 discrimination:1 jα:2 references:1 microstructure:1 einstein:2 operator:11 theoretically:1 log:8 area:1 assumed:4 there:2 start:1 low:2 regard:1 strikes:1 sophisticated:1 irreversible:1 proposal:1 applying:1 ponderomotive:2 ωt:3 agree:1 rust:1 ωf:23 detailed:2 ad:1 af:3 am:2 resultant:1 weff:5 ap:7 examine:1 deem:1 again:1 izvestia:1 phonon:2 field:30 spatial:2 polar:1 congress:1 separate:1 a0:1 important:1 nucleus:1 peak:3 building:1 curve:1 mass:2 starting:1 original:1 sci:3 consider:3 caused:3 follow:1 expressions:5 subjected:1 tp:14 th:1 stochastic:1 presentation:1 eikonal:2 sound:1 far:2 resistance:1 surprise:1 difference:1 deformations:1 condition:1 hamiltonian:4 deficient:1 t2:6 large:3 small:6 biological:1 ten:1 haar:2 so16:1 rate:4 pass:1 further:2 ter:2 canonical:4 what:1 nonlinear:10 advantageous:1 section:9 abs:2 contrast:1 condensed:1 doering:1 answers:1 behaviour:2 inverse:1 operating:1 excess:1 directions:2 strong:12 equations:1 search:1 colored:1 allows:2 action:3 formation:2 via:1 followed:1 excellently:1 establish:1 readily:2 takes:3 probabilities:1 contains:4 charge:2 comparing:1 ψl:3 taken:2 ψf:2 more:9 ejected:5 company:1 emission:7 particular:1 known:2 science:1 equation:7 pioneered:1 ions:8 compare:2 superparticle:1 neglected:2 states:7 sense:1 huge:1 rather:1 stemming:1 petite:9 catalog:1 waves:8 verified:1 evaluations:1 short:2 spectra:1 cjb:1 specifying:1 fundamental:1 ith:6 developed:6 held:2 paper:2 through:2 lasers:2 existence:7 kinetic:5 excitations:3 its:8 sodium:1 energies:1 actually:1 resort:1 detected:2 systems:5 might:2 good:1 ya:2 framework:3 yu:2 2t:1 easily:3 always:1 level:1 inequality:7 found:3 2n:1 characterized:2 england:1 generation:1 energy:34 reduce:1 idea:3 investigated:2 obtains:4 measurement:1 quantum:28 event:1 nuovo:2 since:2 research:1 acting:1 hill:1 print:2 induced:6 confidence:1 base:1 put:2 asi:1 definition:1 major:1 probability:7 number:24 utilized:2 defects:1 plummer:1 perturbation:9 temperature:3 introduction:3 interact:2 least:1 assumption:1 statement:1 essays:5 hundred:1 relationship:2 optical:4 authors:3 focusing:1 off:1 translation:2 double:1 annihilation:1 intensities:1 treated:1 electrodynamics:4 concentration:10 reiss:2 lie:1 depending:1 self:2 majority:1 generalized:2 eff:7 play:1 towards:2 electric:2 reach:1 rarefied:2 significant:2 measured:1 stands:1 southampton:1 mobile:1 kr:2 part:1 electrons:32 velocity:12 ky:1 physics:6 particularly:1 phenomenon:1 fond:2 scattered:2 relation:6 fine:2 find:1 dividing:1 inflection:3 assertion:1 failed:1 experiment:12 subsection:2 kruit:2 factor:4 his:2 triangle:1 gains:1 distance:3 dependent:6 beams:3 during:4 him:1 transversal:1 continuum:5 arxiv:5 timeless:1 remove:1 dovich:2 set:5 ser:2 see:25 individual:1 distinctive:1 dipole:1 probably:2 conditions:2 available:4 eˆz:1 attention:1 incident:10 distinguish:1 inertia:1 both:4 last:3 reverse:1 connection:1 became:1 whole:3 experimental:22 point:9 simple:9 sawada:1 corresponds:2 proton:1 dimensional:1 pp:1 described:7 create:1 due:2 describes:3 pf:1 anisotropic:1 nato:1 ph:7 empty:3 photoionization:1 gas:35 inertons:11 plasmas:1 p0:3 exponential:1 pacs:1 solid:4 straight:3 evaluated:1 while:2 replaced:4 psec:2 herein:2 σn2:12 nanosecond:1 stimulated:2 emphasize:1 widely:1 grand:1 prerequisite:1 used:7 moment:1 moving:6 purpose:1 focal:6 recent:3 analysis:7 solids:1 photoemission:3 λc:1 shape:2 atomic:4 using:2 cut:2 extracted:1 excites:2 theorem:2 contrary:1 excited:2 evaluate:1 smallness:1 dewdney:3 integer:1 follows:4 adiabatic:3 separately:1 flux:8 unstable:1 continua:1 mcgraw:1 mathematical:3 methods:1 growing:1 absolutely:2 creation:1 some:6 understood:1 oscillations:3 scale:3 describing:4 l15:1 l11:1 per:4 prog:2 prof:1 photoelectron:1 agreement:4 intense:2 range:4 consequently:2 block:1 compt:1 into:18 within:2 integral:1 satisfactory:1 proportional:4 uncertainties:1 statistics:2 extremely:2 question:3 gases:6 analyze:1 governs:1 atom:22 russian:14 line:6 considerable:1 up:3 us:5 verification:3 similar:3 called:7 constant:5 reconcile:1 defined:2 stripped:3 metals:3 duration:4 single:4 pˆ:1 formalism:3 defines:1 application:1 elements:3 generates:1 problems:1 generated:1 restoration:1 εmax:6 sides:3 structure:4 implies:1 required:2 kinetics:2 na0:7 correlates:2 came:1 having:4 krainov:2 results:19 eds:3 deterministic:1 intensive:6 include:1 wave:15 electron:65 wishes:1 clement:1 incoherent:1 knight:1 notes:1 try:2 noted:2 smaller:5 sin2:1 subtle:1 notwithstanding:1 indian:1 led:1 ibid:2 respectively:2 jointly:1 following:4 focused:2 lev:1 others:3 consideration:4 eikr:2 deduced:2 ukraine:1 great:5 parameters:2 larger:2 suggests:1 cesium:3 proof:1 makes:1 stabilization:1 summation:1 apply:2 causal:1 cloud:22 use:4 remains:2 mid:1 next:2 calculation:1 totality:1 usp:1 formally:1 ap2:1 becomes:3 cooperate:1 normalized:3 iii:1 account:11 integrating:1 lorentz:1 obvious:1 publications:1 purity:1 links:1 process:4 high:10 assumptions:1 something:4 united:1 holds:1 located:1 unquestionably:1 elliptical:1 sin:2 realized:1 light:36 correspond:1 element:4 gravitons:1 allow:1 produces:1 move:1 interpreted:1 produced:1 own:1 pulses:4 mentioned:3 decay:1 chosen:1 temporal:1 meissner:1 aeff:8 greater:3 orthodox:2 practice:1 february:1 dirac:1 magnitude:1 mode:1 prevailing:1 related:2 constitute:1 deficiency:1 frequency:4 58b:2 58a:3 our:4 special:1 out:12 matt:1 matrix:6 rep:2 rev:11 electronics:1 ref:7 interactions:2 approaches:1 york:3 monographs:1 interaction:18 could:13 feasible:1 length:1 hence:10 reaches:1 publication:1 revealed:2 system:2 occupancy:1 their:6 intermediate:1 final:2 accompany:2 academy:1 standpoints:1 amplitude:4 providing:1 exhibit:1 berestetskii:6 need:4 demonstration:1 clearly:1 angle:1 able:2 gravity:3 mechanism:3 polarization:1 instance:2 mir:1 accuracy:1 heisenberg:1 protopapas:1 who:2 connected:2 but:3 formalisms:1 class:2 consequences:1 neighboring:1 fact:3 absorbing:1 γni:2 agrees:1 decade:1 based:9 jap:1 should:24 molecules:1 postulated:1 employed:1 meant:1 means:8 syst:1 beam:7 words:7 evolution:1 numerous:2 nauk:1 qe:1 fixed:2 view:4 monochromatic:1 multiplying:3 hν:9 irradiation:4 national:1 intensity:56 enhanced:1 operated:1 luminous:2 closer:1 pattern:1 state:14 difficulties:1 tens:2 invariant:2 emitted:2 hypothesis:5 key:1 vri:1 problem:4 interpretations:1 taking:2 la:2 equal:6 2e2:1 hψ:1 figures:1 passing:1 estimation:1 safely:1 strongly:1 ch:1 co:1 author:5 cm:13 harmonic:1 cd:1 keitel:1 news:1 respect:2 ct:1 trajectory:1 slowly:1 treat:1 electr:1 utilizing:2 arises:1 sufficient:1 coherence:1 cos:6 c2:3 general:3 expounded:1 present:10 novel:1 laser:66 ejection:3 appearance:2 value:15 will:5 ar:1 ultra:2 vc:1 vf:2 refs:7 thus:8 surface:2 vs:1 perhaps:1 radiation:12 cross:6 http:4 absorb:1 conceived:1 upon:1 effect:31 v0:6 ion:2 conden:1 αth:1 schr:3 acknowledgement:1 well:6 bohr:1 bohm:3 sets:1 undertaken:1 arising:1 usual:2 spherical:1 less:1 moments:1 wagner:1 obtain:2 web:1 disturbance:1 density:12 absorption:8 nonrelativistic:3 smith:3 reasons:4 book:1 combine:1 saturation:2 increases:3 press:2 immediately:3 loss:1 necessary:2 like:5 success:2 exploiting:2 qualitative:1 alkali:1 martin:2 works:5 page:2 exceed:1 because:3 classical:3 phenomena:8 library:1 growth:1 demonstrates:1 does:3 demonstrated:1 obey:1 journal:1 analysed:4 pressure:1 stage:2 gained:1 about:3 rare:2 carried:4 universe:2 dependence:8 carrier:1 introduced:1 branching:1 dubois:1 ultrasound:1 promise:1 ea0:1 van:1 additional:3 appl:2 mandel:2 specimens:1 naturally:1 function:35 ean:1 femtosecond:1 triangular:1 overlapping:1 volume:15 neutral:1 construction:5 gain:1 kraft:1 he:5 made:3 evident:1 whether:1 signed:1 below:4 distribution:1 mechanics:10 bearing:1 resting:1 int:2 recognize:2 universal:1 denote:1 bombarding:1 relates:1 ind:3 qα:1 functions:3 nonetheless:3 detail:1 virtual:1 other:13 details:1 theor:3 conclusion:2 variation:4 coupling:4 rule:3 αna:3 xenon:3
|
quant-ph9906092.txt |@word ibid:4 limited:1 gu:1 consider:2 crucial:3 varying:2 results:5 existing:1 follow:2 localized:4 preserves:1 calculate:2 alamos:2 tr:1 environment:2 finally:1 program:1 under:6 stochastic:2 division:1 global:1 far:1 supercomputer:1 percival:1 choice:1 lyapunov:12 maali:1 decide:1 difference:1 exact:1 condition:2 induced:1 t8:3 hamiltonian:3 did:1 irreducible:1 solution:1 large:4 vector:1 sensitivity:1 small:6 optics:3 smaller:1 neighborhood:1 direct:1 sign:1 zero:3 christensen:1 design:1 value:4 rigorous:1 further:1 dynamics:11 estimated:1 linear:2 even:5 what:3 errors:1 apparatus:1 goes:1 new:2 ever:1 method:1 satisfy:2 edited:1 evolving:1 simultaneously:1 notions:1 degree:1 heller:1 answers:1 understanding:2 desired:1 tracks:1 objects:1 governing:1 address:3 along:1 strong:1 equations:4 interpret:1 obtained:2 almost:1 rigorously:1 study:2 studied:2 allows:1 eberly:1 amount:4 resulting:4 action:4 assuming:1 makes:2 ρx:1 schack:2 followed:1 projection:1 scales:1 plenum:1 apply:1 total:1 use:1 start:2 remains:2 coupled:1 classically:2 therefore:1 noisy:2 theoretical:2 today:1 more:3 separated:1 flat:1 optimizing:1 successful:1 becomes:5 operators:2 berlin:1 particular:2 central:2 cases:1 must:3 evolves:1 springer:1 mf:1 defines:1 specifying:1 equation:4 averaged:3 values:6 ms:1 freedom:2 following:1 making:1 stroboscopic:3 root:1 example:2 purity:1 compare:3 figure:1 process:5 discussed:1 haroche:1 high:2 effectively:2 vx:3 numbers:1 calculated:1 guarantee:1 information:1 needs:2 ingram:1 provide:1 how:2 maximal:1 optimal:1 verlag:1 parameter:1 simplicity:1 rise:1 may:1 after:1 different:2 flattens:1 demonstrating:1 parallel:1 stress:1 raimond:1 natural:1 dynamical:2 effective:1 separations:1 correspond:1 rather:1 maintain:1 so:4 progressively:1 fundamental:1 kurt:1 order:4 ammann:1 typical:7 wigner:1 produces:2 hierarchy:4 indeed:1 over:5 vary:1 satisfied:4 thermal:2 experiments:3 through:1 during:1 existence:2 satisfies:1 its:1 before:1 jacobs:3 la:1 ln:4 temporal:1 writing:1 late:1 absence:2 degrees:1 systems:13 carmichael:1 ηm:1 correspondence:1 eventually:1 non:1 good:1 thereby:1 practice:1 evolution:8 band:1 effects:1 they:1 now:3 discuss:1 possess:1 term:1 several:1 instances:1 always:3 level:1 substantiate:1 sufficiently:2 turns:1 found:1 higher:1 characterized:1 mean:2 schemes:1 significantly:1 formulate:1 map:2 generation:1 series:2 energy:1 toda:1 expect:1 measurement:35 quantum:45 our:2 extract:2 out:3 emerges:1 dominates:1 matrix:2 driving:1 space:8 open:3 furthermore:1 since:2 interference:1 chaos:14 looking:1 similarly:1 dominated:1 denoted:1 gov:6 ref:1 b285:1 math:1 shows:1 numerical:1 theory:1 localization:7 oskay:1 maintains:1 free:1 completely:1 york:1 estimate:1 dreyer:1 milburn:3 rewritten:1 definition:1 interaction:3 regarding:1 determining:1 could:1 transition:6 motion:3 cos:1 noncommutativity:1 assign:1 first:2 initial:3 number:1 wash:1 done:1 wunderlich:1 directly:1 impossible:2 precisely:1 electronic:3 hood:1 spread:1 given:1 temperature:2 width:2 introduction:1 system:21 master:3 realization:1 white:2 ehrenfest:1 recovered:1 gives:2 excellent:1 relationship:1 explanation:1 continuous:15 accurately:1 x2:3 dt:8 than:3 albeit:1 succeeded:1 measured:3 second:2 exponents:6 future:1 steep:1 extracting:2 remained:1 unchanged:1 locations:1 curves:1 chapman:1 substantial:1 manner:1 qualitatively:1 need:2 any:2 symmetrized:1 strength:9 depending:1 lin:1 able:1 isolated:2 mechanism:3 note:2 idealization:1 eprint:5 negligible:1 strengths:1 evaluated:1 unperturbed:1 heisenberg:1 spectral:1 play:1 regard:1 allow:1 though:2 probed:1 kaj:1 rhs:1 most:2 jul:1 letter:1 quantitative:1 phase:9 extremely:3 observation:2 nonlinearity:2 url:3 neighboring:2 average:5 detectors:1 drive:1 physica:1 points:3 mechanical:1 slope:2 signatures:1 show:5 attempts:1 find:2 considered:1 quoted:1 spite:1 situations:2 explain:2 λt:1 enough:1 elucidated:1 should:3 analytic:1 only:2 implemented:1 developed:1 do:1 above:1 localizing:1 means:1 familiar:1 zurek:1 stop:1 expectation:1 expects:1 closely:1 progress:1 dw:6 quantifier:1 lynn:1 gray:1 processes:1 approach:2 arxiv:1 gutzwiller:1 investigate:1 intervals:1 common:1 contain:1 body:1 requirement:1 art:1 exists:1 achieved:1 cimento:1 national:1 maximum:1 observed:6 habib:3 see:5 result:3 versus:1 terms:2 halliwell:1 belavkin:1 techniques:1 satisfying:1 exponent:6 hagley:1 review:1 ralph:1 case:2 state:8 various:1 between:7 probably:1 caves:2 conditions:6 brune:1 choose:1 comparable:1 recently:1 nature:1 weak:2 however:3 efficiency:1 succeed:1 here:1 unnormalized:1 problem:2 both:6 essentially:2 limits:1 region:2 according:1 against:1 berry:1 variance:4 gisin:1 experimental:4 nearby:1 cxp:1 mechanics:8 key:1 point:5 simple:1 each:2 period:2 semiclassical:3 twin:1 simply:1 actually:1 suppressing:1 considers:1 pq:1 described:1 addition:2 trajectory:10 due:2 been:5 faithfully:1 much:3 change:2 expected:1 microscopic:1 ph:5 fig:9 nuovo:1 direction:1 arises:1 corresponding:5 deeper:1 ωt:1 quantities:1 sufficient:1 coherence:1 covariance:1 argument:1 maps:2 understand:1 demand:2 irrelevant:1 diffuse:1 those:1 applied:1 wiseman:1 pacs:1 variances:2 suitably:1 kimble:1 salman:2 while:1 fiducial:3 behavior:4 korsch:1 irrespective:1 barchielli:2 characterizing:1 identical:1 larger:4 mexico:1 chaotic:6 vi:1 simulations:1 thus:3 them:1 conditioned:3 characterize:1 itself:1 anticipating:1 ready:1 par:1 make:1 indistinguishable:2 same:3 quant:5 split:1 units:1 finite:2 infer:1 difficult:1 development:1 evolve:1 used:3 http:3 trajectories:15 effect:4 hand:2 driven:5 usually:1 bhattacharya:1 weakly:1 nevertheless:2 studies:1 well:1 analysis:1 obviously:1 without:2 solve:1 very:2 position:14 model:2 plotted:2 distances:1 just:1 less:1 moments:4 λx:1 obtain:7 underlying:3 questions:1 using:1 localize:1 macroscopic:2 yet:2 previous:1 disturbance:1 density:2 except:1 mathematically:1 unambiguously:1 lett:9 easy:1 theorem:1 guarantees:1 momentum:4 take:1 real:3 references:1 milonni:1 huberman:1 early:1 possibly:1 raizen:1 immediately:1 emergence:3 formal:2 dimensional:1 necessary:3 particle:1 follows:2 qualitative:1 performing:1 maintained:1 brun:1 unstable:1 either:1 become:2 weiner:1 accuracy:1 reduced:3 smoothness:1 accessible:1 satisfactory:1 because:3 methods:1 classical:45 people:3 some:2 understood:1 deduce:1 prosperi:1 unraveling:2 duration:1 ourselves:1 scale:2 tracked:2 lead:1 confirm:1 demonstrates:1 measurements:2 does:3 maitre:1 provides:5 tends:1 demonstrated:3 refer:1 measuring:1 noise:24 quantph:1 obey:3 dictates:1 agreement:1 interval:1 paper:1 diosi:1 although:1 2m:3 drawn:1 bx:1 bz:1 stage:1 actual:4 tracing:1 introduces:3 o:5 range:2 constraints:1 spiller:1 automatically:1 truncating:1 rev:12 into:2 within:1 ηk:1 doherty:1 bath:1 square:1 ηs:1 operator:1 proportional:1 often:2 72b:1 deal:1 area:1 intrinsic:1 there:1 approximate:1 long:1 los:2 low:2 way:2 function:3 runs:1 governs:1 2ηk:1 but:2 sophisticated:1 hk:1 satisfactorily:1 line:1 tomsovic:1 hogg:1 evident:1 characteristic:2 up:1 quantitatively:1 ur:1 record:6 below:1 limit:12 continuously:4 demonstrate:2 distribution:3 define:1 similar:1 called:1 distance:2 detailed:2 ac:1 required:1 constant:2 int:1 steady:2 describe:2 covers:1 peres:1 single:1 ikeda:1 exist:2 periods:1 laboratory:1 ax:1 work:1 distributions:1 regime:9 compared:1 eq:3 wavefunction:3 when:2 detail:1 field:1 other:3 role:1 theor:1 tic:1 models:2 time:9 reached:1 includes:1 generated:1 important:3 bounded:2 suppression:1 ballentine:1 structure:1 steck:1 algorithm:1 lanl:6 curve:2 lanz:1 quantify:1 decoherence:4 starting:1 having:1 once:1
|
quant-ph9906093.txt |@word partial:1 consider:2 similarity:1 results:2 four:3 lewenstein:5 crete:1 research:1 contributions:1 localized:1 calculate:4 leung:1 young:1 finally:2 present:1 th:1 under:2 γc:6 amplitudes:1 g1:5 without:1 very:2 frequencies:1 splitting:1 wishes:1 resonant:1 experimentally:1 leads:1 level:7 did:1 knight:10 applicable:1 integro:1 optics:5 quicker:1 findings:1 defect:9 approximation:1 rate:1 chen:1 dynamics:1 substitute:2 even:2 employ:1 appear:5 section:9 while:3 above:9 ground:7 method:1 thin:1 edited:3 full:8 angelakis:2 here:3 atoms:4 behaviour:4 consideration:1 strong:1 equations:1 appears:7 obtained:2 parameters:11 shift:2 study:7 studied:1 funded:1 microcavities:3 usually:1 narrow:2 studies:3 involves:1 composed:1 appropriately:2 eiδt:2 via:2 useful:1 family:1 lims:1 modifying:1 summation:1 apply:2 quenching:1 use:6 proceed:2 waveguides:3 commun:4 distinct:3 dωρ:1 next:1 therefore:2 taken:2 type:3 theoretical:1 today:1 more:2 separated:1 becomes:1 emission:34 haroche:1 berlin:1 known:1 cases:2 hold:1 iii:3 springer:2 equation:3 work:2 modified:17 values:3 splittings:1 following:1 spontaneous:35 example:2 give:1 expanding:1 organized:1 confused:1 states:6 council:1 occur:3 verlag:2 lamb:2 requirements:1 decaying:2 buzek:1 rippin:1 disappear:1 influences:1 frontiers:1 l9:1 parameter:1 profile:1 description:2 derived:1 epsrc:1 summarize:1 wave:3 efficiently:1 dynamical:1 effective:1 spectra:1 separations:1 shore:1 so:3 order:1 typical:1 wigner:2 help:1 reservoir:46 vary:1 choose:1 course:1 swain:1 london:2 affect:1 differs:3 existence:6 linewidth:1 jaynes:1 its:3 before:1 ssf:1 lc:1 kofman:1 decay:4 energies:1 lai:1 exhibits:3 fig:25 relate:1 rabi:1 main:3 focussed:1 rwa:2 non:14 pure:2 mølmer:1 outlined:1 material:1 ye:1 investigated:1 band:11 they:3 oxford:2 now:6 densities:1 represents:1 february:1 gets:1 university:2 hamiltonian:2 mode:5 each:1 lorentzian:5 referred:3 differential:1 england:1 kleppner:2 energy:2 barnett:1 frequency:5 obtains:3 amsterdam:1 substantially:1 laboratory:1 bay:2 eq:28 special:1 gaps:2 shown:8 network:1 space:10 rep:1 rev:21 denotes:6 attracted:1 denoted:1 induced:5 occurs:3 foundation:1 mechanisms:1 free:10 quite:1 gλ2:2 definition:1 interaction:8 starts:6 transition:17 motion:1 turn:3 place:1 isotropic:7 incorporated:1 consequence:1 first:3 sanchez:1 probability:2 omitted:1 done:2 defects:4 another:4 mostowski:1 thick:1 smoothing:1 angular:1 xia:1 given:17 long:2 publication:1 glauber:1 introduction:1 eqs:4 system:19 sargent:1 their:4 zeros:1 too:6 scheme:5 structures:1 final:2 recovered:1 accompany:1 than:1 coefficients:3 john:6 third:2 zero:4 submitted:1 smoothed:2 amplitude:2 were:1 bare:1 exhibit:1 lines:21 spectrum:65 manner:1 need:1 seen:2 linked:1 latter:2 note:6 sciences:1 concerns:1 strengths:1 spectral:1 begin:2 altered:1 normal:3 sherman:1 gλ:6 gκ:6 mondragon:1 cummings:1 chap:2 r33:1 considered:1 calculated:2 later:2 g12:4 yang:1 scholarship:1 physics:3 phenomenon:2 show:4 delta:4 rotating:1 purely:1 threshold:1 substituting:1 schenzle:1 find:2 principal:1 2bz:1 weisskopf:2 written:1 should:3 only:3 rich:1 achieve:1 get:1 dependent:2 displayed:1 overall:1 kurizki:1 aλ:2 aκ:2 qs:1 heaviside:1 arxiv:1 summary:1 predicted:7 kernel:2 exists:1 sep:1 violated:1 observed:1 depends:3 college:1 result:5 greece:1 discussions:1 concern:1 materials:5 importance:1 state:15 ωj:1 closed:1 progress:1 approach:2 terms:1 nature:1 initially:4 attention:1 subject:1 however:5 j2i:2 huang:1 article:7 suppressed:1 ωc:2 thank:1 both:1 taking:1 acknowledge:1 equal:1 attributed:2 chosen:1 blackett:1 contribution:1 disappears:2 co:1 simple:1 zubairy:2 scully:4 keitel:3 associated:2 bκ:3 bλ:6 considering:1 described:4 second:4 addition:2 narducci:2 due:3 been:6 commission:1 detuning:13 much:1 interest:3 electrodynamics:1 expected:1 ph:1 define:1 j0i:2 controlled:1 ik:1 gap:11 those:2 case:27 multi:3 laser:15 exponential:1 pacs:1 solid:1 originate:1 engineering:2 value:4 spontaneously:3 will:5 near:3 sw7:1 opt:9 vectors:1 coupled:3 vol:1 systems:1 iv:2 ii:1 reads:3 elsevier:1 mod:5 ib:6 interacts:2 ig:4 agarwal:2 different:5 verified:1 quang:5 acknowledgments:1 zakrzewski:2 same:5 any:1 quant:1 units:4 several:1 iγ:5 european:1 used:5 peaks:2 see:4 singapore:1 fulfilment:1 effect:1 lambropoulos:2 driven:5 kim:1 changing:1 expand:1 schr:2 modes:37 mention:1 well:4 obviously:1 academic:1 edge:3 position:1 model:3 usual:2 yeh:1 being:2 obtain:9 photonic:10 shape:1 atomic:8 predicts:1 previous:6 density:31 absorption:1 character:1 except:1 potential:1 combine:1 lett:7 theorem:2 occurring:1 excited:5 real:5 couple:1 term:1 dark:38 inhibition:1 vacuum:9 press:2 using:5 formal:1 like:1 follows:1 reduces:2 performing:1 niels:1 specific:6 yields:1 either:4 arbitrary:1 δg:54 δc:11 because:1 qed:1 understood:1 choosing:1 b3:3 ωb2:1 pronounced:1 tmr:1 describing:1 lead:1 cavity:2 investigations:1 integration:1 does:1 ωij:1 δb3:1 bi:1 expansion:3 step:1 although:1 properties:2 central:2 would:3 extension:1 hellenic:1 discussed:2 o:4 wolf:1 greatly:1 financial:1 markovian:30 j1i:2 into:5 three:2 tackle:1 appropriate:2 schemes:3 ei:3 methods:1 assumed:5 support:1 there:2 transform:5 specifically:2 imperial:1 dispersion:1 width:1 describes:1 crucially:1 was:2 garraway:2 function:7 considerably:1 complete:2 form:3 atom:15 elimination:1 line:20 zhu:6 msc:1 us:4 ωi:1 meschede:2 decays:1 limit:2 uk:1 problem:1 similar:1 laplace:6 ωg:7 constant:2 b2:28 certain:1 describe:1 influence:1 general:3 quantum:5 single:2 exist:2 our:5 physical:1 compared:1 dotted:8 no:6 dashed:10 when:1 reality:1 field:3 other:5 dt:4 department:1 picture:2 elements:1 superposition:3 zhou:1 models:5 berman:1 odinger:2 peak:1 variable:1 structure:5 tailored:1 coupling:13 dω:1 assume:2 curve:24 time:6 meystre:2
|
quant-ph9906094.txt |@word limited:1 partial:1 consider:3 gp:2 rev:10 magnetic:2 global:1 results:2 existing:1 roy:1 gb:8 computation:7 edu:2 contributions:1 gj:16 whose:1 depend:1 alamos:2 switched:1 environment:3 finally:1 those:1 th:3 under:13 tc:18 resources:8 alternating:1 case:9 belonging:1 lations:1 straightforward:1 very:1 focus:1 exact:2 dim:3 swapping:1 hamiltonian:29 turns:1 t2:1 t1:1 large:5 small:1 lloyd:3 hsb:4 averaged:1 zh:13 direct:1 pulse:8 centralizer:10 rate:1 cost:1 perspective:2 insertion:1 equal:1 further:2 dynamics:8 implemented:2 quite:1 linear:2 even:4 trick:1 what:2 iterating:1 clock:1 trivial:1 sum:1 selected:2 hp:1 reasoning:1 3k:1 above:6 shared:1 net:1 appeal:1 ever:1 method:1 quenched:1 full:8 simultaneously:1 degree:1 respectively:2 component:2 here:1 elimination:1 desired:3 selective:2 possibility:1 separation:1 address:1 alone:1 ratio:1 appropriate:2 strong:1 box:2 algebra:4 institute:1 involved:1 losses:1 allows:1 approaches:2 commonly:1 exploitation:1 amount:1 resulting:1 loop:2 knill:5 action:6 resonance:2 implement:4 suitable:3 uniquely:1 control:36 followed:1 projection:1 classification:1 extra:5 inducing:1 private:1 replace:1 modulated:1 issue:2 apply:3 resolutions:1 total:1 unit:1 cluster:1 projector:1 recalling:1 continuous:1 coupled:1 properties:2 almost:1 memory:1 generators:1 historically:1 more:1 separated:1 introducing:3 clearly:1 becomes:1 operators:7 equipped:1 validity:1 controlling:1 virtue:1 particular:1 known:3 central:1 symmetrize:1 eα:5 circumstances:1 springer:1 characterize:1 science:2 challenge:1 tremendously:1 modified:1 worth:1 correctable:1 stabilizer:1 following:1 making:1 stroboscopic:1 example:1 decoupled:8 performed:2 beautiful:1 weaker:1 modulation:2 synchronized:2 discussed:1 stressing:1 effectively:6 minimum:4 attain:1 want:1 potentially:1 times:3 verlag:1 compatible:1 end:6 goal:2 eng:1 provide:1 feature:1 unitaries:1 nontrivial:1 criterion:2 reject:1 instead:2 map:1 description:1 information:4 may:5 impulsive:1 corrections:1 designed:1 gottesman:1 choice:2 parallel:3 processors:1 realized:1 short:1 natural:2 dynamical:3 effective:8 whenever:1 spectra:1 correspond:1 stimulate:1 emanuel:1 generic:1 ones:2 negligible:1 allow:1 correlation:3 acknowledges:1 order:3 se:1 typical:1 operations:21 interpretation:1 reservoir:1 hierarchy:1 developed:1 over:9 spectral:1 soc:1 burkard:1 lanl:3 computational:1 through:3 still:4 its:1 before:1 perfect:1 group:16 subinterval:3 how:2 chosen:1 temporal:1 encompasses:1 τc:5 pulses:6 actually:1 better:1 whether:1 window:1 degrees:2 systems:8 communication:1 reachable:1 lx:1 maximal:1 non:1 good:1 thereby:3 powerful:1 practice:3 aro:1 evolution:13 introduce:1 slicing:1 bang:4 effects:2 front:1 rotation:2 now:6 represents:2 term:3 always:2 presented:1 assembled:1 identified:1 capability:4 realistic:2 each:2 characterized:1 constraints:1 el:1 schemes:4 initiative:1 guo:1 energy:1 ef:3 idea:1 related:1 challenges:1 extended:1 gates:2 combining:2 quantum:31 laboratory:2 operation:2 avoided:2 eq:2 ep:1 out:3 living:1 shown:1 space:16 restricted:1 rep:1 since:7 crucial:1 denotes:1 looking:1 re:1 seriously:1 performs:1 conjectured:1 print:2 gov:1 suffices:1 occurs:1 strategies:1 counterpart:1 theory:2 interactions:9 divincenzo:3 free:3 standard:1 completely:1 unwanted:2 york:1 imagine:1 intermediate:1 ord:1 sophistication:1 beginning:3 shortest:1 pairs:1 interaction:2 retained:2 language:1 created:1 determining:2 could:4 programming:6 so:4 tolerant:5 motion:1 turn:2 kwiat:1 removing:2 consequence:1 bodenhausen:1 corrupting:1 support:2 first:3 lond:1 symmetry:3 striking:1 mit:2 coding:2 number:3 twisted:3 enlarged:1 amenable:1 fast:9 directly:2 comprises:1 reached:1 precisely:1 open:5 synchronously:1 given:7 necessarily:1 πg:13 leading:1 system:16 response:1 their:1 assumption:2 scheme:2 inserting:4 frame:2 speaking:1 preserved:1 option:1 exactly:1 environmental:3 part:1 occurring:1 representing:1 specify:1 distance:1 kind:1 determines:1 showed:1 cyclic:1 double:1 require:2 typically:1 second:1 preparation:1 determined:2 toward:1 solely:1 steer:1 zanardi:1 register:1 quence:1 seth:1 correction:3 turned:2 say:1 qualitatively:1 need:1 constrained:1 demonstration:1 any:8 relatively:1 symmetrized:1 lie:3 subsystems:1 strength:6 convenient:2 latter:2 interferes:1 able:3 note:4 instance:3 ideal:1 potential:1 best:1 hs:5 ancillary:1 new:4 acquires:1 switching:4 edited:1 heisenberg:1 bilinear:2 begin:1 sure:1 unless:1 shall:5 denoting:2 simplify:1 involving:1 connected:1 but:2 letter:1 pair:1 future:1 inserted:1 class:2 advantageous:1 considered:1 average:4 circuits:1 points:1 principle:5 exp:3 mechanical:1 combinations:1 physics:1 imagining:1 shor:2 trol:1 supported:1 contemporary:1 purely:3 stringent:1 chuang:1 solutions:1 carefully:1 d2:1 d1:1 access:1 slow:5 based:6 knowledge:7 spite:1 situations:2 delays:1 less:1 enough:1 controls:1 should:1 only:5 supporting:1 black:2 factor:1 hamiltonians:8 achieve:2 do:3 dj:1 dependent:2 zurek:1 de:1 overall:1 truly:1 cannot:3 words:1 devising:1 timing:2 during:3 procedures:1 areas:1 processes:1 approach:1 arxiv:1 bandwidth:1 influenced:1 including:1 cycles:3 traceless:1 view:1 requirement:1 set:10 exists:1 achieved:3 physically:1 robustness:1 national:1 coupler:1 operates:1 see:1 computer:2 result:4 eliminating:1 suited:1 contains:2 lel:1 incorporating:1 techniques:1 exploited:1 commutation:2 ways:1 nuclear:3 tend:1 state:1 protected:2 various:2 between:2 affecting:1 invariant:1 geometric:1 conditions:3 available:14 notice:1 terms:2 nature:1 qubits:2 darpa:1 weak:2 however:1 implementing:1 modeling:1 restrictions:2 realizable:5 prescription:1 met:1 fault:2 σa:8 according:7 demanded:1 enabling:1 etc:1 σy:2 σx:2 logic:1 ernst:1 contribution:1 whole:1 experimental:1 con:1 arbitrarily:4 strongly:1 relevant:3 groups:2 point:1 simple:1 dimensional:1 exploit:1 reported:1 anti:1 bα:2 sequences:1 accordingly:2 factors:1 along:1 combines:1 described:2 transformations:3 decoupling:29 capable:1 addition:4 due:2 been:5 strategy:1 devise:1 reduction:1 slowly:1 combined:1 interest:2 expected:2 ph:3 spoiling:1 obtained:2 corresponding:4 both:4 sufficient:1 subspace:1 repertoire:2 controller:1 ensuring:2 specifically:1 demand:1 c2:1 despite:1 denote:2 present:3 applied:2 look:1 engineering:3 will:8 while:4 eib:1 suppose:6 theoretical:1 behavior:1 error:12 situation:3 property:1 couplings:1 procedure:1 periods:1 unitary:8 mexico:1 memoryless:1 averaging:4 thus:2 encountered:1 ih:1 itself:1 duan:1 contract:1 baths:1 ia:1 ib:1 technology:3 different:2 qecc:1 anymore:1 σz:2 perform:3 make:1 same:3 toggling:1 nonmarkovian:1 quant:3 viola:3 universality:3 finite:4 subalgebra:1 difficult:1 development:1 evolve:2 used:2 singapore:1 effect:2 displace:1 phy:1 potentials:1 qubit:4 cycle:13 implements:1 prescribed:1 task:1 off:2 whereby:1 scenario:3 ua:1 no:3 well:2 steane:3 analysis:1 obviously:1 without:3 biosciences:1 components:1 reintroduce:2 subgroup:1 comment:1 world:1 responsible:1 just:1 mimicked:1 being:5 rotated:2 obtain:1 judiciously:1 oxford:1 shape:1 identify:1 immediately:1 useful:1 previous:1 letting:1 field:1 scales:2 guaranteed:1 capabilities:1 belongs:1 transformed:1 lett:5 easy:1 pling:1 complements:1 ruled:2 transformation:2 scientific:1 identical:2 quic:1 easily:1 replaced:1 tc2:1 possible:4 spanned:1 tc1:1 possibly:2 press:1 using:3 heightened:1 desire:1 loss:1 necessary:1 like:1 exploiting:1 collective:2 performing:2 addressed:1 translates:1 imposes:1 either:1 evolutions:4 output:1 essential:1 preskill:1 sketch:1 laflamme:2 methods:2 sequence:5 successfully:1 some:1 supplementary:1 complete:3 duration:3 multiple:1 provided:3 scale:5 describing:1 swaps:1 lead:1 synchronize:1 opposite:1 manipulations:4 models:1 does:1 assuming:1 prog:1 proc:1 measuring:1 implying:3 noise:11 nmr:1 ba:2 power:1 processing:1 accomplishing:1 bj:1 constructive:1 clarendon:1 step:2 hilbert:4 noisy:1 actual:1 markovian:1 instantaneously:1 freedom:3 bgj:1 compatibly:1 meaning:1 o:4 practical:1 distinct:1 ensure:1 efforts:1 introduced:2 bath:2 mechanics:1 cambridge:1 significant:1 presence:2 nsa:1 within:1 rotations:2 nsf:1 three:1 accommodate:1 hermitian:2 raises:1 physical:1 whaley:1 span:1 r2493:1 assumed:2 suffice:1 question:1 u0:2 long:3 lidar:1 los:2 hef:7 way:1 conceivable:1 analyze:1 was:3 propagator:1 economics:1 elsewhere:1 form:5 concatenated:1 becoming:1 jun:1 cyclicity:1 principles:1 construction:1 hb:2 attainable:1 optical:1 trying:1 dissipative:1 longer:1 made:3 fulfilling:1 relaxed:1 us:3 achieving:2 limit:3 squareroot:1 spectroscopy:1 demonstrate:1 problem:2 alternate:1 similar:2 called:2 ub:1 detailed:1 viable:1 controllability:1 interval:4 associated:3 defined:1 certain:1 universal:14 received:1 influence:1 advancements:1 general:2 ap:1 single:7 ingredients:1 interchanged:1 controlled:2 work:2 check:1 defines:1 effected:1 again:1 compared:1 ideally:1 variety:1 amounts:3 when:1 application:2 other:1 details:1 department:2 conclusion:2 picture:1 briefly:1 accounted:1 separate:1 keep:1 includes:1 hamil:1 generated:6 bounded:1 massachusetts:2 suppression:2 dissipation:1 n2:1 dimensions:1 implies:2 coupling:3 practically:1 assume:2 established:1 proposed:1 required:5 together:2 attaining:1 time:26 far:1 n1:1 decoherence:4 requires:1 original:4 once:1
|
quant-ph9906095.txt |@word secondly:1 monte:11 code:27 sci:1 consider:14 kε:5 represent:6 reversibility:1 results:1 illustrated:3 roy:3 proposition:1 generalize:1 comments:1 computation:25 consists:4 gm:7 gl:1 gk:6 gj:6 gi:7 gr:31 relationships:1 whose:6 c0:16 mδ:4 r5:2 equivalence:2 factoring:12 languages:11 reductions:1 finally:3 tk:2 bqp:12 under:8 opt:1 analogous:2 kξ:4 inform:1 summarizes:1 applied:1 amplitudes:5 string:38 g1:53 orthogonal:4 far:1 observables:2 implicitly:1 rise:1 springer:1 αm:7 vegas:22 every:12 entries:4 ma:1 em:2 papadimitriou:1 exact:10 condition:16 ibm:1 school:2 subsets:3 level:1 did:1 turns:1 notes:1 p5:1 list:11 applicable:1 t0:2 t1:2 discrete:9 convenience:1 vector:8 math:2 science:3 small:2 ρk:11 configurations:5 inserting:1 approximately:1 zi:1 zj:1 deutsch:10 ρm:2 prevents:1 go:3 zero:4 abbreviates:2 rigorous:2 further:1 implemented:6 carlo:11 machines:14 canonical:2 even:4 index:1 what:14 errors:1 plays:1 appear:2 iterating:2 performs:1 diag:2 section:11 transforms:2 analogously:1 uniform:53 3k:3 public:1 version:1 above:20 3l:6 ˆi:2 l1:5 consisting:5 counters:3 satisfy:4 q1:9 margolus:1 simultaneously:2 notions:1 degree:2 q0:33 respectively:11 aij:2 component:3 xmn:1 answers:4 canonically:1 explore:1 simon:1 represented:9 path:1 constructive:1 equations:1 z1:3 change:3 obtained:7 remark:7 accomplishes:1 tapes:4 surveys:1 35th:2 study:2 studied:2 allows:1 expression:1 round:1 p2:2 simultaneous:1 bennett:4 permutation:11 usually:1 implement:1 fourier:5 y11:1 writes:2 y12:1 uniquely:4 deterministic:4 projection:3 family:1 extra:2 merely:7 logical:1 outcomes:2 hadamard:1 boolean:18 summation:3 controlled:2 total:3 unit:4 solovay:4 use:5 lecture:1 would:1 prove:3 remains:1 positive:14 objectives:1 contains:6 uniformly:18 nagoya:2 induction:1 properties:1 comparing:1 linear:2 bases:1 m1:10 cε:1 m3:2 m2:17 taken:3 candidates:2 25th:1 type:8 theoretical:3 decomposable:12 more:7 sort:1 permutations:1 formally:5 th:24 integers:5 afford:1 operators:1 ti:3 x12:1 concatenation:2 reversible:9 particular:6 known:6 foundations:3 cardinality:3 producing:1 weaknesses:1 must:3 logarithm:2 evolves:2 none:2 valued:1 defines:1 language:17 thanks:1 indexed:2 ml:1 equation:2 work:1 mi:4 modified:1 mu:19 ij:3 values:2 three:2 modifying:1 following:30 dec:1 considering:1 example:5 proof:41 control:1 claim:1 computers:6 figure:12 give:9 process:10 accepts:6 ak:1 arise:2 organized:1 πj:6 states:1 dm:1 recognized:9 allowed:3 conversely:2 absolute:1 needs:1 ni1:1 end:4 advantage:1 rather:1 s2:6 s1:7 holds:6 carries:34 bn:1 write:10 how:2 fourth:4 answer:1 ensure:1 those:3 verlag:1 sin:3 brassard:2 simplicity:1 product:2 blanks:1 may:4 turing:32 after:7 mapping:3 produce:2 designed:1 verified:9 fk:15 2l0:3 types:6 efficiently:15 z2t:3 natural:8 varieties:1 third:4 sets:2 computations:3 lemmas:3 counter:5 element:10 sk:3 sj:2 complexity:25 ones:7 algorithms:25 sn:2 solely:1 alphabet:8 definitions:6 order:8 operations:1 s3:2 produces:10 numbers:26 indeed:1 pointed:2 move:3 mainly:1 satisfied:3 symbols:3 looping:6 paper:6 including:2 statistical:1 mentioned:1 japan:1 satisfies:10 still:2 ieee:6 its:9 τn:1 machine:18 τm:2 τk:4 τi:9 tracks:10 matrices:2 fix:1 xm:3 lj:3 lk:3 writing:1 late:1 h2:2 parts:1 microscopic:1 systems:1 communication:1 schmidt:1 might:1 correspondence:3 eventually:1 them:6 πl:2 ym:3 yn:2 processes:1 introduce:6 yasuo:1 they:3 gate:55 yp:2 now:19 discuss:1 qt:1 2t:38 represents:8 several:2 s11:1 always:2 university:1 hamiltonian:2 b3:2 identified:2 divides:1 orthonormal:6 sufficiently:1 inequality:1 l2:3 l0:33 each:21 found:4 2n:18 polynomially:1 2i:1 constraints:2 subset:3 domain:2 transforming:1 g2:19 formulate:2 t2:2 reduce:1 related:1 slowdown:11 elementary:8 literature:2 computable:18 logc:1 measurement:1 quantum:198 our:3 operation:8 2πi:7 eq:5 special:2 out:62 shown:5 lastly:1 divide:2 matrix:11 space:17 restricted:3 furthermore:1 since:14 rev:2 denotes:7 increase:2 re:2 ajk:1 u2p:1 adapt:2 rational:2 denoted:15 formula:1 current:1 rh:1 correct:2 rj:3 shows:3 working:1 huang:4 theory:8 1p:1 contain:1 diagonal:2 possibility:3 quite:1 vazirani:11 approaches:1 carried:10 verify:1 put:2 jozsa:3 ri:6 additional:1 r4:2 definition:15 fixed:1 benioff:2 r1:9 r2:9 r3:11 aj1:1 lanl:1 transition:20 times:6 turn:1 length:19 place:1 circuit:71 πk:6 hence:1 uses:1 closure:1 xij:1 first:24 xk:8 initial:13 xn:10 probability:48 encoding:5 bijection:1 powerful:3 number:21 reaches:1 transform:5 restrict:1 networks:1 xy:1 done:1 specifically:2 another:4 blank:2 carry:11 array:2 πm:9 open:3 xt:1 size:55 gpc:9 given:33 fair:1 their:6 introduction:1 eqp:4 eqs:1 πi:6 system:10 least:15 yij:1 indicate:3 unitarity:1 appl:1 statement:3 realization:1 programmable:1 majority:1 las:22 bits:2 final:11 eip:1 1n:11 qσ1:1 preserved:1 m0:1 relationship:2 tuple:1 exactly:7 proving:1 larger:20 part:5 simulate:6 x0:1 x1:20 representing:6 than:28 coefficients:2 finitely:1 distance:3 john:1 determines:1 target:1 dtm:12 rairo:1 sections:1 require:2 see:15 recording:1 whenever:2 ppp:1 classes:15 amplitude:4 were:1 exp:3 nishimura:2 powers:2 projections:1 bridge:1 logarithms:1 cn:1 generality:2 correction:1 modern:2 argument:3 generalization:2 discussions:1 say:25 constructible:2 archive:1 need:4 carrying:4 s1k:1 st:1 any:87 contents:1 decomposing:2 mij:3 computationally:5 depending:1 efficient:4 studying:1 internat:1 si:11 note:1 sciences:1 k1:17 s21:1 take:1 k4:2 xi:2 so:10 strengths:1 accuracy:26 s2k:1 spectral:1 sure:1 multiple:1 normal:7 track:44 s31:1 friedman:2 object:1 church:1 most:16 ker:1 said:19 connected:10 representation:1 pair:3 iterate:1 coin:1 probabilistic:8 class:10 interacting:1 tξ:3 branching:4 ka:3 constructed:17 characterizes:1 considered:4 kj:7 actually:1 later:2 coincides:1 kn:67 kl:1 countable:2 feynman:2 proceedings:3 points:1 principle:1 ku:2 mechanical:2 kz:1 physics:2 notion:5 fact:6 shor:20 kg:17 show:19 rtm:4 halts:1 12n:1 notations:2 spaces:1 relation:3 keywords:1 decoding:5 trivial:2 find:1 fifth:1 d1:1 completion:5 computability:2 partially:1 q2:4 based:33 simulating:9 ser:3 explain:1 less:3 written:4 should:4 lemma:47 only:16 explicitly:1 tape:95 judged:2 factor:20 identification:1 bernstein:11 local:1 over:17 ymn:1 σ1k:8 scans:2 σ1i:7 his:2 sense:1 subspaces:2 viewpoint:2 means:5 uncountable:1 addison:1 flips:1 next:4 cannot:5 new:4 applying:6 dt:3 αk:11 prime:5 acm:2 evolution:3 qu:3 showed:2 prequantum:7 conditions:18 arxiv:1 factorization:1 method:1 whether:7 investigate:4 experiments:1 cf:2 statist:1 qf:18 qi:6 london:3 qj:4 approximations:1 view:3 composite:3 hλ:6 set:61 res:1 computed:5 exists:7 x11:1 physically:2 frame:3 testing:6 j0:3 j1:11 y1:6 depends:6 computer:10 result:5 existence:8 primality:7 σ3i:6 qtm:114 preparation:4 wire:6 αt:2 αy:1 αx:2 siam:5 σnk:1 state:48 determined:13 various:6 closed:1 between:6 αi:2 consecutive:1 sorts:3 reading:1 approach:2 available:1 notice:1 barenco:2 extend:4 completes:1 confusion:2 complement:1 analogues:1 however:7 jl:3 implementing:14 jn:6 inclusions:2 hypothesis:1 here:4 key:1 jk:2 sleator:1 configuration:33 distribution:5 thank:1 suggested:3 σj:5 σi:17 kr:1 σn:2 σm:2 efficiency:1 many:3 annual:4 according:4 k1n:1 chosen:1 figures:1 passing:1 mean:1 adapted:1 σu:3 otherwise:6 among:5 ci:3 abbreviate:1 cm:6 point:3 ca:3 wp:6 cg:6 corresponds:1 poly:1 alamitos:3 dimensional:7 interrelations:1 polynomial:102 proved:5 throughout:2 ct:1 pr:4 ensures:2 abelian:1 transformations:3 second:11 basis:10 addition:10 zpp:3 due:1 been:9 mark:1 pc:17 yao:6 basic:2 expected:1 ph:2 abstract:2 empty:2 define:18 σk:18 direction:2 relations:1 families:10 both:1 σ2k:5 sufficient:2 5j:1 subspace:3 cos:3 wires:19 kitaev:2 essentially:1 constructing:4 c2:4 c1:8 denote:13 present:3 case:15 k2:16 multi:25 exponential:1 ujk:1 henceforth:11 examine:4 value:6 will:5 while:5 associates:1 suppose:6 error:5 u1p:1 di:23 2k:11 eim:1 real:5 detailed:5 unitary:17 σ2i:6 satisfying:21 cell:22 ip:1 thus:27 non:6 equal:4 ii:10 characterize:2 reads:1 examined:1 im:6 il:2 triple:1 claimed:4 ib:1 id:2 investigated:1 binary:9 different:7 weinfurter:1 develop:2 s2i:1 suggests:1 lengths:1 suggest:1 make:3 σn1:1 eigenvalue:1 uj1:1 same:5 clearly:1 c12:1 complex:8 quant:2 arguments:2 modification:1 finite:27 solution:1 independent:8 used:6 solved:1 nim:1 i1:18 i3:4 i2:10 nj:1 hand:5 moving:1 purpose:2 dk:9 supposing:1 infinite:4 cr:9 six:1 identity:3 simulates:23 shortly:2 unlike:1 changes:3 stationarity:1 well:4 obviously:4 dn:3 without:3 comes:3 components:4 simulated:11 model:3 dimension:2 left:2 gates:39 gu:19 construct:16 fast:1 proposed:1 cj:1 numbering:1 obtain:3 p4:2 identify:2 ozawa:2 human:1 integer:11 comput:6 lately:1 yet:1 σni:1 vπ:3 york:2 rapid:1 candidate:1 field:4 berthiaume:1 conclude:2 except:3 theoret:2 realize:1 transformed:2 easy:12 theorem:68 input:74 mod:6 transformation:12 gave:1 identical:4 σ2t:2 iλ:1 bij:2 easily:2 read:1 decomposed:5 subcircuit:2 possible:3 spanned:8 desired:3 early:1 greatest:2 know:1 similarly:3 press:4 using:13 bit:84 21m:1 decomposes:1 formal:4 loss:2 synchronization:9 theor:1 necessary:1 c1n:1 semi:10 identifying:1 follows:32 δu:1 serves:1 specific:2 bpp:2 private:1 preliminary:1 steps:32 either:1 arbitrary:6 output:36 qtms:84 stationary:9 reduced:1 gp:1 mathematical:3 pertaining:1 sketch:2 right:1 often:2 classical:9 sequence:2 do:1 sequences:6 some:15 back:1 certain:1 16t:1 s1i:1 repeat:1 b1:10 b2:4 moreover:20 proper:2 extended:1 proofs:1 recognition:1 proceeding:1 eiθ:2 watrous:1 shall:17 recorded:1 subclass:3 get:1 does:4 adleman:4 ik:3 straightforward:1 minimal:3 refer:3 measuring:1 ei1:1 run:2 power:3 performed:1 sixth:1 equivalent:17 δi:2 aj:1 pp:6 bj:2 bk:8 wesley:1 step:41 ln:8 variation:3 qˆ:6 informatics:2 therefore:7 refers:1 hilbert:11 xπ:2 orthonormalization:1 acc:8 comparison:1 works:1 a1:3 uniformity:9 extension:8 algebraic:3 jm:6 theorems:3 discussed:5 chance:1 o:25 simulation:9 strassen:2 range:7 unidirectional:16 recognizes:24 introduced:3 y2t:1 processor:18 automatically:1 22n:1 soc:3 computational:22 statements:2 computes:3 inclusion:2 measurements:1 toffoli:1 into:12 h1:4 negative:2 recognize:2 reducible:1 appropriate:2 because:2 references:1 operator:10 vp:8 factorized:2 rounds:1 qed:8 acknowledgements:1 log:24 fields:1 inductive:1 measured:1 indispensable:1 there:56 u1:4 approximate:6 long:1 los:3 quadratic:1 way:17 proc:3 call:1 gim:1 was:3 qcf:42 function:42 head:12 complete:2 form:8 kb:4 attempted:1 smolin:1 kronecker:1 but:13 hj:3 construction:5 34th:1 delta:1 russian:1 encoded:2 injection:2 true:2 he:2 count:3 iterates:1 made:1 compute:5 s3i:1 gi1:1 society:3 circuits:17 cij:1 cells:5 up:4 us:3 until:4 um:3 record:2 s3k:1 un:1 ui:2 uj:1 continuously:1 problem:5 similar:11 called:51 cryptosystems:1 recognizing:2 mechanics:1 instead:4 required:2 constant:10 pin:3 computing:14 defined:23 ko:2 universal:22 specified:1 general:5 single:17 scanned:1 exist:3 formulation:6 corresponding:10 moves:2 distributions:2 check:3 physical:3 incorrect:1 ni:7 functions:5 codes:3 no:5 ekert:2 when:14 detail:1 graduate:1 started:1 other:8 role:1 helpful:2 investigations:2 test:1 scan:1 er:3 observable:2 symposium:4 elements:5 superposition:2 calculating:1 models:20 symbol:23 problems:3 visits:1 includes:1 replace:4 oracle:1 generated:3 important:3 bounded:21 vectors:5 included:4 transfers:2 structure:1 rejects:6 independently:1 implies:1 bilateral:1 algorithm:38 assume:7 typically:1 4t:3 interval:1 zqp:14 bb:1 itself:1 appendix:3 time:83 cleve:1 n1:1 n2:1 n3:1 requires:1 strings:9
|
quant-ph9906096.txt |@word essay:2 magnetic:1 alternatives:1 results:1 existing:1 eds:1 broader:1 go:1 contributions:2 localized:1 whose:1 depend:1 editors:1 nonlocal:1 spirit:1 charge:1 those:2 under:2 brown:2 rise:1 choice:1 exact:1 condition:2 presented:1 positions:3 notes:1 applicable:1 direct:1 sign:1 surrounding:1 zero:2 perspective:2 essence:1 saw:3 jaeger:1 current:1 version:2 above:1 collins:1 increasing:1 ever:1 contrast:1 paradoxical:1 full:1 component:1 understanding:1 them:1 others:4 alone:3 along:1 strong:1 change:1 great:1 tunneling:1 difficulty:1 study:1 stimulating:1 natures:1 proof:1 makes:1 options:1 involves:2 pairings:1 elect:1 ask:1 addressed:1 causal:8 use:1 takes:2 would:2 contains:2 predictions:2 subsumed:1 therefore:1 relativistic:1 taken:1 more:1 sort:1 zanghi:1 apparent:1 acausality:4 foundations:1 must:1 ma:1 recall:1 equation:2 work:2 theories:7 concepts:1 abandon:1 arrive:1 appraisal:1 nino:1 history:1 heart:1 give:1 ontologically:1 sense:2 abner:1 critic:1 coincident:1 allowed:1 david:1 cushing:1 recovery:1 eng:1 rather:1 divided:1 how:2 answer:1 instead:1 tension:2 undergoing:1 may:3 after:1 variant:1 collection:3 applications:2 wave:1 response:2 advocated:1 dynamical:1 ordinarily:1 trevor:1 exhibited:1 advocates:3 fundamental:2 suggest:1 order:1 interpretation:1 indeed:1 move:1 mainly:1 years:1 paper:1 through:1 motions:1 existence:1 its:10 position:3 reluctance:1 distinguishing:1 microscopic:1 systems:4 jacobi:1 derivative:1 hidden:4 non:1 motivated:1 thereby:1 views:3 framework:2 walls:1 compelled:2 they:1 inception:1 now:1 discuss:1 inheriting:1 realist:3 goldstein:2 james:1 university:1 found:1 realism:3 significantly:1 related:1 measurement:5 quantum:26 beyond:3 special:2 out:5 fundamentally:1 space:1 robert:1 since:4 particles:2 acting:1 emerged:1 issue:1 foundation:1 philosophy:1 theory:33 little:1 standard:7 attributed:3 reason:1 put:1 beginning:2 times:2 motion:3 turn:1 neglect:1 initial:2 radical:1 variables:3 number:1 engenders:1 philosophical:3 another:2 clarity:1 george:1 given:1 reference:1 similarly:1 introduction:2 system:2 relations:1 their:3 assumption:1 john:1 gives:2 option:1 part:3 abandoning:1 holland:4 accordance:1 matter:1 future:1 contrary:1 historical:1 were:1 traveling:1 pre:1 sees:1 boston:2 turned:1 argument:1 already:1 manner:1 seen:2 st:2 occupied:2 metaphysics:1 viewed:3 elsewhere:1 form:2 exploratory:1 latter:2 potential:4 take:1 observationally:1 concern:1 though:4 any:2 price:2 who:1 paid:2 most:2 importantly:2 but:1 significant:1 claims:1 pair:2 treats:1 later:2 acausal:1 points:3 mechanical:3 velocity:2 physics:2 review:1 incorporate:1 show:1 sceptical:1 contemporary:3 bring:1 relation:1 carefully:2 parsimony:2 fine:3 duerr:1 microphysics:1 based:1 parameters:2 situations:3 guidance:6 written:1 should:2 only:1 explicitly:1 reducibility:1 developed:1 harvey:1 his:6 means:1 between:4 broadest:1 preferred:1 cannot:2 during:3 conjunction:1 well:1 regarding:1 fields:2 arxiv:1 physicists:2 explanations:2 view:11 observer:1 acquired:1 frame:2 inquiry:1 bears:1 relative:1 result:1 subject:1 closer:2 gravitation:1 generosity:2 speed:1 shimony:1 definite:2 favor:1 state:2 various:1 simplest:1 conceptual:1 approach:2 accord:1 mature:1 nature:1 comp:1 complement:1 however:2 samols:2 reproduces:1 hypothesis:3 extent:1 tug:1 both:1 career:1 argues:1 presentations:1 detlef:1 faces:1 valentini:1 attributes:1 contribution:1 argue:1 workers:1 among:2 nonrelativistic:1 had:1 simply:1 away:1 factors:1 unusual:1 mara:1 addition:2 millard:1 due:1 been:2 offers:2 ph:1 mary:1 disclosed:1 sufficient:2 andrew:1 bohmian:23 compromised:1 cosmology:1 resisted:1 worked:1 careful:1 former:3 present:1 pilot:1 case:1 appearance:1 dept:1 while:1 behavior:2 situation:1 antony:1 robin:1 epistemological:1 surprisingly:1 optimistic:1 ramifications:1 threatens:1 clearly:1 attributing:1 quant:1 pauli:1 several:1 horton:1 status:1 independent:2 everett:1 trajectories:2 hand:1 renaissance:1 moment:1 chris:1 potentials:1 tradition:1 successors:1 center:1 epr:2 analysis:1 bohr:3 bohm:19 components:2 consistency:2 hamilton:1 model:2 arising:1 proposed:1 being:3 when:1 newton:1 numbering:1 against:1 questions:2 alternative:3 scattering:2 yet:1 adding:1 sheldon:2 regarded:1 bell:1 character:1 source:1 book:4 treatment:1 resolved:1 motivating:1 gregg:1 phenomenology:1 possible:1 dewdney:1 hiley:1 entangled:2 burden:1 world:1 emergence:1 formal:1 loss:5 necessary:1 particle:3 vibrant:1 manifest:1 specific:1 arthur:2 either:1 essential:1 variants:1 classical:7 phenomena:5 born:1 critique:2 peter:1 provided:2 measurements:1 does:4 provides:1 demonstrated:1 measuring:1 equivalent:1 agreement:1 notably:1 corpuscle:4 analyses:1 exciting:1 properties:3 extending:1 accepts:1 dependence:2 recognized:1 practical:3 range:1 stand:2 act:1 own:1 presence:1 into:2 within:5 locus:1 down:1 variable:1 raises:1 determine:1 einstein:2 bosonic:1 statistics:1 holism:1 additional:1 support:3 there:2 question:3 long:2 inner:1 way:1 conceivable:1 was:6 war:1 assumes:1 interferometry:1 function:2 complete:1 newtonian:1 enough:1 regard:1 jun:1 amongst:2 volume:2 understandable:1 he:1 intuitive:2 whether:1 prevents:1 up:2 us:2 maturity:1 dispensing:1 demonstrate:1 similar:1 mechanics:29 bearing:1 associated:3 contributors:2 stripped:1 universal:1 proper:1 single:2 formulation:1 formalism:1 denying:1 physical:6 completeness:1 whereas:1 generally:2 reality:1 field:2 other:4 conclusion:1 explaining:1 ideological:1 includes:1 important:1 included:2 structure:1 auxiliary:1 inevitability:1 photonics:1 required:1 rule:1 impossibility:1 mass:2 time:2 original:1
|
quant-ph9906097.txt |@word represent:2 partial:1 consider:2 caused:1 varying:1 results:2 four:1 roy:1 scalar:1 mile:1 entropy:1 follow:1 whose:4 depend:1 4ns:1 editors:1 preserved:3 stochastic:6 include:1 norm:2 case:3 amplitudes:3 g2:1 straightforward:1 very:5 wave:7 difference:2 treating:1 hamiltonian:4 die:1 solution:1 t0:1 t1:1 deals:1 discrete:1 convenience:1 vector:1 small:2 added:1 consistent:2 qmw:1 past:1 second:9 further:1 dynamics:14 canonical:5 even:2 what:2 nonlinear:2 appear:2 giving:1 section:1 expressed:1 uniform:1 current:2 above:1 coefficient:1 princeton:2 here:5 localisation:1 believed:1 operating:1 equations:24 appears:4 box:1 approaches:2 contradiction:1 durch:1 published:1 real:5 suitable:1 makes:3 involves:1 scales:1 ipj:2 highly:1 hardy:1 apply:1 total:2 unit:6 handled:1 would:1 remains:1 next:1 ψj:10 linear:1 approach:3 doubling:1 type:1 today:1 separated:1 formally:1 hermitean:2 initial:1 operators:2 apparent:1 odinger:4 particular:3 known:1 hold:1 must:1 evolves:1 quantized:5 equation:16 theories:6 remain:1 era:1 den:1 canonically:1 making:1 example:1 give:2 process:6 states:5 sphere:7 allowed:1 influenced:1 rays:1 end:1 turn:1 rather:1 discussion:1 write:2 far:3 influences:1 significance:2 simplifies:1 instead:1 ordinary:1 ensemble:2 simplicity:2 express:1 galactic:1 singular:2 reconciled:1 derived:2 waves:1 cambridge:2 attempt:1 dynamical:8 so:14 representation:2 operations:1 interpretation:1 produces:1 over:3 vary:1 satisfied:2 produced:1 held:1 experiments:3 london:3 satisfies:1 its:5 before:3 derive:1 lc:5 energies:1 coordinates:13 detected:1 parts:1 differently:1 clusters:1 them:1 practice:1 evolution:1 hamilton:4 they:6 rotation:1 now:1 nor:1 represents:2 term:2 university:3 realistic:3 each:1 mean:1 differential:2 england:1 ej:1 energy:6 principles:2 extended:1 measurement:26 quantum:52 laboratory:2 special:1 prelude:1 space:22 itˆo:2 since:3 lagrangian:10 particles:1 reformulate:1 lorentzinvariant:1 oscillators:4 theory:28 localization:1 free:3 standard:2 reason:1 ian:1 complicated:1 nonunitarity:1 e1:1 definition:1 cosmic:2 times:3 motion:13 introduction:2 generalizations:1 first:6 already:1 features:1 number:2 long:1 carry:1 impossible:1 open:2 given:5 necessarily:1 similarly:1 unitarity:5 system:7 relations:2 their:1 conservation:1 white:1 gives:2 shifted:1 shell:1 continuous:3 part:1 representing:1 than:3 diffusion:20 jump:1 iωq:1 roles:2 dtl:1 rate:1 submitted:1 limiting:2 annihilation:6 future:1 amplitude:3 treated:3 iωj:3 fluctuation:1 ann:1 modern:1 conjugate:21 need:2 seek:1 any:3 relatively:1 zero:2 convenient:2 isolated:1 primed:2 note:1 generalized:1 destroy:1 subject:1 gψ:2 calculus:1 play:1 broglie:5 trace:1 though:1 price:2 xψ:5 most:2 letter:3 phase:9 measured:1 mineral:1 consequences:1 considered:1 later:2 points:1 physics:2 violation:2 queen:1 d3:5 principal:1 slow:1 based:2 uders:1 freedoms:1 only:4 going:1 factor:1 local:1 get:1 dependent:1 zurek:1 de:5 expectation:1 cannot:1 nearly:1 during:1 dt:6 processes:3 fields:7 arxiv:1 twice:1 including:1 qj:5 satisfy:2 set:2 problem:4 violated:1 depends:1 college:1 result:1 concern:1 commutation:2 away:1 state:28 identification:1 between:5 probably:2 conditions:1 wide:1 terms:4 initially:1 however:4 conjugates:3 configuration:16 come:1 distribution:3 both:5 last:1 ilc:1 according:3 quantization:9 hψ:1 contribution:1 experimental:1 uber:1 point:2 simple:1 lagrangians:2 leipzig:1 cg:1 dimensional:1 lagrange:2 respect:5 cq:1 branes:2 unusual:1 puts:1 trajectory:1 absence:1 been:4 basic:1 pj:5 ph:2 mary:1 systems:5 obtained:1 corresponding:4 qsd:21 wheeler:1 derivative:1 c2:1 denote:1 those:3 applied:2 conserved:2 value:1 will:3 suppose:1 applies:2 identical:1 unitary:5 surface:2 equal:2 qj2:1 nonunitary:1 different:2 make:1 radiation:1 indistinguishable:1 same:8 shorter:1 complex:18 quant:1 nonphysical:1 finite:2 difficult:2 independent:7 used:2 absorb:1 upon:1 action:5 schr:4 onedimensional:1 analysis:1 bohr:2 without:1 components:1 coordinate:4 model:2 usual:6 unified:1 just:5 being:1 obtain:1 press:1 identify:2 momenta:7 eigenstates:2 rapid:1 density:2 nonrelativistic:2 except:1 iψ:3 lett:3 theorem:6 transformation:1 momentum:10 resolved:1 dislocations:1 possible:2 early:1 know:2 background:1 vacuum:2 confined:2 formal:4 necessary:1 lost:1 particle:5 identifying:1 follows:2 ignore:1 integrals:1 starred:1 stationary:1 reduced:2 heisenberg:6 because:3 methods:1 classical:15 picture:1 creation:5 some:2 towards:3 pψ:3 anisotropies:1 scale:1 measurements:2 integration:1 does:7 proc:1 noise:1 equivalent:3 imaginary:1 properties:2 simpler:1 decoupling:2 universe:1 recognized:1 essential:1 ensure:1 greatly:1 consequently:2 road:1 soc:1 rev:2 into:3 integral:1 hermitian:1 references:1 einstein:1 operator:17 additional:2 there:6 fast:1 dispersion:1 start:1 detectable:1 way:1 function:3 form:2 jun:1 but:16 gaussian:1 volume:4 themselves:1 made:1 abstract:1 liouville:7 ωj:6 iqj:1 fluctuations:2 percival:7 gisin:4 mechanics:1 constant:1 reconcile:1 defined:1 universal:1 contribute:1 influence:1 resultant:1 dξ:7 single:1 formulation:5 crystals:1 distributions:1 physical:9 us:1 no:12 whereas:2 when:2 field:33 other:4 role:4 details:1 department:1 happens:1 problems:1 variation:3 includes:1 deriving:1 meaning:1 important:5 bounded:1 variable:3 qψ:2 needed:3 longer:3 normally:1 factors:1 together:1 time:7 westfield:1 strings:2
|
quant-ph9906098.txt |@word replacing:2 secondly:1 partial:4 varying:1 results:9 quadrature:1 entropy:4 go:1 follow:1 whose:2 inverse:4 depend:1 calculate:2 producing:1 equivalence:1 presents:2 finally:1 behave:1 squeezing:1 protocols:1 under:3 dominated:1 analogous:2 include:2 gaussians:4 case:3 provides:1 orthogonal:4 far:1 difficult:2 difference:1 encounter:1 splitter:1 obvious:1 swapping:13 presented:2 knight:2 tanh:1 solution:3 herbert:1 leave:1 discrete:18 vector:1 λni:1 indices:1 eigenvalues:14 optics:3 accumulation:1 upper:1 rohrlich:1 foundation:2 direct:1 sign:1 approximation:1 second:3 further:2 chem:1 obey:1 even:1 aim:1 subadditivity:2 appear:2 giving:1 sum:4 networks:1 version:1 bαβ:4 above:9 bαα:1 shared:5 increasing:1 method:5 coefficient:1 gµ:2 full:1 degree:1 respectively:1 teleportation:6 here:4 ranges:2 plenio:1 xβ:1 strong:1 equations:9 change:2 essentials:1 obtained:3 great:1 leaves:1 changed:1 allows:1 kofke:1 amount:4 resulting:2 procedure:23 schumacher:1 action:1 bob:7 fourier:1 changes:3 entangling:2 spatially:1 projection:3 leonhardt:1 outcomes:3 decrease:1 tools:3 post:1 linearly:3 use:2 proceed:3 would:3 next:4 calculation:2 call:3 therefore:5 themselves:1 theoretical:3 more:6 separated:2 becomes:3 operators:1 odinger:1 particular:5 projective:1 iii:2 must:3 high:3 indicates:1 science:2 equation:22 work:3 cat:15 reproduce:1 values:9 erb:2 tracing:1 following:2 making:4 unconditional:1 initial:3 f1:3 compare:2 figure:4 give:2 process:3 bennett:2 distillation:1 states:48 effectively:1 performed:1 council:1 unphysical:1 validated:1 available:1 united:1 rather:1 holds:1 off:1 how:2 ρn1:2 pure:5 very:4 gate:3 parameter:8 simplicity:1 product:1 description:2 undergoing:1 may:3 after:1 epsrc:1 less:3 produce:1 share:1 cambridge:1 horizontal:1 types:1 e24:1 natural:1 succeeded:1 e23:1 6th:1 purify:1 purification:29 perform:2 cannot:3 so:13 allow:2 reduced:2 looking:1 bipartite:8 operations:2 horne:1 enk:1 developed:2 over:4 move:2 vary:1 produced:1 course:4 paper:3 london:1 statistical:1 mentioned:1 fidelity:1 y2:1 its:8 discretizing:1 outer:1 located:1 chosen:2 interesting:2 writing:1 complex:2 degrees:1 systems:24 covered:1 schmidt:8 yi:2 measurement:8 non:1 greater:1 thereby:1 ekert:2 practice:1 fig:5 introduce:1 primary:3 yy:1 they:8 half:1 now:13 eigenvalue:20 february:1 2r:4 always:2 university:1 level:8 2x:1 appropriate:1 2d:5 inequality:1 l2:5 mode:8 2b:1 each:5 found:2 2n:3 limit:3 macchiavello:1 side:2 mean:1 square:1 england:1 primarily:1 lam:1 doing:1 idea:2 related:2 ey:1 expect:2 measure:4 quantum:9 laboratory:1 operation:2 beyond:1 special:1 out:3 divincenzo:1 shown:8 matrix:2 space:1 quantify:1 rev:15 research:1 increase:3 transforming:2 wavepackets:1 dxdx:1 dxdy:8 performs:2 dominate:1 induction:1 occurs:1 sinh2:2 wiley:1 log2:6 linear:1 polkinghorne:1 diagonal:2 standard:2 york:1 ask:1 jozsa:1 generate:1 milburn:1 definition:1 recast:1 widths:2 could:1 turn:1 length:6 plane:3 wehrl:1 quadratically:1 onto:2 first:9 xi:2 swapped:3 vedral:2 variables:10 number:3 approximate:1 entanglement:77 xx:1 another:2 imperial:1 quality:1 given:4 rewritten:1 indicate:2 introduction:1 unknown:1 eu:1 deutsch:1 system:12 their:2 calculations:2 wootters:1 final:6 gives:2 eigenvectors:1 continuous:35 proving:1 part:2 deterministic:1 manipulation:1 x2:13 shortly:1 july:1 x1:8 than:5 coefficients:5 distance:1 critically:1 fuchs:1 was:5 measured:1 see:5 classes:8 were:4 outcome:1 powers:1 projections:2 popescu:3 well:1 unchanged:1 locations:1 generalization:1 reassuring:2 already:1 say:1 manner:1 weinfurter:1 any:4 ax2:1 subsystems:2 zero:3 depending:1 convenient:3 latter:1 able:4 aside:2 converges:2 note:5 sciences:1 absorbed:1 generalized:3 eprint:4 new:1 modulus:1 smolin:1 accuracy:1 exactly:1 gβ:2 trace:4 decreasing:2 what:3 most:3 attempt:3 λr:2 plan:1 significant:2 preliminary:1 pair:7 assessed:1 analytically:3 inserted:1 class:6 deviations:1 calculated:3 dimension:1 braunstein:6 points:1 exp:11 mechanical:1 quantifying:1 section:10 fact:5 dbh:1 parker:1 particularly:2 show:3 absorbing:1 supported:1 converge:1 corresponded:1 loock:1 carefully:1 analogue:1 find:6 copy:3 based:1 2bz:1 parameters:8 e12:2 state:42 should:2 only:5 explicitly:2 indeed:2 integrable:2 adequate:2 local:2 rectangle:1 do:5 triangle:1 quantph:2 means:1 dependent:2 express:1 quantified:1 beam:1 ones:1 dz:1 dx:10 dy:8 during:1 procedures:4 processes:1 covering:1 conditions:1 arxiv:1 european:1 analytical:4 nδ:1 approaching:1 kernel:7 set:9 exists:2 achieved:5 enabled:1 δjk:2 maximum:1 depends:2 college:1 result:4 terms:6 satisfies:1 techniques:3 still:2 mechanically:1 eigenfunctions:9 ways:1 ralph:2 symmetric:1 written:4 various:1 correctly:1 between:4 invariant:1 before:2 approach:2 2pq:1 notice:3 recently:2 however:7 efficiency:1 answers:1 key:1 2d2:1 bose:3 tricomi:1 both:4 reverse:1 limits:2 many:3 taking:1 density:7 equal:3 against:2 etc:1 involve:1 figures:2 context:1 contribution:1 expression:1 otherwise:1 relevant:1 afterwards:1 point:4 acted:1 sampling:1 normalisation:3 trust:1 kernels:6 light:1 basis:14 copies:1 been:11 confident:1 much:3 pg:2 basic:1 ph:3 define:1 sanders:1 graphical:1 aj:4 controlled:3 quantities:1 sufficient:1 formed:2 precision:2 modelling:1 spectrum:1 neumann:1 decreased:1 c2:1 general:1 spirit:1 present:3 2ia:1 p2:1 p0:2 exponential:2 pacs:1 reliable:1 harder:1 engineering:1 value:4 will:22 suppose:1 squeezed:4 study:1 sw7:1 discretize:1 kingdom:1 unitary:2 characteristics:1 von:1 formulation:1 procrustean:1 iv:2 ii:2 middle:1 ax:2 partner:1 around:3 φp:1 develop:3 lengths:1 make:2 same:5 unity:1 concavity:1 quant:3 largest:1 units:1 φi:18 dimensionless:1 finite:7 pan:1 higher:2 independent:7 normalise:1 used:6 numerical:12 hand:1 levels:1 infinite:6 invariance:1 generalize:1 relies:1 schr:1 sørensen:1 epr:1 analysis:2 vaidman:1 directly:2 solve:3 greatest:1 sets:1 firstly:1 position:2 model:2 possesses:1 usual:1 λs:1 gates:5 cosh2:2 just:4 λt:1 being:2 accurate:2 sanpera:1 obtain:1 unclear:1 correspondences:1 useful:1 λi:9 leverhulme:1 eigenstates:1 previous:1 sampled:2 cut:1 conclusions:2 bell:6 except:2 parts:1 setting:1 transformed:2 lett:6 versa:1 constant:3 c12:4 remaining:2 momentum:1 real:1 increased:6 easily:3 replaced:1 showing:2 decomposed:1 sums:1 possible:3 increases:3 zukowski:1 entangled:23 vacuum:1 press:1 using:10 highly:1 mod:1 necessary:5 like:5 success:1 follows:3 alice:5 either:5 become:3 essential:2 mathematical:5 because:1 methods:4 classical:1 some:6 library:1 respect:1 provided:2 tmr:1 scale:7 gα:2 measurements:3 2xy:1 2xx:2 does:3 decomposition:1 expressing:1 particles:3 demonstrated:3 measuring:1 reasonable:1 cosh:1 infinitely:2 equivalent:1 wavefunctions:1 expansion:1 imperfectly:1 although:2 substitution:1 hadamard:2 approximating:1 properties:2 cnot:1 simpler:1 about:1 polzik:1 freedom:1 dependence:1 simulation:1 range:3 furusawa:2 importantly:2 introduced:2 own:2 arcsinh:1 communication:1 into:7 integral:10 three:1 hermitian:4 right:1 determine:1 parties:1 operator:5 often:2 acknowledgements:1 van:2 deal:1 area:3 normalised:2 probabilistic:3 strictly:1 there:6 u1:5 transform:7 u2:2 width:4 way:2 sections:1 knowledge:1 himself:1 complete:1 form:10 attempted:3 becoming:2 jun:1 gerry:1 but:12 gaussian:2 hk:1 curiously:1 convergence:5 true:2 partially:7 october:1 applying:1 wish:4 ρpq:2 particle:5 us:3 achieving:1 those:4 planes:1 demonstrate:1 problem:2 similar:2 called:1 blackett:1 yα2:1 mechanics:1 ab:1 proved:1 certain:3 ak:1 describe:1 condition:1 denote:1 quantification:3 kimble:2 our:10 corresponding:1 distributions:1 check:3 physical:1 again:4 functions:1 bouwmeester:1 nag:1 integrability:1 no:5 dashed:1 whereas:1 when:5 other:3 holding:1 2db:2 test:1 mathematics:5 elements:1 superposition:1 calculating:2 problems:1 polynomials:1 a1:9 a0:16 important:1 variable:8 maximally:5 goursat:1 zeilinger:2 independently:2 correlated:9 vice:1 normally:1 lanl:4 rule:1 inaccuracy:1 resolution:2 original:6
|
quant-ph9906099.txt |@word represent:1 consider:2 scalar:2 inverse:1 dα1:1 dα2:1 tr:5 containing:1 ıa:1 answered:1 quasi:1 infinitesimally:4 those:1 th:4 under:1 conjecture:1 provides:1 straightforward:2 orthogonal:3 rise:3 springer:3 choice:1 experimentally:1 matrices:2 entire:1 hamiltonian:4 irreducible:1 accidentally:1 discrete:10 vector:14 small:3 configurations:1 upper:1 det:3 second:2 arnold:1 further:1 ˆs:5 giving:1 selected:1 possibilites:1 reconstruction:1 obvious:1 method:2 satisfy:1 degree:1 respectively:2 component:1 equals:1 here:1 courtens:1 desired:2 directions:2 obtained:2 technical:1 vectors:7 permit:1 symmetrical:1 conveniently:1 proof:2 appropriately:1 formulated:1 projection:3 family:1 iph:1 replace:1 weigert:4 put:1 unit:10 takes:1 would:2 positive:1 finally:1 dnk:1 bases:2 m1:1 therefore:5 more:1 nonredundant:1 elliptic:1 hermitean:6 operators:20 berlin:2 particular:2 must:1 involve:1 keeping:1 mn:13 oscillator:1 mk:7 iα2:1 values:15 cibils:1 exceptions:1 example:2 history:1 give:1 states:18 sphere:5 numbers:2 orbits:1 occur:1 axis:1 information:2 turn:2 provide:1 s2:5 discussion:1 write:2 located:1 pure:1 sin:4 product:3 quantenmechanik:1 algebra:1 may:1 ladder:1 npa:1 mapping:1 collection:2 applications:1 plane:3 data:2 man:2 sz:1 sy:1 sx:1 natural:1 explicit:2 correspond:2 su:1 st:3 their:1 fictitious:1 so:1 allow:1 keeps:1 representation:4 subsequently:2 acknowledges:1 words:3 order:1 restriction:1 least:2 wigner:3 reversal:1 indeed:1 over:1 soc:1 symbols:9 paper:1 through:2 mentioned:1 its:9 before:1 group:1 render:1 chosen:1 tori:1 coordinates:1 systems:1 might:1 weber:1 maximal:1 non:7 combination:2 arilly:1 they:2 now:3 represents:1 inversion:1 2s:10 identified:1 ensemble:2 each:2 found:1 universit:1 side:1 characterized:1 referred:2 subset:1 weyl:4 financial:1 arecchi:1 weight:1 energy:3 related:4 constitute:1 measure:1 quantum:4 emerges:1 shown:6 matrix:8 space:20 gradient:1 restricted:1 furthermore:1 since:5 rev:3 looking:1 acting:4 reader:1 denoted:2 unifying:1 linear:5 contain:1 standard:1 york:2 ask:2 starts:1 motion:1 introduction:2 onto:1 support:1 first:2 already:1 probability:3 timeindependent:1 number:4 system:2 xy:1 specifically:1 open:1 given:7 hyperbolic:1 ordering:1 adjoint:1 twisted:1 relations:1 needed:1 appl:1 statement:1 gives:1 commutativity:1 recursively:1 exactly:2 sˆ:1 coefficients:5 zero:8 contravariant:1 annihilation:2 contrary:1 were:1 providing:2 ann:1 argument:1 constellations:3 separatrices:2 say:2 redundant:8 seen:1 recover:1 any:8 angle:1 physique:1 coplanar:1 take:1 analogy:2 δnn:1 continuous:1 though:1 track:1 measures:1 fails:1 most:2 regular:1 phase:7 acknowledgements:1 class:1 quorum:1 considered:2 calculated:1 phil:1 flow:1 countable:2 points:9 exp:2 thomas:2 show:1 rotating:1 implying:1 relation:1 corner:1 analogue:1 d2:1 submatrices:1 q1:1 o:1 parameters:2 written:1 should:1 only:2 explicitly:2 integrable:1 constant:3 do:2 above:1 means:2 de:2 expectation:9 methods:1 cannot:1 closely:2 new:2 reconstruct:2 dt:1 following:1 evolution:1 approach:2 arxiv:1 qa:9 gram:2 mapped:1 switzerland:1 including:1 qk:2 fixed:5 qn:16 set:1 smooth:1 depends:2 differentiable:1 close:6 dµ:2 constellation:12 collinear:1 phases:1 satisfying:2 commutation:2 state:8 closed:2 between:1 αm:1 αn:1 knowing:1 ends:1 terms:5 visualise:1 however:2 moyal:2 job:1 unnormalized:1 both:1 cos:3 ir3:1 according:2 quantization:1 und:1 exceeds:1 passing:1 bond:1 expression:1 arbitrarily:3 among:1 ch:2 co:2 point:1 reasons:1 leipzig:1 harmonic:1 dimensional:4 anti:2 spans:1 polynomial:3 ordered:1 basis:14 addition:1 three:2 been:4 pa:4 foliated:1 ph:3 ko:2 differently:1 cambr:1 direction:1 corresponding:1 sufficient:3 coherent:16 determination:1 curves:2 spin:17 present:2 kaufman:1 srivastava:1 subsets:2 value:1 choices:1 will:7 while:1 suppose:1 gnn:4 procedure:1 unitary:1 almost:4 von:1 thus:2 them:2 surface:1 equal:1 characterize:1 itself:1 dual:4 agarwal:1 different:5 thereby:1 generic:1 formulations:1 same:1 complex:2 quant:3 widely:1 finite:2 independent:2 used:1 conceived:1 upon:1 hand:1 parametrized:1 levels:1 purpose:2 nationalfonds:1 expand:1 eigenvectors:1 sˆx:1 nevertheless:1 no:1 well:1 components:4 jean:1 dimension:1 left:1 just:1 being:1 obtain:1 select:1 underlying:1 uller:1 eigenstates:1 unique:1 density:3 regarded:1 greub:1 other:6 transformation:1 generalized:1 real:2 possible:3 corresponds:1 possibly:1 highly:1 rotate:1 necessary:1 particle:6 follows:1 specific:2 either:1 arbitrary:1 essential:1 mathematical:1 right:1 often:1 classical:3 smoothly:1 creation:2 some:2 pierre:1 economic:1 gilmore:2 respect:3 gracia:1 nonzero:1 provided:1 exhausts:1 normal:2 integration:1 linearly:2 expressing:1 proc:1 minimal:1 infinitely:1 equivalent:1 stefan:2 expansion:8 rue:1 accompanied:1 hilbert:5 projector:2 about:2 working:1 freedom:1 urged:1 carries:1 act:1 mixed:1 introduced:3 consequently:3 projectors:6 perelomov:1 outlook:1 into:2 integral:1 m0k:4 down:1 references:1 determine:5 operator:18 nowadays:1 neumann:1 institut:1 suffice:1 there:4 question:2 long:1 describes:1 way:4 naturally:1 function:6 form:3 vanishing:1 hs:7 jun:1 but:1 hk:4 ns2:1 made:1 whether:1 variations:1 up:1 us:2 below:1 distribution:2 define:1 similar:1 called:1 mechanics:1 associated:5 defined:3 certain:1 abstract:1 am:1 determinant:6 denote:1 aq:1 single:1 defines:1 iˆ:2 functions:2 nk:11 sˆz:1 entirely:1 nn:5 sˆy:1 amounts:1 when:1 nz:10 unambiguously:2 details:1 spatial:1 ns:21 happens:1 elements:4 symbol:23 june:1 generated:1 l65:1 theor:1 equivalently:1 time:3 observables:1 requires:1 original:2 once:1
|
quant-ph9906100.txt |@word inverse:2 partial:1 consider:5 maximum:1 interference:5 magnetic:8 varying:1 desirable:1 results:7 extensively:1 comments:1 follow:2 expressions:3 reasoning:1 devoted:1 whose:4 compose:1 const:2 subjected:2 april:1 tj:3 those:6 under:5 tf:9 include:1 cm1:3 consequently:1 evolves:2 far:2 edn:1 schur:1 assuming:1 choice:4 every:1 rm:9 resonant:1 experimentally:1 difference:1 matrices:2 encounter:2 trigonometry:1 cml:1 hamiltonian:9 irreducible:2 integrating:1 vertex:1 solution:3 occurs:1 try:2 strayer:1 vector:19 enjoy:1 after:2 version:1 miller:1 literature:1 sign:1 approximation:1 second:2 evaluated:1 reunion:1 further:1 canonical:10 putting:1 will:9 what:7 plays:2 appear:1 brackets:1 section:4 contracted:1 expressed:2 agrees:1 current:1 experiment:2 goes:1 overcomplete:1 new:5 3a:3 momentum:1 method:3 satisfy:1 compact:1 evolving:2 full:2 led:1 satchler:1 respectively:1 here:5 perpendicular:1 iφm:1 bkc:1 operating:1 groups:3 aid:2 represented:2 path:24 along:1 equations:7 appears:1 change:2 z3:6 obtained:6 2mπ:1 great:1 brink:1 wesley:1 study:3 vectors:13 allows:2 approaches:1 trial:1 resulting:1 produced:1 lightwave:1 action:2 resonance:1 therein:3 suitable:3 composed:2 named:1 via:6 useful:1 members:2 merely:2 vii:1 integrations:1 courtens:1 highly:2 brought:1 sincerely:1 unitary:2 apply:2 total:1 tools:1 unit:2 readily:4 θdφ:1 conventional:10 proceed:1 commun:2 contains:1 physics:8 properties:5 linear:3 call:2 therefore:1 ψl:2 m2:7 taken:2 generators:2 type:2 asahi:1 today:1 more:6 brings:4 operators:3 ti:9 s3:1 appendix:5 controlling:1 normalized:2 excellent:1 known:3 cases:4 hold:3 iii:1 high:3 springer:1 ma:2 room:1 permits:1 mm:2 ml:2 equation:2 work:1 labeled:1 infinitesimal:1 obvious:1 following:6 making:1 obtain:1 example:1 proof:3 compare:1 radcliffe:2 give:6 neglected:1 states:12 indicates:1 numbers:1 want:1 iφ:7 tan:4 calculated:1 axis:1 information:3 needs:1 sphere:2 turn:1 provide:1 verify:1 discussion:1 verified:2 berlin:1 orthogonality:1 revisit:1 vital:1 stemming:1 significance:1 sin:55 simplicity:1 product:2 proc:1 algebra:3 may:8 warm:1 earlier:2 derived:1 reflect:1 consequence:2 produce:1 designed:1 twofold:1 χm1:1 wave:2 parallel:1 natural:4 collective:1 beam:5 light:2 author:1 appreciate:1 differentiations:1 su:29 element:1 perform:3 ones:2 so:7 fundamental:1 definitions:1 order:2 typical:2 restriction:1 holds:1 wigner:1 help:1 developed:1 over:1 insight:2 mainly:1 matsumoto:7 experiments:1 through:1 lasers:1 differs:2 japan:1 satisfies:1 june:1 its:7 before:1 derive:1 group:4 symmetry:1 fit:1 chosen:1 actually:1 better:1 usp:1 complex:2 choose:2 mail:1 main:2 split:4 them:6 combination:2 propose:1 often:1 walls:2 effects:3 they:5 half:1 oxford:1 nov:1 now:2 developments:1 easily:2 term:19 stated:1 hereafter:2 2s:8 north:1 always:2 university:2 possibilities:1 fringes:2 2b:2 each:2 disregard:1 found:3 quarter:1 2i:1 mean:1 domain:1 weyl:1 dωi:1 doing:1 mesoscopic:1 osaka:1 frequency:1 gaussian:1 related:4 constitute:1 used:2 static:1 expect:1 changed:2 quantum:6 our:3 happen:1 reprints:1 special:8 out:4 matrix:10 3rd:1 space:6 since:13 lagrangian:3 semi:1 denotes:1 looking:1 re:1 adapt:1 intensity:1 formula:5 get:1 succesive:1 plural:1 correct:1 math:5 shows:1 mφ:1 theory:2 written:2 possibility:1 reason:1 subtended:1 york:1 besides:2 imagine:1 put:4 wanted:1 care:1 skagerstam:2 applications:9 starts:1 transition:2 rather:1 motion:2 ordering:2 hence:3 ritsumeikan:1 first:3 origin:2 zl:1 initial:1 xn:1 manuscript:1 variables:1 number:4 done:1 construct:1 another:3 representations:2 reached:2 electronic:1 angular:1 affords:1 wilczek:1 given:8 necessarily:1 singular:1 introduction:1 amsterdam:1 system:4 adopted:1 their:11 calculations:1 convention:1 ordered:1 variational:1 final:1 gives:6 reversed:1 continuous:1 proving:2 appreciation:1 part:1 because:4 somewhat:1 authors:1 than:2 coefficients:3 past:1 colleagues:1 holland:1 roles:1 cyclic:7 was:5 see:14 suzuki:1 classes:2 contrary:1 amplitude:2 wiley:1 treated:4 function:2 enumerated:1 sees:1 derivative:1 explicit:4 topics:1 modern:1 argument:1 generalization:1 yielding:1 tom:1 manner:1 need:5 seen:1 seek:1 any:13 elsewhere:2 lie:4 strength:3 angle:2 rotations:5 barut:1 lim:1 latter:2 note:2 fictitious:1 take:8 heisenberg:1 even:2 exactly:1 sm:2 iφ2:1 normal:3 serve:1 who:1 most:3 detect:1 plan:1 formulae:2 phase:15 cleared:1 extremely:1 why:1 stands:1 especially:2 considered:1 clear:3 later:7 stronger:2 playing:1 points:2 principle:1 exp:54 nuclear:1 omit:1 liberate:1 fact:2 superfluidity:1 incorporate:2 thomas:1 dωf:1 teich:1 rotating:1 bring:1 stems:1 relation:12 trivial:1 find:4 decade:1 principal:1 o:2 feng:1 based:6 parameters:5 original:4 state:15 topological:2 should:4 lemma:1 only:2 explicitly:1 enriched:1 subsection:1 indeed:1 employed:2 hope:1 do:1 his:2 above:1 invoke:1 means:1 dependent:2 familiar:1 simplest:1 masao:1 expectation:3 addison:1 truly:1 aim:1 cannot:3 reading:1 words:1 3b:3 combinations:1 during:2 dt:7 gen:2 reveal:1 singapore:5 caves:1 fields:4 arxiv:1 summary:2 inomata:1 investigate:3 paper:8 conforms:1 including:1 fixed:2 set:7 motions:1 exists:3 physically:1 unpublished:1 klauder:4 ends:1 ωt:14 edition:1 depends:4 result:6 discussions:1 best:1 rmm:3 sˆ:19 phases:20 satisfying:1 probable:1 pattern:2 below:1 yet:2 µm:1 concretely:1 enough:2 determined:3 various:5 between:4 geometric:26 previous:1 numerous:1 µb:1 rm2:1 notice:2 terms:7 nature:1 sole:1 jp:2 however:6 vanishing:1 extent:1 distinguish:1 atoms:1 come:1 prospects:2 prescription:1 cot:3 solely:2 according:2 quantization:1 energies:1 hω:3 berry:1 subsections:2 contribution:1 candidates:1 expression:2 messiah:2 experimental:1 comment:1 among:2 key:1 cm:55 point:3 simple:3 seems:4 ca:1 vast:1 period:3 semiclassical:2 anti:1 lagrange:1 wider:5 moreover:2 pp:2 matumoto:2 addition:1 trajectory:1 locally:1 three:3 been:8 strategy:1 reduction:1 much:1 treat:2 beams:3 basic:2 ph:3 algebras:1 universal:1 systems:3 gerry:1 generating:1 relations:3 partly:2 deeper:1 θl:3 quantities:1 concerning:3 cos:61 coherent:15 deep:1 angles:8 ours:1 last:1 resultant:2 spin:34 former:2 present:10 case:19 unlike:1 pacs:1 solid:1 appearance:1 value:3 employ:2 near:1 b02:4 fiducial:24 evaluating:1 squeezed:1 situation:5 property:1 unsatisfactory:1 studied:1 saleh:1 century:1 almost:1 vi:2 thus:9 site:1 encouragement:1 iv:1 ii:1 reads:2 cone:1 turns:1 vanish:1 different:2 develop:1 combining:1 generic:3 acknowledgments:1 submission:1 same:3 clearly:3 unity:3 parts:1 quant:3 arguments:3 survey:1 physical:3 φl:3 higher:1 development:1 independent:3 investigated:2 http:1 closest:1 paths:1 upon:2 effect:11 hand:1 arrived:1 hospitality:1 hπ:2 identity:1 recent:1 holonomic:1 disappears:2 well:6 deal:2 concrete:1 comes:1 components:1 sets:2 model:2 recombine:1 usual:2 spherical:1 world:5 just:3 being:4 resolution:2 valuable:1 reviewed:1 abbreviation:1 thanks:2 integer:2 macroscopic:2 rotation:6 projection:1 preprint:3 application:1 products:1 had:2 parametrization:1 iψ:13 add:1 lett:3 easy:1 spin1:1 eigenstate:2 euler:10 generalized:3 iθ:2 evaluation:1 rnn:1 represents:1 possible:1 corresponds:1 press:1 using:1 replace:1 formal:1 necessary:1 like:2 particle:10 follows:6 reduces:2 adiabatic:6 δs:2 serves:1 manifest:1 communications:1 detections:2 δm:4 yields:4 integrals:12 arbitrary:11 expresses:1 works:1 reduced:1 mathematical:3 www:2 performing:1 2form:1 classical:2 vortices:1 successfully:1 some:8 back:1 cs:59 experienced:1 b0:18 choosing:2 specified:4 happens:1 describing:2 though:1 future:2 integration:3 overlap:2 does:2 decomposition:1 tends:2 prof:2 mined:1 closely:1 particular:1 scientific:5 performed:2 kyoto:3 use:8 clarendon:1 step:1 described:5 prepared:3 notation:1 hilbert:2 bz:1 about:1 central:1 carried:1 extension:5 discussed:2 recognized:1 essential:1 a2:4 plus:1 obeys:2 slightly:1 perelomov:3 specifies:1 soc:1 rev:4 into:7 successive:3 integral:3 accumulates:1 yabu:1 square:1 references:4 arecchi:1 sov:1 operator:3 proportional:2 next:6 methods:1 additional:3 prepare:2 assumed:1 there:4 approximate:1 specifically:2 start:1 describes:1 way:2 ed:4 m1:7 sections:2 propagator:2 lowest:1 µb0:4 complete:2 form:13 shapere:1 phenomena:2 superradiance:1 extended:3 symbolized:1 construction:2 hb:2 considerable:1 he:1 condition:3 made:2 fulfilling:1 girardello:1 2πm:1 up:4 us:10 theoretical:1 ωi:8 assume:3 mth:1 converted:1 limit:5 ωl:2 mature:2 gilmore:2 problem:2 monopole:5 similar:2 called:3 ωf:8 mechanics:1 ac:2 sometimes:1 associated:3 ln:1 defined:2 curve:1 abstract:2 describe:4 influence:1 direction:1 covers:2 general:8 chap:1 right:1 trix:1 dθ:4 formulation:1 formalism:5 viewpoint:2 constructed:2 functions:3 no:5 amounts:1 when:10 vanishes:3 field:7 other:4 role:2 branch:1 becomes:1 department:1 vanished:1 sufficient:2 elements:5 intend:1 problems:1 miscellaneous:2 variation:4 includes:1 a1:15 a0:13 a3:13 important:3 a5:2 a4:7 a7:3 a6:2 variable:1 a8:3 dψ:4 dω:5 dφ:3 requires:2 interval:2 sˆ2:1 sˆ3:11 together:1 sˆ1:2 overcompleteness:2 neighbouring:2 reprinted:6 time:5 starting:2 having:4 once:2
|
quant-ph9906101.txt |@word limited:1 consider:4 represent:4 rev:1 doubts:2 alternatives:1 results:7 four:3 gf:1 gd:1 computation:4 edu:1 follow:2 expressions:8 whose:4 certainly:1 dimensionality:2 quantenphysik:1 equivalence:34 lukasiewicz:2 send:1 tn:3 program:2 under:4 analogous:2 presentation:1 ingredient:1 case:1 predicate:1 far:2 dispense:1 pages:4 none:1 indication:1 electron:1 birkhoff:2 figs:1 condition:4 obvious:4 die:1 applicable:1 t1:3 try:1 ascribed:1 proposition:1 1r:4 der:3 monomorphic:1 consistent:2 direct:5 past:1 fold:1 second:1 bernays:1 further:3 specker:2 even:5 nothing:5 what:9 gabbay:2 appear:1 section:5 selected:1 analogously:2 tarski:3 abs:1 establishes:1 new:8 paviˇci:8 contrast:2 satisfy:3 edited:4 respectively:4 manipulating:1 never:1 fields:1 here:4 foulis:1 plenio:1 them:7 lindenbaum:9 others:1 along:1 equations:1 appears:2 change:1 ascribing:1 obtained:3 derivable:2 remark:1 orthomodular:65 technical:1 wdl:7 completely:1 contradiction:1 adopt:1 compatibilities:1 m3k:1 procedure:2 published:23 usually:5 opinion:1 hexagon:1 makes:7 point:1 9h:1 formulated:1 inference:9 substitution:1 logical:11 9f:1 first:11 boolean:19 contradictions:1 modus:1 ortholattice:28 post:2 use:7 russell:1 would:15 prove:23 distinct:3 contains:3 helvetica:23 definition:11 hilbert:8 going:1 call:5 opposed:2 taken:2 themselves:2 more:4 thus:9 apparent:1 fraenkel:1 odinger:1 mccune:2 berlin:1 mladen:1 particular:5 known:4 foundations:1 hold:13 iii:1 nodes:2 must:8 account:1 valued:5 ma:1 science:1 equation:3 work:2 london:2 theories:1 grover:2 values:3 concepts:2 following:19 making:2 example:5 def:21 proof:47 define:2 claim:2 compare:1 omit:6 figure:3 give:6 organized:1 conjecture:2 states:1 assumptions:1 numbers:2 want:1 difference:5 beran:1 axiomatization:1 information:1 argonne:2 end:2 turn:4 provide:1 verify:4 get:6 write:6 maps:7 pure:1 answer:1 acta:24 l9:2 explains:1 map:3 levy:1 blocks:1 description:1 algebra:39 after:2 derived:1 mapping:8 lab:1 reflect:2 metamathematics:2 hence:10 disproved:1 law:6 repeat:1 ambiguous:1 realized:1 transitive:1 natural:3 computations:2 lemmas:5 correspond:2 redundant:1 st:1 hypotheses:1 ortho:2 algorithms:2 fundamental:1 every:2 subsequently:1 acknowledges:1 transitivity:4 order:9 operations:9 ackermann:2 bull:1 holds:27 help:2 over:2 raised:1 symbols:1 ended:2 paper:3 including:1 satisfies:2 still:3 its:26 find:3 systeme:1 group:1 thank:1 how:2 lo:2 weaker:1 actually:2 better:3 absence:1 systems:5 constitutes:2 mail:2 hidden:1 main:1 might:1 non:22 zagreb:2 chelsea:1 repercussions:3 wom:5 introduce:3 ql3:1 asymmetrical:3 they:7 half:1 oxford:2 now:5 discuss:1 nor:3 instructions:1 easily:1 term:1 equality:3 products:1 always:1 university:2 philosophical:2 l6:10 l7:4 l4:2 l5:2 l2:2 l3:3 truth:1 l1:13 cl4:1 cl5:1 soc:1 side:2 l8:26 mean:1 different:4 directly:2 simplicity:1 doing:1 reduce:2 idea:1 literature:2 alfred:1 obtains:1 measurement:2 quantum:69 our:13 operation:4 beyond:1 eq:10 leblanc:1 out:3 emerges:2 shown:10 fundamentally:1 space:7 open:1 rep:1 since:11 crucial:1 ry:1 looking:1 reformulate:1 contained:2 investigation:1 reader:3 formula:3 hooker:1 gov:2 evaluation:4 math:4 shows:2 numerical:3 theory:12 found:2 possibility:3 standard:18 admits:1 reason:2 rows:1 york:1 put:1 wanted:2 monographs:1 axioms:11 definition:9 organic:1 language:4 applications:3 kochen:2 chiara:2 computers:7 confirmation:1 categoricity:1 concrete:1 schemata:1 consequence:6 generalizations:1 think:1 first:2 origin:1 already:1 features:2 probability:3 vedral:1 variables:1 ql2:2 number:1 quantentheorie:1 ql1:6 peculiarity:1 symmetry:2 phil:1 least:2 another:4 impossible:1 distributive:36 precisely:1 miss:1 given:10 necessarily:3 checked:1 categorical:10 introduction:2 system:4 relations:1 name:1 their:7 ule:1 allows:1 calculations:1 typing:1 ordered:1 structures:2 boil:1 gives:5 shell:1 statement:2 asymmetric:1 exactly:1 definitions:3 immediate:5 part:1 simulate:1 authors:2 representing:1 than:6 semantics:2 holland:5 bits:1 require:1 dalla:2 submitted:1 classes:7 archimedean:2 were:3 providing:1 7b:1 anl:1 boston:1 ann:1 measure:1 say:2 tables:1 kleene:1 sentences:1 need:3 seen:1 seem:1 element:1 apparently:1 any:30 mappings:5 something:1 latter:8 able:3 definite:1 note:2 build:1 finding:1 so:27 coincide:3 mit:1 calculus:5 formulas:11 play:5 added:8 norman:1 axiomatic:1 shall:1 proving:1 precluded:1 algebraic:3 mace:1 representation:1 phase:1 why:2 especially:1 considered:2 clear:2 later:1 implications:3 physica:23 simulators:1 principle:1 left:3 physics:2 incomplete:1 impression:1 shor:2 show:11 contemporary:1 syntax:1 helv:1 relation:33 peano:1 keywords:1 substituting:1 find:1 make:6 pick:1 computability:1 bind:1 based:4 simulating:1 spite:1 valuation:4 explain:2 enough:1 should:4 lemma:32 only:16 explicitly:1 subsection:6 rich:1 five:5 interested:1 columns:1 do:14 dl:2 above:6 means:7 hillel:1 between:6 straightforwardly:1 satisfied:1 ones:6 words:1 relational:1 lattices:15 parlance:2 neither:5 deductive:1 scientific:1 runs:1 bar:1 approach:2 arxiv:1 ascribable:1 investigate:2 croatia:2 she:1 mapped:2 through:2 implication:3 grad:1 ql:14 preserve:1 requirement:1 set:11 aspect:1 sep:1 national:1 testing:1 arrives:1 valuated:1 see:8 computer:5 sec:9 result:7 fail:5 precursors:2 nonstandard:1 fails:3 inappropriate:1 subsequent:1 review:1 pulmannov:1 symmetric:3 written:2 determined:1 closed:2 simplest:1 irb:1 reading:2 conditions:2 counterexample:1 suffices:2 comparable:1 infinite:3 terms:3 extend:1 web:1 qubits:6 however:6 jr:1 oml:15 hypothesis:3 wr:1 premise:3 modeling:4 come:1 both:8 parentheses:1 last:1 retrievable:1 many:4 taking:1 according:3 deduction:1 etc:3 connection:1 nicht:1 context:1 logic:109 qubit:1 expression:3 comes:1 methodological:1 conclude:1 simple:1 had:1 corresponds:1 dimensional:3 pm:1 m12:1 simply:2 church:1 polynomial:2 table:2 throughout:1 considering:1 pt:1 addition:4 associativity:1 offers:1 three:1 been:5 int:4 odel:2 describes:1 expected:1 ph:2 algebras:2 abstract:2 fig:7 direction:2 enable:2 corresponding:2 versa:6 theorem:42 consolidation:1 else:1 ordering:1 understand:2 stems:1 c1:1 denote:3 mcs:1 former:2 those:3 sound:1 look:1 pacs:1 wff:4 value:1 ministry:1 will:5 proves:1 cannot:2 applies:1 property:21 xxx:1 kolmogorovian:1 principia:1 unitary:1 century:2 endowed:1 von:2 keller:1 belmont:1 surprisingly:2 discrepancy:2 ii:1 itself:4 il:1 weakest:1 corrolary:2 elements:1 whitehead:1 develop:1 perhaps:1 seek:1 granted:2 same:6 member:2 unity:1 complex:1 quant:3 soundness:9 several:1 used:7 http:3 barenco:1 complemented:1 stressed:1 structurally:1 counterparts:2 hand:6 equational:1 purpose:2 hilbertian:2 distributivity:8 ponens:1 identity:7 weakly:25 schr:1 programs:1 nevertheless:2 modeled:2 well:7 obviously:1 defining:1 without:2 solve:1 very:5 model:45 axiom:3 possesses:2 usual:4 gates:2 newest:1 just:2 theorems:3 obtain:11 unary:1 questions:2 immediately:1 yes:3 briefly:1 mittelstaedt:2 previous:7 letting:1 alum:1 secondly:1 kluwer:1 cl:7 seems:2 lattice:78 add:2 valid:3 easy:7 propositions:10 usage:3 input:1 remaining:2 take:2 real:2 references:1 reflexive:1 rules:7 papers:1 possible:6 lanl:1 five:1 9g:1 press:3 using:12 interchangeable:1 unique:1 formal:2 necessary:2 like:1 follows:13 reduces:4 serves:1 yields:2 either:6 arbitrary:2 served:1 works:1 page:1 mathematical:5 reidel:4 www:1 because:6 could:2 neumann:2 classical:45 sequence:3 conditional:1 some:4 strongest:1 ols:1 connectives:3 effect:1 proper:6 home:3 finite:2 proofs:10 happens:2 merge:1 opposite:1 l10:3 iff:4 ak:1 specific:1 does:15 connecting:1 expressing:1 prog:1 o6:30 cl3:1 run:1 power:1 equivalent:8 each:4 substituted:2 although:2 putting:1 propositional:7 properties:7 bz:1 stage:1 zur:1 om:3 ol:15 affect:1 carried:1 anything:1 most:2 finding:1 introduces:1 o:86 cl1:3 compatible:2 faust:1 cl2:1 mixed:1 introduced:1 morphism:6 primitive:3 differences:1 previously:1 into:7 numerically:1 isomorphic:3 due:1 down:1 lies:2 ceva:1 wherefrom:2 raises:1 determine:1 elementary:4 amsterdam:3 greechie:2 soon:1 methods:2 rely:2 logics:9 additional:4 assumed:1 support:1 there:9 question:1 faithfully:1 noticed:1 handbook:2 way:8 decisive:2 analyze:1 was:1 opens:1 therefore:13 academic:2 north:3 complete:4 form:9 hr:3 quaternionic:1 simulator:1 but:22 principles:1 volume:3 deductions:1 automated:1 line:2 true:18 he:1 oa:4 applying:1 whether:5 vice:6 up:2 us:13 dordrecht:5 below:2 critical:1 define:4 eine:1 called:5 mechanics:3 instead:3 sometimes:2 proved:8 defined:9 stronger:2 universal:1 congruence:5 am:2 6b:2 general:4 peres:1 satisfied:4 single:1 ar:1 right:2 together:4 identities:6 check:3 incorrect:1 again:1 completeness:23 nm:1 no:10 mathematica:1 when:8 defined:7 other:14 role:5 investigations:1 becomes:3 defines:1 theor:4 conclusion:2 formed:2 superposition:2 models:24 class:3 stay:1 william:1 meaning:1 important:1 variable:1 structure:10 acknowledgment:1 implies:3 syntactical:8 quantifiers:1 assume:5 starting:1 required:3 rule:7 mimic:1 fact:1 time:2 requires:2
|
quant-ph9906102.txt |@word sci:2 sch:1 rev:3 comparatively:1 results:1 four:1 gf:1 consists:2 causes:2 consider:1 fta:1 calculate:1 concerned:1 tu:1 tr:1 uniqueness:1 efficiencies:2 excluded:1 under:2 analogous:1 include:2 case:3 confirmation:2 straightforward:1 susceptible:1 very:8 void:2 wave:8 englert:1 figs:1 stays:1 difference:1 condition:1 splitter:7 pbs:2 presented:2 did:1 turns:4 notes:1 proposals:1 solution:1 travels:1 solved:1 evades:1 harry:1 small:3 der:2 croatian:1 measuring:1 smaller:1 version:1 direct:1 pulse:1 outcomes:1 go:1 likely:3 design:1 switchable:3 concludes:1 rigorous:1 bacteria:1 substitute:1 even:4 will:1 what:1 appear:1 analogously:1 experiment:13 localized:1 scientists:1 new:1 paviˇci:25 contributes:1 acknowledgments:1 opposition:1 full:1 simultaneously:1 submitted:1 exchange:1 respectively:2 aten:2 never:1 here:3 localisation:1 objects:10 cos2:1 path:11 november:1 coupling:1 obtained:1 incoming:8 rests:1 losses:14 allows:1 round:9 calculations:2 throughput:4 loop:1 symmetrical:1 suitable:2 changes:1 york:1 named:1 formulated:1 krenn:1 suddenly:1 problematic:1 plenum:1 logical:1 highly:1 neutrons:2 visible:1 austria:2 achievable:4 condensates:1 coatings:2 total:18 select:1 vienna:3 use:3 takes:1 would:8 prove:1 probabilities:2 give:1 next:1 doubt:1 therefore:2 taken:2 resonator:22 theoretical:1 more:2 separated:1 entrance:5 formally:1 knows:1 coating:2 tested:1 berlin:6 mladen:1 particular:2 known:1 foundations:1 cases:2 must:3 account:2 science:1 originally:1 work:1 theories:2 remain:2 values:5 ms:1 following:4 making:1 scatter:2 figure:11 mirrors:5 calculation:1 share:1 high:3 lorentz:1 numbers:1 counting:1 ratio:1 rays:1 end:1 eng:1 rather:2 s2:2 s1:2 ωres:6 foreseen:1 far:2 numerous:1 adjacent:1 gate:1 flow:1 exits:2 circular:1 description:1 after:7 lab:1 3rd:1 applications:4 produce:1 designed:1 physik:1 response:2 times:1 outline:1 correspond:1 st:1 frustrated:6 so:9 sm:5 keeps:1 acknowledges:1 order:2 erasing:1 over:3 soc:1 years:1 produced:1 experiments:7 through:6 same:3 lasers:3 er:1 mentioned:1 linewidth:1 its:4 before:2 horizontally:5 thank:1 energies:1 polarizing:3 fix:1 reacting:2 scully:2 recombines:1 absence:5 systems:3 mail:4 loophole:1 kasevich:2 inefficiency:1 them:7 good:1 zagreb:3 propose:1 safe:1 introduce:2 reflected:7 example:1 asymmetrical:2 they:2 hundred:1 arriving:1 now:1 yu:1 bigger:2 easily:1 term:1 reflectivities:2 name:2 always:2 university:5 level:1 realistic:31 fringes:1 transmitted:4 bonn:1 lorentzinvariant:1 each:8 found:2 universit:2 referred:1 ei:6 significantly:2 belgrade:1 mesoscopic:1 energy:7 hard:1 gaussian:1 applicable:2 prisms:8 interferometer:2 fires:1 gaps:2 obtains:1 measure:2 quantum:16 our:3 eq:3 really:1 leave:1 shown:6 ftr:4 resonators:3 since:2 interference:8 increase:1 multiply:1 gaussians:1 am:2 medicine:2 got:1 ref:6 integrated:1 shows:2 foundation:1 assured:2 free:43 standard:2 welcher:1 ftir:1 ork:1 element:1 put:2 detecting:5 r4:3 definition:1 pairs:1 interaction:44 r1:20 r2:17 r3:3 could:4 ati:1 length:4 plane:2 arrived:1 discussions:1 first:2 initial:1 humboldt:3 probability:9 blown:1 number:3 least:1 another:1 type:1 carry:2 precisely:1 passes:1 given:6 introduction:1 unknown:1 sep:1 system:4 reflectivity:5 realistically:1 their:3 too:2 passed:1 realization:2 postulate:1 scheme:1 cite:1 inner:1 elaboration:1 imperfect:1 fraction:1 mostly:1 continuous:2 immediate:1 resulted:1 optical:6 than:1 plausible:1 polarized:7 showed:1 enabled:1 aims:1 preparation:3 minimize:1 patients:1 computer:2 amplitude:2 were:5 feeling:1 treated:1 unchanged:1 already:2 disturbing:1 seen:1 bohr:2 apparently:1 any:4 ray:3 foundational:2 paths:1 conversion:1 angle:2 depending:1 latter:4 able:1 phase:5 polarization:5 ideal:4 internal:3 take:2 obviously:2 destroy:3 detector:11 tunnels:3 added:2 fundamental:1 dissertation:1 object:24 reach:1 react:1 most:2 germany:2 nothing:2 extremely:1 interferometry:1 mach:2 considered:3 calculated:1 detectors:3 km:2 face:2 part:2 principle:1 exp:3 mechanical:3 kz:3 physics:1 fejer:1 fact:2 phenomenon:1 show:4 supported:1 keywords:1 find:1 unanimously:1 based:4 knowledge:1 window:2 incidence:1 should:7 only:6 going:1 geometric:1 local:1 ger:1 hit:2 means:3 beams:1 photography:1 de:2 obtain:1 beam:28 joins:1 parlance:1 dr:12 net:1 alexander:1 gray:1 perrot:1 conclusion:1 approach:1 arxiv:1 yield:2 method:1 supp:1 proposing:1 paper:2 croatia:2 cycles:6 limitations:1 setup:3 set:3 constructing:1 achieved:2 testing:3 packet:1 ωt:3 detection:24 intensity:3 individual:1 sec:1 result:2 khz:1 close:3 news:1 best:1 detect:3 mechanically:1 brewster:1 subsequent:1 nature:2 µs:1 enough:1 disprove:1 between:1 invariant:1 irb:1 conditions:4 available:1 recently:2 do:3 opening:1 however:5 supports:1 agencies:1 efficiency:16 incident:2 comm:1 recent:1 bose:1 killing:1 byer:1 suggested:1 both:3 essentially:1 improved:1 fused:1 many:4 region:5 equal:1 against:1 etc:1 figures:3 faces:3 passing:1 argue:1 progression:1 experimental:3 karlsson:1 mechanics:4 ci:1 extent:1 point:5 simple:1 cf:2 johann:1 consideration:1 moreover:1 actually:1 cw:1 pr:2 pp:3 described:1 zeno:1 cavities:1 capable:1 wien:1 detected:1 been:11 hitting:3 defined:2 reduction:1 much:1 detrimental:1 expected:1 reflective:1 ph:5 hardly:1 ann:1 fig:7 elitzur:3 quantities:1 transferring:4 photon:26 interpretations:2 gap:1 zeilinger:3 angles:2 covered:1 c2:1 present:4 applied:1 laser:7 pacs:1 straight:1 value:1 rectangular:1 employ:1 technical:1 optimization:1 walther:1 rotator:2 situation:1 taking:1 procedure:2 opt:4 larger:1 orientation:1 coupled:3 almost:2 von:1 ir:2 thus:5 downconversion:3 summhammer:3 according:2 ii:3 exiting:2 different:3 weinfurter:3 make:1 radiation:1 verify:1 shifts:2 quant:4 schematic:1 lengthening:1 several:2 grows:1 neutron:1 used:5 schiller:1 zehnder:2 conceived:1 effect:5 monolithic:5 hand:1 moment:1 uses:1 purpose:1 resonance:3 dark:1 totally:2 outputs:2 cycle:3 relies:1 tunnelling:1 lower:2 narrow:1 reflection:15 nevertheless:1 makes:2 well:4 hafner:1 vaidman:4 directly:2 without:8 allow:1 does:2 fail:1 parametric:2 dimension:1 left:3 background:1 just:1 being:6 nd:1 guided:2 hese:1 valuable:1 reviewed:1 press:1 distant:1 facts:1 paul:20 hardy:1 macroscopic:1 ministry:1 previous:4 enters:2 weg:1 candidate:1 absorption:3 photons:6 bell:1 source:1 other:4 lett:4 usage:1 input:1 remaining:1 match:1 build:1 real:1 around:1 complementarity:2 measurement:4 possible:11 corresponds:1 early:1 test:1 know:1 afore:1 confined:1 using:3 accepted:1 apart:1 vertically:2 theor:1 necessary:2 like:1 herzog:2 follows:1 performing:1 niels:1 detections:3 either:4 setups:1 output:1 malus:1 essential:1 acad:1 because:6 often:1 successfully:1 some:1 somehow:1 b0:1 b1:1 choosing:1 mirror:5 proper:1 indistinguishability:1 counts:1 provided:1 scale:1 sufficiently:1 cavity:7 measurements:10 nonclassical:1 exceeding:1 gurvitz:1 strahlung:2 exit:4 yag:1 inserting:3 knew:1 run:1 reaching:1 selecting:1 equivalent:1 perpendicular:1 bj:1 inherent:1 eiψ:5 includes:1 svozil:1 bz:1 tuning:1 about:2 central:1 carried:4 anything:1 certainty:1 firing:4 discussed:2 chance:1 o:2 kwiat:6 range:4 exposing:1 faust:1 mean:1 slightly:1 seeing:1 equally:1 presence:3 into:20 within:5 due:2 down:3 device:14 appropriate:1 ceva:1 references:1 determine:2 einstein:1 rely:1 statistics:1 multilayer:3 inserted:1 there:20 question:1 long:2 start:2 detectable:1 tun:1 low:3 way:4 ed:1 forward:2 was:5 assumes:1 opposed:2 function:2 hr:2 forming:1 registered:1 but:4 principles:1 failure:1 repeated:1 atom:3 true:1 proposal:4 he:1 whether:1 pn:1 practically:2 up:7 us:2 until:1 crystal:1 below:3 frequency:4 problem:2 define:1 trips:2 detailed:2 oth:1 ac:1 strengthening:1 ag:2 int:1 certain:1 describe:1 influence:1 general:2 loops:3 single:12 right:5 formulation:1 crystals:1 moves:1 trip:7 physical:5 again:1 ideally:3 no:15 cos:3 when:18 reality:1 application:7 prism:5 unambiguously:1 dt:12 spatial:1 department:1 mathematics:1 out:10 reflections:6 coherence:7 superposition:1 resembles:1 problems:1 stay:1 generated:1 fabry:2 suppression:2 structure:1 building:1 correlated:1 implies:1 longer:1 dω:8 photonics:1 proposed:5 antireflection:4 portion:3 dot:1 time:11 silica:1
|
quant-ph9906103.txt |@word limited:1 desirable:1 idealised:1 integrity:2 equiprobable:1 whose:3 calculate:1 γm:3 under:1 worth:2 conjecture:4 kent:5 p1:12 every:6 affect:3 reiterating:1 ref:5 solution:1 solid:1 convenience:1 heading:1 consistent:5 estimates:2 elections:1 approximation:2 elegant:1 second:19 sustaining:5 implemented:9 even:7 established:3 supplied:2 above:9 supplies:2 increasing:4 simultaneously:1 abstractly:1 here:15 refinement:1 active:1 rigorously:1 stipulated:1 spacetime:7 appropriately:1 secure:56 tensored:1 highly:1 specifics:1 achievable:1 total:5 cheating:19 would:21 insecurity:2 chooses:13 paramater:1 noting:1 call:5 m2:5 type:2 until:5 separated:6 tolerated:1 successful:5 must:16 me:2 locked:1 mm:3 work:4 mi:1 theories:1 my:1 example:2 give:3 relativistic:41 cited:1 bennett:3 stressing:1 implementations:4 involve:1 want:1 times:4 guarantee:10 end:1 provide:1 verify:3 travel:2 feature:5 how:3 adjacent:1 symposium:3 brassard:8 description:4 insecure:10 after:16 parallel:2 attempt:2 third:5 neglect:1 complexity:1 maintain:8 enter:1 order:19 operations:7 over:5 vary:1 xi:2 before:7 writing:1 better:2 distinguishing:1 compelling:1 potentially:2 eventually:1 them:14 combination:1 weakness:1 safe:11 they:30 represents:3 each:33 cheaters:1 mean:1 schemes:5 t2:2 principles:2 literature:1 laboratory:7 extract:1 rr:7 restricted:1 content:1 fellowship:1 adapt:1 mγ:1 conjectured:1 newly:1 ri:3 independence:3 foundation:2 log2:3 assured:1 little:2 standard:4 assures:1 estimate:1 certified:1 incorporates:1 r0:1 messages:5 eavesdroppers:1 ist:2 corrections:1 onto:1 sigact:1 already:1 features:2 render:1 coding:6 channels:2 another:8 unruh:4 electronic:1 similarly:13 approximately:1 needed:4 rates:2 hypothetical:1 tool:1 convention:7 begins:1 distance:1 circa:1 showed:2 bits:41 iteration:3 zero:7 project:1 matter:1 classes:1 historical:2 fashion:1 boston:2 contents:2 convenient:1 latter:3 responsible:2 transmit:2 committing:4 though:6 proving:1 simplify:1 phase:7 coin:2 reputation:1 principle:7 sum:1 inspire:1 reductions:1 labels:1 attempts:1 participate:1 earth:1 just:5 implementation:3 explain:1 adequate:2 oct:1 do:11 cryptography:12 stop:1 new:13 reconstruct:1 runs:3 textbooks:1 public:1 34th:1 respond:2 fair:1 detection:2 depends:3 radius:2 projections:2 fail:3 best:1 subject:2 said:1 capacity:1 simplest:2 drawn:2 terms:1 however:12 extent:1 news:1 improve:1 suggested:2 received:10 essentially:4 against:55 participating:1 cod:1 receives:5 distinction:6 qubit:6 minimises:1 discontinued:1 oblivious:3 trust:7 speak:1 conference:1 asks:4 basis:2 been:7 confident:1 much:2 basic:2 expected:1 argument:4 coherent:1 maximally:2 applied:1 suitably:2 near:7 suppose:15 viii:1 applies:1 property:5 procedure:4 ix:1 spacelike:2 tions:1 iv:2 ii:5 disjoint:3 experts:1 containing:1 perform:1 suggest:1 make:6 linked:1 complex:3 quant:5 avoids:1 showing:3 perimeter:1 independent:3 hand:2 prescribed:4 suitable:3 kept:2 scenario:2 unconditionally:18 failing:3 world:3 protocol:120 popescu:2 identify:2 yet:2 previous:5 monitored:1 27th:1 regarded:1 royal:1 transformed:1 easy:1 gave:1 breaks:1 possible:14 possibly:1 whichever:1 background:1 unique:1 advanced:1 contradict:1 alice:74 10km:1 specific:1 arbitrary:3 security:74 sends:5 successfully:13 confusing:1 collect:1 comments:2 asking:1 illustration:1 properties:1 proceed:2 attacks:17 accepts:3 distinct:2 ensure:7 commit:15 slightly:1 primitive:2 bound:5 reducing:1 rounds:5 methods:1 occupying:1 initial:2 approximate:1 why:2 way:10 m1:3 was:23 far:3 form:6 attempted:2 differences:4 failure:1 sustained:5 true:1 slope:1 bounds:1 devices:2 pinpoints:1 examples:2 relabelling:1 adopt:1 proved:3 sight:2 computing:4 stronger:2 abstract:2 proven:2 evidence:4 prover:1 exist:2 a1m:2 face:1 commuting:1 check:2 physical:14 ni:7 nj:16 nk:2 nm:3 no:23 ekert:2 generally:2 setting:2 role:2 papers:2 test:3 superposition:3 models:2 preceding:1 faster:4 tested:3 assume:14 proposed:1 interval:1 together:6 cheater:1 time:25 n1:9 n2:3 precise:3 remarkable:1 skip:1 computation:5 certainly:4 depend:2 technique:3 permanently:1 string:3 advantage:1 orthogonal:1 choice:4 trouble:2 exact:1 level:2 pursue:1 science:2 round:47 dependently:1 upper:1 revolution:1 cost:4 appear:2 celebrated:1 cryptographers:1 uniform:1 current:6 goes:2 illustrations:1 reply:8 satisfy:1 understanding:2 address:1 supplying:1 wait:1 box:4 sending:8 institute:2 timings:1 hospitality:1 bob:51 genuinely:1 tasks:4 regardless:4 langlois:2 alamitos:1 prove:5 positive:3 stored:1 scope:3 theoretical:5 sharing:1 outputs:1 envelope:3 appendix:1 virtue:1 cases:3 insights:1 avoiding:1 inertial:1 modified:1 values:13 hope:2 cam:1 following:10 arrive:1 unconditional:2 numbers:23 dedicated:1 arise:1 agent:2 locks:1 unveiled:6 allowed:3 requirements:1 s2:2 discussion:10 s0:1 till:1 fourth:3 optimal:5 parameter:10 map:1 information:30 may:23 max:7 use:19 applications:2 produce:3 improving:1 revealed:2 natural:3 whenever:3 yielding:1 ghz:2 si:2 so:22 definitions:13 blowup:1 indeed:6 pointed:5 soc:1 entity:1 course:7 argued:1 still:4 ieee:3 thank:1 interesting:7 vicinity:1 coordinates:3 forms:2 continue:3 constitutes:2 main:3 non:6 unveiling:36 transmissions:2 compelled:1 now:17 discuss:1 maintaining:1 term:2 equality:1 establishing:1 possibilities:3 realistic:1 entirely:1 domain:1 significantly:2 ef:1 ec:1 conventions:1 begun:2 happen:1 worried:1 shown:4 opened:1 space:4 increase:1 investigation:1 rational:1 suggesting:1 receiving:3 correct:5 shows:1 earlier:7 theory:11 possibility:8 orn:2 california:1 besides:1 remainder:2 advance:2 fixed:2 initiate:6 place:12 think:1 first:31 exotic:1 intuition:1 simplifies:1 saving:1 carry:3 impossible:11 message:10 open:3 singling:1 size:2 given:14 necessarily:1 remotely:1 anyone:1 returns:3 1f:3 1j:1 participated:2 speaking:3 gives:4 inefficient:1 circulated:1 x2:3 x1:3 representing:1 than:17 specify:1 impractical:3 effective:1 wiesner:2 require:10 were:4 inferring:1 generality:4 turned:1 locations:4 say:9 exchanging:2 invalidates:1 any:36 computationally:1 efficient:2 aside:1 note:9 sciences:1 ideal:3 potential:2 take:16 forming:1 channel:4 begin:1 opposite:3 detect:1 successive:5 pair:7 surprising:1 considered:3 later:14 defeating:1 conservatively:1 laws:2 2m2:1 2m4:1 show:3 cheat:2 sites:2 discovered:1 inconsistent:1 decompositions:1 data:8 enough:1 only:13 going:1 black:3 equipped:5 get:1 expectation:1 cannot:11 reveal:1 summary:1 reveals:2 physically:1 maximum:5 relative:2 namely:2 actively:2 eliminating:1 uncorrelated:2 satisfying:2 ways:2 definite:3 commitments:57 outside:4 between:14 sited:1 reading:1 checks:2 arrival:1 comp:1 densely:1 successes:1 many:4 region:13 according:3 dated:1 duty:1 among:6 deviating:2 period:1 maintained:4 iterations:1 constant:5 considering:3 combines:1 workshop:2 wants:1 external:1 irrelevant:1 former:2 those:4 case:19 disconnected:2 slippery:1 editorial:1 promising:1 distinctions:1 nomenclature:2 primitives:1 supremum:2 technology:6 binary:4 different:10 participant:1 distributions:2 same:19 arguments:2 extended:2 running:1 entanglement:2 relies:2 roughly:6 without:13 relied:1 coordinate:3 model:7 laboratories:20 dimension:1 justify:1 being:9 when:13 actions:4 speed:3 favouring:1 except:1 interested:1 lett:4 versa:1 real:1 around:4 read:1 usefully:2 early:3 using:20 recipient:1 serves:1 either:25 output:2 reduced:1 preskill:2 satisfactory:4 deduce:1 specified:3 duration:2 a10:2 provided:3 dimensions:1 footing:1 recorded:1 kilian:2 critical:1 decomposition:3 provides:1 refer:2 measuring:1 scientific:1 power:6 seconds:1 equivalent:1 communicate:1 mayers:30 broken:1 2m:16 stations:1 theorems:1 discussed:3 acm:4 practical:4 mutually:1 road:1 cambridge:2 flawed:1 unbounded:1 image:1 references:1 einstein:1 elementary:17 classicality:8 her:38 area:1 assumed:4 strictly:2 there:14 start:1 sealed:2 labelling:1 irreversibly:1 cryptographic:16 complete:3 change:1 attainable:4 applying:2 minkowski:6 practically:1 unveils:3 agree:4 detailed:1 ac:1 ai:24 certain:1 describe:2 am:2 general:14 examine:2 reliability:4 ensuing:1 controlled:1 incorrect:2 again:4 synchronised:1 completeness:1 field:1 valid:12 spatial:4 mathematics:1 briefly:2 separate:1 includes:3 a1:45 a0:3 a2:33 bounded:4 serious:2 included:1 impossibility:5 signalling:11 original:2 represent:2 epeau:5 consider:13 follow:4 research:3 protocols:30 subtleties:2 belonging:1 very:3 difference:3 securely:3 treating:1 list:4 applicable:1 t1:2 large:8 small:4 20th:1 programme:1 grateful:1 past:1 rate:10 further:9 what:2 sub:3 section:7 version:9 sup:14 acknowledgments:1 revealing:3 full:1 escaping:1 answers:1 behaviour:2 b2j:2 berkeley:1 strong:1 table:1 provably:1 allows:7 published:1 options:1 point:23 via:1 followed:5 requiring:2 vii:2 send:9 establish:5 archived:2 takes:9 probabilities:6 taken:1 iteratively:2 2y2:1 more:10 flat:1 initiated:6 surprisingly:1 initiates:1 particular:10 known:4 projective:2 producing:4 recall:1 remain:1 paragraph:1 caveat:1 learn:1 abandon:3 strategies:6 history:3 computers:6 share:11 states:14 minimum:2 attain:1 sense:8 exclude:1 huge:1 needs:8 rather:2 breaking:1 derived:1 develop:2 response:1 specifying:1 fundamental:1 help:1 developed:1 soon:3 paper:8 through:4 committed:61 y1:4 existence:3 y2:4 its:5 actually:2 detected:5 systems:1 might:9 alter:1 focussed:1 good:2 propose:1 focusses:1 oxford:1 easily:4 imprisoned:1 always:1 evade:1 2f:3 inequality:1 stopped:1 found:2 2j:4 2k:1 england:2 generation:1 hard:3 idea:2 mm2:1 obtains:1 measurement:2 quantum:104 beyond:2 really:1 since:15 trusts:1 participants:1 sustain:9 commits:3 difficulty:2 reason:3 imagine:1 generate:5 definition:18 pairs:34 needing:1 noted:4 relativistically:1 exponentially:8 pure:1 indebted:1 major:1 probability:36 prevent:1 number:9 linking:17 done:1 least:7 passes:1 introduction:1 construct:2 assumption:1 passed:1 scheme:6 store:1 implements:1 imperfect:1 calculations:2 part:7 believe:2 kindly:1 instruction:1 risks:1 interactive:1 randomly:4 substantial:1 conjugate:1 vulnerable:3 option:3 built:1 speculative:1 conforming:1 analogy:1 added:1 inference:1 reach:1 singlet:1 most:9 significant:4 nothing:5 stands:2 salvail:2 mobile:1 clear:2 sometimes:1 cover:1 km:2 exp:2 physics:12 particularly:3 relation:2 find:1 causality:1 parameters:2 writes:2 distributed:1 technologically:1 factor:4 his:3 notation:2 dependent:1 valuable:1 shared:11 during:14 him:3 arxiv:1 remove:2 underlying:1 common:2 set:17 ancillae:2 unpublished:4 see:5 individual:5 sec:2 learns:2 representatives:1 various:2 conditions:1 supposed:6 available:5 initially:2 attention:2 both:26 last:7 annual:3 context:1 finds:1 arbitrarily:6 supply:4 simple:3 seems:6 corresponds:3 whatever:2 agents:13 faraday:1 indefinite:1 ensures:1 described:9 raise:1 create:1 strategy:18 secret:6 describes:1 ensured:3 pj:10 ph:5 pi:13 partly:1 else:2 understand:1 representative:1 unnecessarily:1 p2:14 p3:3 practicality:1 exponential:1 indefinitely:9 reliable:3 batch:3 evaluated:1 receive:8 while:7 superposed:6 error:1 dominic:1 unitary:1 von:1 probabilistically:17 ready:1 vanish:1 belong:1 rules:4 used:13 temporary:1 assignment:2 moment:2 levels:2 uses:2 purpose:1 unveil:26 recent:2 lower:1 task:7 persuasive:1 analysis:3 obviously:2 person:1 shape:1 intervals:3 0wa:1 useful:4 alternative:2 letting:1 readers:1 alternate:1 guaranteed:4 signals:8 location:1 theorem:2 relevance:2 input:1 guarantees:6 remaining:8 bij:2 characterise:1 emanating:1 entangled:6 integer:3 bit:197 helpful:1 follows:7 signal:5 communications:12 individuals:1 indication:1 essential:4 terminology:3 mathematical:1 neumann:1 absolutely:1 some:30 back:1 b0:3 b1:57 b2:47 b3:3 intractability:1 measurements:7 per:13 tends:11 minimal:1 processing:2 continuing:1 bi:18 step:1 analysing:1 integers:3 anything:1 constraint:4 4mm:2 deserves:1 range:5 computational:5 into:5 within:27 retaining:1 appropriate:1 because:4 steven:1 proportional:1 criticisms:1 question:2 long:1 certification:1 sections:1 opens:2 adjusting:1 properly:2 link:1 line:2 consist:1 up:4 us:1 international:1 uk:1 similar:3 bell:1 storing:3 ordered:1 defined:16 single:2 chau:20 rewriting:1 application:2 points:2 coded:1 department:1 realisable:1 explaining:1 elements:1 generates:1 calculating:1 generated:10 allowing:4 claude:1 structure:2 ago:1 independently:11 implies:4 vice:1 required:13 b1j:7 b1k:1 neighbouring:1 oracle:1 redundantly:1 requires:19 having:2 once:3 results:3 broader:1 go:5 query:1 subtly:1 factoring:1 excluded:1 include:6 sent:12 random:28 wished:1 implicitly:1 wishes:3 continued:2 arrange:1 transmission:4 fewer:1 originally:1 configurations:2 smaller:1 imply:4 subtle:1 manipulating:3 odd:1 index:2 giving:4 consistently:2 experiment:1 3m:1 chose:1 degree:1 exchange:6 respectively:5 gilles:1 believed:1 separation:8 others:1 remark:3 technical:1 goldwasser:2 suggests:1 implement:7 makes:5 involves:1 collaborating:1 private:2 outcomes:1 apply:5 causal:2 manipulate:1 confidence:2 asymptotic:1 certificate:8 next:1 classically:2 fet:1 doubt:2 possession:2 becomes:1 carrying:1 labelled:2 iii:2 account:5 announcing:1 anywhere:1 proof:8 control:3 process:1 purposes:2 high:1 effectively:26 assumptions:8 something:4 optimised:2 destroying:1 arrangement:5 regions:8 located:2 instead:1 superluminal:3 watch:1 inst:2 disproved:1 efficiently:2 computations:1 light:9 correspond:5 redundant:13 honestly:6 allow:11 subsequently:4 s1:2 unbreakable:1 arithmetic:1 insight:1 produced:1 localised:1 including:1 perfect:11 immune:2 chosen:4 lo:21 relativity:7 choose:5 communication:18 covered:1 defining:7 greater:1 practice:2 cage:1 psup:6 february:1 university:2 identified:1 sufficiently:6 transmitted:2 accounts:3 constraints:14 subset:5 inputs:3 doing:4 proliferating:1 parties:21 related:1 constitute:4 society:1 measure:1 our:17 tenth:1 special:4 out:15 rev:7 postpone:1 suffices:1 disclose:1 8m:1 maintains:1 completely:2 york:3 jozsa:2 could:12 keep:2 length:5 adrian:1 hence:4 repeats:1 platonic:1 succeeds:1 powerful:4 date:1 reached:2 precisely:6 los:1 ordering:2 unknown:2 achieved:1 system:4 relations:2 their:32 attack:7 intermediate:1 perfectly:12 final:1 stars:1 completed:2 exactly:1 lists:3 herself:3 completes:1 observed:1 ben:2 inversely:1 appealing:1 result:5 enforced:1 kitaev:2 discussions:2 need:26 curved:1 clearly:1 able:10 mechanism:2 instance:4 unless:7 centre:2 who:6 device:2 class:2 afresh:1 request:3 32m:1 proceedings:6 fact:6 agreed:6 supported:1 q1:10 q2:8 based:6 knowledge:2 produces:1 should:10 lemma:7 ambiguity:1 attained:3 local:1 achieve:3 exchanged:1 means:5 familiar:1 joint:1 words:2 timing:3 ended:1 optimally:1 she:57 queries:2 qi:6 qj:1 temporarily:2 modulo:5 notational:1 tossing:2 frame:2 computer:3 phases:1 puts:1 attempting:3 tend:3 state:9 correctly:6 progress:1 neither:5 outsiders:1 interfere:1 implementing:2 key:10 configuration:2 distribution:6 taking:3 equal:7 passing:4 otherwise:3 comment:1 relevant:5 dominique:2 cm:2 environments:1 sequences:2 cr:5 superselection:2 flourishing:1 addition:1 yao:2 agreements:1 minimise:1 define:21 corresponding:4 sufficient:1 improved:4 present:1 multi:2 unlike:1 value:22 choices:3 will:23 discoveries:1 almost:3 vi:2 damtp:1 thus:21 site:3 respected:1 examined:1 lifetime:1 claimed:2 partner:1 perhaps:4 adverse:1 largest:1 units:1 party:13 finite:4 infer:3 ball:2 infinity:8 upon:1 requests:1 identity:3 nonetheless:1 well:4 sets:1 arising:1 drawing:1 usual:3 less:3 obtain:6 clocks:2 distant:1 uller:4 onward:1 other:21 extends:1 developments:1 details:4 identical:1 tests:10 checking:1 elapsed:1 increases:1 know:4 nor:5 press:2 immediately:1 loss:4 like:1 exploiting:1 simply:3 preclude:1 parity:2 wilberforce:1 retractable:2 qed:2 classical:39 sequence:3 phenomena:1 choosing:1 proofs:1 throughout:2 lead:1 demonstrates:1 avoid:1 overlap:1 does:10 assuming:2 pp:4 analyses:3 simpler:1 about:17 actual:1 carried:1 extension:1 cb3:1 certainty:1 important:3 outset:1 own:5 previously:4 commitment:167 demonstrably:1 additional:2 transfer:3 naturally:1 function:5 receipt:1 but:26 construction:1 illustrative:1 he:9 made:10 places:2 whether:1 wish:2 placed:1 below:5 convince:1 demonstrate:1 problem:1 piece:2 suprema:2 devise:1 ing:1 proceeds:3 mutual:1 variety:1 onwards:1 shannon:1 inherently:1 strings:1 4m:4
|
quant-ph9906104.txt |@word consider:3 dynamic:1 results:2 leads:2 entropy:1 grateful:1 reson:1 follow:1 environment:1 those:1 under:1 analogous:2 very:1 wave:2 every:1 kazan:2 hamiltonian:2 did:1 tanh:1 large:3 small:3 noted:1 insignificant:1 jump:1 consisting:1 vitali:1 thermodynamically:1 behaviour:2 others:1 consideration:1 observing:1 search:1 allows:1 commonly:1 tagirov:1 usually:1 opinion:1 highly:1 total:1 use:1 takes:1 would:4 prove:1 mysterious:1 becomes:1 naive:1 odinger:2 reversible:2 known:1 states:11 ρi:1 equation:4 work:1 remain:1 values:5 following:2 fulfill:1 spontaneous:2 example:2 process:1 high:1 numbers:1 feasible:1 turn:2 provide:1 discussion:1 ghirardi:1 fourth:1 establishment:1 ensemble:1 description:2 different:4 faculty:1 geometrical:1 data:1 curve:3 natural:2 ones:1 allow:2 order:1 help:1 over:4 move:1 years:1 stability:1 experiments:3 through:1 statistical:4 existence:3 its:1 temporal:1 fruitful:2 choose:1 wellknown:1 weber:1 non:3 fig:2 framework:1 they:1 now:1 february:1 equality:1 university:1 instability:1 mean:3 energy:10 ec:7 books:1 measurement:1 quantum:18 our:2 transitions:4 out:3 shown:1 matrix:2 space:10 izi:12 izj:1 rev:2 chaos:3 particles:4 re:1 occurs:1 foundation:1 interactions:1 divergence:1 possibility:1 imagine:1 could:1 computers:1 correctness:2 times:1 iz1:2 iz2:2 iz3:2 place:1 assumed:1 consequence:4 first:1 intuition:1 initial:4 probability:2 number:4 system:20 least:1 their:1 microscopical:1 calculations:1 inconvenient:1 gives:1 rimini:1 collapse:1 explanation:1 continuous:1 part:1 manifestation:1 separability:6 coefficients:3 determines:1 jumps:15 matter:1 determined:1 grigolini:1 russia:1 function:1 turned:1 seen:1 seem:1 intersecting:1 note:1 though:2 reach:1 phase:5 extremely:1 manifested:1 probable:1 observation:3 consequences:1 considered:4 calculated:1 cover:1 typeset:1 exp:1 mechanical:3 physics:2 fact:1 show:1 random:6 discovered:1 bring:2 attempts:1 solutions:1 explain:2 state:8 should:2 only:2 equilibrium:1 do:1 means:2 macroscopical:1 cannot:3 words:1 during:1 dt:1 evolution:8 arxiv:1 factorization:1 acknowledgments:1 view:2 requirement:1 see:1 result:5 discussions:1 surfaces:9 detect:1 interacting:2 enough:2 various:1 between:3 probably:1 conditions:3 nature:1 however:2 hypothesis:1 magn:1 essentially:2 density:1 equal:4 zeeman:1 fulfilled:1 connection:1 figures:1 experimental:1 ci:1 cn:6 point:2 simple:1 corresponds:1 described:1 basis:2 addition:1 equations:3 three:3 been:1 ph:1 systems:8 arises:1 precision:1 hmn:1 demand:4 c2:1 spin:8 present:1 case:3 exponential:1 pacs:1 solid:1 expanded:1 value:5 will:3 procedure:1 real:3 iz:1 orientation:1 averaging:5 metric:1 thus:4 them:1 surface:3 examined:1 containing:1 make:2 belong:1 same:3 strange:1 quant:1 runge:1 φk:1 φn:1 difficult:1 kutta:1 investigated:1 numerical:1 upon:1 mutual:1 authors:2 arrived:1 infinite:1 changing:1 normalization:1 schr:2 usual:1 being:1 infinitely:1 seems:2 add:1 easy:1 identical:2 possible:4 using:2 accepted:1 necessary:1 like:2 particle:1 follows:1 arbitrary:1 works:3 essential:2 spins:6 because:1 classical:2 some:1 isoenergetic:1 energetic:3 provided:1 integration:1 does:2 eliminate:1 prof:1 demonstrated:2 refer:1 eigenfunctions:1 dcm:1 equivalent:2 agreement:1 substituted:1 revtex:1 periodically:1 bz:1 about:1 actual:1 ρˆi:1 metrical:3 dependence:1 ideology:1 equally:2 into:2 lies:1 references:1 operator:2 ovchinnikov:1 transfer:1 there:1 question:1 appl:1 low:2 way:1 was:5 hz:2 irreversibility:3 great:1 jun:1 line:3 considerable:1 hd:2 made:1 evident:2 maximum:1 below:1 frequency:2 demonstrate:1 problem:1 mechanics:5 proved:1 certain:1 abstract:1 influence:2 conserved:1 exist:1 av:8 physical:1 functions:7 dotted:2 no:1 when:1 other:1 conclusion:1 superposition:2 condens:1 disclosed:1 meaning:1 algorithm:1 assume:1 hnm:1 time:7
|
quant-ph9906105.txt |@word limited:2 consider:1 remarkable:1 priori:3 rev:2 results:1 existing:1 four:1 scalar:1 entropy:4 comments:1 grateful:1 expressions:2 research:1 whose:1 maximally:1 depend:2 violate:1 zone:7 segments:2 tr:1 posteriori:1 finally:1 th:2 resources:1 applied:2 orthogonal:2 very:3 choice:2 manipulated:1 telling:1 exact:2 presented:1 transmission:7 suffices:1 list:4 deals:1 vector:7 study:1 shows:1 noted:1 consistent:2 sign:5 past:1 cost:1 perspective:1 notwithstanding:1 estimated:1 hopefully:1 even:5 index:1 what:1 appear:1 giving:2 sum:1 celebrated:1 expressed:2 steiner:5 goes:1 3l:2 new:2 method:1 contrast:1 led:1 realizations:2 teleportation:19 here:1 following:4 dimensionality:1 them:2 du1:1 causality:1 calculate:2 obtained:5 remark:1 increments:2 sender:3 inspired:1 vectors:6 allows:1 ignoring:1 prior:2 amount:18 resulting:1 whereupon:1 bob:53 concerned:1 extra:4 requiring:1 private:1 achievable:3 total:3 predicted:1 use:6 projector:1 would:1 probabilities:3 positive:2 chooses:4 properties:1 classically:3 therefore:3 taken:1 predictions:2 themselves:1 achieving:1 minor:1 more:6 separated:1 sharing:1 knows:1 ecole:1 carrying:3 ignorant:1 normalized:2 particular:3 known:9 easiest:1 must:7 account:1 valued:2 science:3 averaged:2 reproduce:1 sent:3 ulb:1 example:1 numbers:8 boschi:1 give:1 process:1 accepts:2 sense:1 share:5 accept:1 states:1 sphere:9 iterate:1 minimum:3 performed:2 allowed:1 νk:15 information:15 end:1 goal:1 verify:1 means:1 how:1 pure:1 reject:1 instead:2 sin:1 brassard:3 product:1 description:3 communicating:1 may:1 suppose:1 consequence:1 parallel:2 slightly:1 register:1 june:1 projectors:1 lhv:2 so:5 specifying:2 fundamental:1 correlation:1 acknowledges:1 order:1 operations:3 interpretation:2 closely:1 essence:1 over:2 flips:2 years:1 course:1 experiments:3 during:1 differs:1 fidelity:4 still:3 oblivious:1 its:2 refs:2 before:2 supplemented:4 group:1 symmetry:1 chosen:5 matrices:1 decreases:1 actually:3 better:1 systems:2 hidden:6 loophole:1 correspondence:1 non:1 similar:1 reflected:1 they:3 qal:4 now:2 possess:2 university:3 b3:2 divides:1 transmitted:3 each:5 found:2 entirely:1 characterized:1 schemes:1 financial:1 significantly:2 reduce:1 related:1 constitute:1 measure:1 quantum:31 our:8 summary:1 eq:6 shannon:3 out:7 shown:2 funding:1 space:2 restricted:3 since:5 crucial:1 denotes:1 content:1 similarly:3 contained:1 performs:2 denoted:1 receiving:1 ref:2 announced:1 she:9 foundation:2 log2:2 theory:5 little:1 free:2 completely:1 surely:1 put:1 jozsa:1 generate:2 starts:1 could:1 rejects:1 times:1 counterpart:1 exponentially:1 hence:3 exhibited:2 first:2 features:1 probability:15 u1:8 variables:8 coding:4 number:9 restrict:1 entanglement:6 another:2 carry:2 quality:1 given:13 necessarily:1 service:1 needed:8 unknown:5 system:2 least:1 their:1 returns:1 scheme:4 bits:33 national:2 gives:2 terminates:2 geneva:2 exactly:1 lists:1 part:2 simulate:5 authors:1 bennett:1 than:7 zones:2 perfectly:1 accordance:1 iteration:5 computes:1 normalizing:1 kth:3 light:1 tion:1 outcome:18 exhibit:1 explicit:1 generalization:3 randomly:3 manuscript:1 close:1 exchanging:1 seen:1 apparently:1 any:6 affairs:1 issue:1 able:1 inform:1 efficient:2 latter:3 physique:1 oriented:1 instance:1 concerns:1 transmit:1 though:2 sets:1 compress:1 singlet:5 most:2 importantly:1 letter:1 pair:4 accepting:3 surprising:1 average:13 coincides:1 physics:1 fact:2 quantity:3 optimal:1 show:4 random:5 discovered:1 minimizing:1 relation:3 find:1 tapp:1 based:4 simulating:4 distributed:4 should:5 only:10 indeed:2 attained:1 local:7 exchanged:1 do:2 his:2 correctly:1 get:1 de:1 cannot:4 words:1 shared:2 compute:1 aλ:7 du:2 aν:4 him:3 qr:5 heaviside:1 communicates:1 arxiv:1 consisting:1 qa:2 twice:1 common:1 switzerland:1 communicated:5 available:1 set:5 above:2 achieved:1 frame:1 correlations:5 detection:1 see:2 result:1 discussions:1 terms:1 best:2 inequalities:1 yet:1 initially:3 state:18 unable:1 jth:1 µk:14 between:3 probably:1 conditions:1 checks:2 knowing:1 triplet:4 recently:1 nature:1 qubits:4 however:1 equals:1 reproduces:1 problem:1 thank:1 observable:1 cos:1 σb:2 taking:1 uncertainty:1 equal:1 qaµ:1 objective:1 receives:2 receiver:3 qubit:15 adapted:1 experimental:1 bell:4 asymptotically:1 corresponds:1 dimensional:4 simply:2 iterations:1 respect:2 cp:2 pr:4 described:2 addition:2 acceptance:3 three:2 been:4 defined:1 describes:1 basic:2 ph:5 choose:3 corresponding:2 received:1 sufficient:3 gap:1 fund:1 angles:2 general:2 present:1 case:1 novel:1 paµ:2 pacs:1 value:1 will:5 while:3 replaced:1 shall:3 many:2 situation:1 du2:1 σa:2 identical:2 larger:2 orientation:1 fill:1 von:7 thus:5 surprisingly:3 perhaps:1 make:1 same:1 quant:5 emphasize:1 pauli:1 party:2 finite:1 pal:5 infer:1 european:1 independent:2 used:6 trivially:1 upon:1 hand:2 moment:1 uses:4 infinite:8 brussels:4 recent:1 simulates:2 task:2 integral:1 scenario:7 possibly:1 well:1 analysis:1 vaidman:3 without:2 simulated:6 swiss:1 termination:1 model:3 know:2 protocol:17 proposed:1 less:3 transmitting:4 generally:1 obtain:2 stored:1 asserting:1 λk:20 emergence:1 discipline:1 note:2 preprint:1 point:1 had:2 belongs:2 lett:3 real:6 aspects:1 possible:1 eorique:1 increases:2 entangled:4 belgium:2 using:4 bit:12 accepted:10 enumerable:1 modifications:1 necessary:3 helpful:2 identifying:1 exploiting:1 alice:43 wooters:1 steps:1 polytechnique:1 arbitrary:4 works:1 shed:1 neumann:7 classical:34 anticorrelations:1 sends:5 belonged:1 conditional:2 some:3 back:2 isotropy:1 b4:1 b1:3 b2:2 moreover:1 happens:1 provided:1 informationtheoretic:1 measurements:7 per:2 conditionally:2 does:2 demonstrated:1 scientific:1 σb1:1 uniformly:3 equivalent:2 communicate:2 bj:19 step:4 verifications:1 eiφ:1 hilbert:2 bz:1 comparison:1 cautious:1 central:2 carried:1 discussed:1 simulation:4 carries:2 plus:1 consequently:2 bloch:9 block:4 allowing:1 raised:1 follows:1 previously:1 communication:19 into:2 preexisting:1 numerically:1 negative:1 prepares:1 raises:1 parties:1 operator:2 proportional:1 refined:1 statistics:3 span:1 additional:1 her:7 few:4 support:1 there:1 question:2 specifically:1 u2:7 restricts:1 pa:6 low:1 way:5 triplets:3 analyze:1 was:8 function:1 himself:1 complete:1 form:1 jun:1 but:6 crepeau:1 repeated:1 aµ:4 he:10 made:1 rejection:2 whether:5 bounds:1 us:2 until:1 below:1 exploration:1 reflects:1 uk:16 highlight:1 distribution:2 belgian:1 informational:1 called:2 gisin:4 mechanics:8 required:1 choosing:1 povm:7 measurement:18 denote:2 peres:1 single:1 dλ:4 check:1 physical:1 compared:1 completeness:1 no:5 whereas:2 when:4 envisaged:1 σb2:1 supplementing:1 other:5 role:1 details:1 elements:1 separate:1 models:1 problems:1 a1:3 cleve:5 a3:1 a2:4 a4:2 variable:5 independently:2 correlated:1 algorithm:1 assume:2 interval:2 necessitates:1 together:1 furusawa:1 teleported:3 presenting:1 far:1 requires:6 having:1 once:3
|
quant-ph9906106.txt |@word concept:1 gs:2 consider:2 springer:2 caused:1 magnetic:9 fabricated:1 scalar:1 per:1 grateful:1 foundations:1 go:1 localized:8 sch:1 whose:1 inverse:1 subjected:2 tr:2 editors:1 rightmost:1 program:2 those:1 under:1 vrijen:1 kσ:1 case:3 fond:1 advantage:1 kraus:1 account:1 wave:1 electron:35 figs:2 resonant:2 matrices:1 quantized:2 level:8 tra:1 anisotropy:1 solution:1 large:1 solved:1 εkl:1 trs:1 prins:1 employing:2 sige:1 ten:1 deutsch:1 blatter:1 pulse:2 prevents:1 zero:2 rigorous:1 further:1 dynamics:6 estimated:1 kempen:1 nano:1 ere:1 sun:1 current:14 gi:1 above:4 flowing:2 new:1 increasing:1 method:1 filled:2 cτ1:1 respectively:3 realizations:1 component:1 here:2 atoms:1 reported:1 smearing:1 represented:1 change:1 obtained:1 turchette:1 tunneling:7 institute:1 vectors:1 reports:1 intradot:1 resulting:2 resonance:7 suitable:2 santa:1 clark:1 technologies:1 plenum:1 logical:1 unitary:3 operational:2 asi:1 unit:2 wang:1 gaas:1 usc:1 usa:1 remains:1 grabowski:1 coupled:2 charge:2 hong:1 few:2 therefore:1 taken:1 becomes:2 berlin:1 particular:2 known:2 retained:1 ρa:10 high:1 ρc:2 ma:5 ibm:1 mc:2 tunnel:8 science:3 work:1 mk:1 mt:2 ρs:11 ρr:4 obvious:1 ρt:1 transparency:1 following:1 metal:7 example:3 proof:1 ions:1 lσ:1 figure:2 escapes:2 clσ:3 sample:3 effectively:1 performed:2 times:3 axis:1 information:1 recovery:1 gci:1 discussion:1 algorithms:1 chemical:3 located:1 adjacent:1 gate:15 shortens:1 verlag:1 product:1 description:1 ancilla:10 after:4 mapping:1 br:1 applications:1 fe:1 magnetizations:3 parallel:1 consisting:1 man:1 realized:1 short:1 jiang:1 remember:1 third:1 si:2 negligible:1 allow:2 turnstile:2 pulled:1 order:2 grabert:1 typical:4 operations:1 hierarchy:1 vary:1 years:1 through:3 statistical:1 cold:1 still:1 ieee:1 its:2 before:2 sciences:1 group:1 apex:2 τdyn:8 lateral:1 tsc:1 actually:3 subsurface:2 fig:3 annual:1 instantly:2 non:3 similar:1 outlined:1 processes:1 effects:1 symposium:1 sσ:2 now:1 yu:1 discuss:1 represents:1 term:1 double:1 always:1 hamiltonian:6 mckinnon:1 2e:1 magnitude:2 each:2 found:1 notes:1 schemes:2 τe0:1 ed:1 energy:2 kane:4 µb:2 valiev:1 measurement:10 quantum:32 our:1 eq:1 mat:1 divincenzo:1 matrix:10 factors:1 since:4 rev:8 holevo:1 research:1 semiconductor:1 acting:1 vector:6 lecture:1 gov:2 ref:1 shows:1 turning:2 theory:2 barrier:4 contain:1 possibility:3 york:1 coey:1 org:2 estimate:1 jozsa:1 milburn:2 molotkov:5 interaction:11 organic:1 geometry:1 tolerant:1 silicon:4 thing:1 barriers:1 gif:4 first:2 exotic:1 dzurak:1 initial:3 probability:5 possessing:1 wiesendanger:2 devices:1 done:1 directly:2 size:2 given:2 temperature:2 district:1 los:1 interact:1 amsterdam:1 system:20 least:1 their:3 normalization:1 realization:1 scheme:4 bits:2 speaking:1 academy:1 moscow:1 transistor:1 larger:1 optical:1 authors:1 than:1 havel:1 relative:1 polarized:2 holland:1 stm:5 depends:5 preformed:1 preparation:2 states:7 determined:1 were:2 abstracts:1 russia:1 hz:1 comput:1 generality:1 geshkenbein:1 measure:3 kitaev:1 qualitatively:1 any:4 lie:1 efficient:1 isolated:3 εs:1 metallic:1 polarization:2 εl:1 lifts:1 take:1 finding:2 so:4 εc:3 added:1 shall:2 price:1 molecule:1 most:1 measured:3 observation:1 considered:2 chosen:1 steady:1 physica:1 proceedings:1 electrons:4 exp:1 subsequent:1 physics:3 dot:24 quantity:1 shor:1 tkl:2 supported:1 ioffe:1 chuang:1 line:1 finally:2 based:6 just:2 parameters:2 written:4 should:6 only:3 explicitly:1 he:1 local:2 do:1 gaalas:1 dependent:1 feigel:1 joint:8 cannot:1 combinations:1 during:3 dt:1 lahti:1 evolution:5 precession:2 densities:1 conditions:1 goldwasser:1 arxiv:3 microscopy:1 tuned:2 microscope:1 nauk:1 wish:1 pulses:5 fixed:3 voltage:4 scanning:2 set:1 electrodes:15 detection:7 see:3 computer:2 bare:1 result:2 recently:1 electrode:16 inversely:1 placed:1 nuclear:2 τres:14 dipole:2 µl:2 state:19 various:1 between:8 balandin:1 diagonalized:1 paramagnetic:1 discovery:1 available:2 pushing:1 terms:2 nature:3 initially:1 however:3 jr:1 suggested:1 both:4 last:1 fault:1 region:1 density:7 according:2 zeeman:1 quantization:1 tlc:1 sensitive:1 contribution:1 temporal:1 arbitrarily:1 among:1 point:2 dimensional:1 cirac:1 constant:2 pr:3 ps:2 described:4 tuning:1 three:2 reduction:2 describes:1 basic:1 ph:4 empty:2 systems:2 dots:19 isotopes:1 direction:2 arises:1 corresponding:1 restrictions:1 turned:2 concerning:1 xxx:2 coincides:1 zhetf:4 determination:1 external:3 spin:30 present:1 applied:4 josephson:1 structures:1 solid:1 appearance:1 will:1 while:1 suppose:2 behavior:1 situation:1 ultra:1 35th:1 demuth:2 procedure:3 devoret:1 studied:2 played:1 almost:1 thus:1 shvets:1 surface:7 equal:1 itself:1 cond:1 conf:1 march:1 busch:1 technology:1 different:4 make:1 format:2 same:2 quant:4 split:1 finite:1 castellano:1 difficult:1 evolve:1 used:1 http:2 barenco:1 numerical:1 effect:1 moment:8 levels:8 purpose:1 potentials:1 fabrication:1 identity:1 recent:1 dopant:1 task:1 off:4 center:1 well:2 without:1 materials:2 components:1 corporation:1 gsi:1 position:2 model:2 left:17 gates:5 magnetization:2 proposed:5 being:2 when:4 tcr:1 tcl:2 atomic:3 εr:1 heterostructures:1 note:1 zoller:1 hint:3 wen:1 instrument:3 potential:2 nato:1 lett:7 usage:1 untherodt:3 wiseman:1 gave:1 aspects:1 increased:1 easily:1 b53:1 results:2 possible:1 lanl:2 tunnelling:1 smallness:1 chernogolovka:1 vacuum:1 press:1 advanced:2 occurring:1 loss:1 tl:2 appearing:1 splitting:1 signal:1 specific:1 imposes:1 arbitrary:3 spins:10 specifies:1 exceed:1 right:10 some:1 back:1 growth:1 uspekhi:1 escape:2 duration:6 indirect:1 employment:1 separately:1 scale:5 describing:4 contacts:1 cσ:1 avoid:1 measurements:5 overlap:2 does:2 inject:1 provides:1 prof:1 leftmost:1 demonstrated:1 measuring:3 alamitos:1 detuned:2 ruf:1 bi:1 step:1 references:1 p31:2 cory:1 stage:1 about:1 central:24 discussed:1 repulsion:3 larmor:2 consequently:1 soc:1 publishing:1 into:5 within:1 obtaining:1 down:1 accounts:1 determine:1 proportional:2 spinors:1 van:1 additional:1 assumed:1 strictly:1 there:2 width:3 appl:1 way:2 kang:1 was:4 function:1 project:3 north:1 complete:4 form:3 hs:1 jun:1 shnirman:1 cycle:1 atom:3 russian:2 injection:1 proposal:1 coupling:1 made:1 whether:1 characteristic:6 ωr:2 probabilistic:1 up:2 us:3 ur:6 ul:5 below:4 problem:2 stages:2 ua:5 called:1 uc:1 required:1 associated:1 computing:1 int:1 certain:2 abstract:1 describe:1 general:1 single:15 dλ:8 accounting:1 pis:3 functions:1 compared:1 nl:2 nm:1 no:4 dashed:1 ekert:1 nc:1 tip:5 field:4 nlσ:1 role:1 papers:1 nr:2 ns:1 sufficient:1 mechanical:1 problems:1 prepared:1 crσ:3 generated:1 important:1 nucleus:7 allowing:2 previous:1 proceeding:1 structure:1 ago:1 auxiliary:1 coulomb:3 assume:6 requires:3 interval:2 microelectronics:1 together:1 time:30 jansen:1 resolution:1
|
quant-ph9906107.txt |@word limited:2 partial:2 consider:5 remarkable:1 varying:4 desirable:1 results:7 leads:4 grateful:1 maxima:1 go:1 spaced:3 expressions:2 denotes:2 contributions:1 carpet:15 increase:2 depend:1 calculate:1 aug:1 tn:3 german:2 finally:5 th:2 under:2 connecting:1 analogous:4 must:1 amplitudes:21 advantage:1 very:2 edn:1 implicitly:1 rise:1 wave:21 specific:1 associated:13 difference:1 exact:3 condition:16 states:1 generalised:8 entire:3 moderate:2 presented:1 permits:1 michael:1 applicable:2 t0:3 large:2 discrete:1 affect:1 small:15 enhance:1 referred:1 upper:2 unexpected:2 prediction:4 hillery:1 sign:3 approximation:5 generalisations:1 second:5 evaluated:4 follow:1 further:12 estimated:2 odd:11 substitute:1 even:16 index:2 appear:2 giving:1 sum:3 3v:4 expressed:1 uniform:5 en:10 3n:1 above:6 fractional:1 new:3 coordinates:1 method:1 contrast:3 leeuwen:1 2kv:2 predicting:1 simultaneously:1 respectively:8 slov:1 here:10 perpendicular:1 localisation:3 met:3 represented:1 consideration:1 along:20 standard:1 box:5 antisymmetric:3 52a:1 root:1 study:1 studied:3 completely:1 prior:1 periodic:8 resulting:1 professor:1 fourier:1 spacetime:12 cancellation:2 involves:2 carpets:6 via:21 useful:3 extra:1 summations:2 substitution:3 highly:1 modulated:1 decrease:2 summation:12 ipx:1 total:1 2φn:1 landscape:19 9v:2 plot:7 use:3 quasi:1 takes:3 would:1 recalling:4 positive:4 contains:1 predictions:3 periodically:3 comparing:1 noting:2 ψn:39 therefore:2 ψm:16 australian:1 type:1 theoretical:1 more:6 zeroes:1 formally:1 comparison:2 incident:2 becomes:1 factor:2 odinger:1 visibility:1 surprisingly:1 appendix:4 rigid:6 diffracted:5 particular:22 known:1 cases:5 hold:3 iii:1 easiest:1 dot:1 nπx:2 4l:2 account:1 crosses:1 effectively:1 equation:4 averaged:1 perpendicularly:1 remain:1 values:14 den:1 ulm:2 following:3 averages:1 example:23 vary:1 proof:1 figure:25 give:2 predict:9 dxp:3 high:4 indicates:1 minimum:2 dxk:4 dropped:1 arise:2 sharp:1 conversely:2 calculated:3 guarantee:1 lamb:1 information:5 end:3 provide:3 s2:1 s1:3 holds:1 s6:1 fortunate:1 regions:1 how:4 varies:2 significance:1 instead:1 axis:6 sin:10 product:1 sommerfeld:1 may:23 demonstrates:2 earlier:1 derived:3 plane:4 waves:7 requirements:1 horizontal:3 destructive:29 parallel:1 2l2:3 natural:2 effective:1 pv:1 whenever:1 light:5 lines:2 correspond:9 sk:27 rather:2 negligible:1 martina:1 representation:1 acknowledges:1 order:2 least:1 wigner:13 canberra:1 produces:1 numbers:1 developed:2 over:6 dy:1 constrained:1 satisfied:2 interpreted:1 including:2 2v:2 statistical:1 left:4 differs:1 captions:1 satisfies:2 wherein:1 its:1 before:1 destructively:1 write:1 group:1 symmetry:4 chosen:3 fractal:2 ll:13 vicinity:2 decreases:1 h2:2 humboldt:1 fig:1 travelling:19 πm:1 bialynicki:2 them:2 good:4 motivated:1 greater:1 wolfgang:1 introduce:1 primary:2 newman:1 φˆn:3 walls:3 φˆk:4 subtraction:1 they:3 acta:1 oxford:1 now:6 hall:1 structural:1 easily:3 february:1 2r:1 verifying:1 always:2 university:1 hamiltonian:1 sufficiently:4 davydov:1 magnitude:2 each:3 2l:18 found:2 universit:1 side:3 mean:1 afforded:1 weighted:2 ei:4 unravelling:1 series:1 energy:27 gaussian:9 related:2 solution:1 investigated:2 obtains:1 measure:2 quantum:19 wavelength:1 approximated:1 beyond:1 eq:1 special:4 borne:1 shown:10 restricted:1 rep:1 since:4 interference:36 semi:1 cancels:1 reineker:1 particles:3 re:3 rational:1 max:1 formula:4 2k:2 integrated:1 shows:1 foundation:1 numerical:1 turning:2 linear:14 free:1 quite:1 approaches:3 loinaz:1 elsewhere:1 eigenvalues:1 van:1 estimate:1 publication:1 degeneracies:2 pairs:1 derivation:2 recovering:1 widths:6 appearing:1 length:3 place:4 πk:5 hence:12 first:17 chopped:2 xk:5 there:4 xn:5 features:5 probability:46 ignored:2 supposing:1 number:7 channels:20 ranges:3 simplified:1 relations:2 directly:10 impossible:1 precisely:2 angular:1 passes:1 given:18 silent:1 similarly:6 introduction:2 leading:1 top:2 approximately:5 heights:2 their:2 assumption:1 πv:2 observations:1 πz:3 πx:5 πy:1 structures:45 ias:1 gives:3 relationship:1 ratio:1 explanation:3 shallow:1 accurately:1 optical:2 explained:2 x0:28 copy:1 than:7 coefficients:3 wide:3 superposed:1 determines:1 expansions:2 showed:1 sections:1 mh:1 see:5 propagator:1 incompleteness:1 determined:3 intensities:1 amplitude:15 were:1 providing:5 minus:1 enhancement:1 collecting:1 rewrite:3 correction:1 connell:1 locations:11 yielding:2 say:1 width:4 manner:1 close:1 need:2 seen:18 recover:1 clearly:3 relatively:11 lie:1 rearranged:1 zero:4 min:1 convenient:4 latter:6 coresponding:1 able:2 note:10 k2:3 potential:3 square:1 take:2 analogy:1 kaplan:4 so:1 many:1 channel:47 accuracy:1 heisenberg:1 led:1 though:1 who:2 phases:3 depths:6 most:3 involving:1 germany:1 ensure:1 significant:4 position:9 phase:14 analytically:1 extremely:2 class:1 patterned:1 considered:2 average:29 righthand:3 kl:10 2nd:1 points:4 generalising:1 kv:33 narrow:1 velocity:5 usual:2 physics:1 section:17 fact:3 slope:14 particularly:1 show:3 nπ:3 random:1 discovered:1 x2:1 bright:1 relation:3 kx0:1 substituting:5 analogue:2 trivial:1 ambit:1 based:4 dividing:1 scr:1 much:1 explain:2 outside:4 elucidated:1 analytic:2 only:12 subsection:1 indeed:7 mechanics:1 tude:1 pointed:1 dn:1 his:1 intersect:3 klein:1 distance:2 dependent:2 landscapes:2 connections:2 simplest:1 overall:2 expects:2 beam:2 cannot:1 dx:7 propagated:1 dt:4 subscript:2 2ml:1 alexander:1 greens:1 indicated:1 approach:32 arxiv:1 bodenschatz:2 yield:3 quasirandom:1 investigate:1 predicted:15 flanked:2 through:1 fixed:2 predictive:1 set:1 national:1 generalisation:1 maximum:3 observed:20 intensity:5 sec:1 usefulness:3 enhanced:1 recently:1 wψ:7 analog:1 saif:1 fails:2 αt:1 eigenstates:2 symmetric:5 written:1 various:4 between:12 consecutive:3 boundary:1 conditions:7 across:1 terms:7 reproduced:2 jz:1 nature:4 initially:2 suppose:3 analogues:1 however:8 jr:1 interfere:1 lefthand:2 vanishing:1 extent:1 jk:2 rapidly:1 eipx:1 suppressed:4 2pn:1 suggested:1 both:1 cos:12 last:1 2n:1 numerically:1 desired:1 freely:3 region:2 conclusions:2 equal:7 against:2 agree:1 propagation:1 berry:8 context:5 variance:1 passing:1 grossmann:1 expression:9 finds:2 otherwise:2 minima:2 alternate:1 cn:2 point:7 simple:8 corresponds:12 height:4 dimensional:16 directions:1 simply:2 πkl:1 applicability:2 moreover:5 schleich:6 considering:1 sine:1 described:1 illustrated:1 quantisation:1 trajectory:18 px:1 been:16 cosine:2 slowly:8 interest:1 kronecker:1 expected:4 pk:16 ph:3 pn:12 define:4 obtained:5 direction:5 arises:3 corresponding:19 quantities:1 essentially:1 corner:4 denote:2 those:2 case:26 p1:1 solid:4 appearance:2 value:1 eigenstate:1 will:15 kθ:1 while:3 replaced:5 evaluating:1 intercepts:1 rotator:6 endpoints:2 opt:2 cylinder:1 uncertainty:1 πjk:1 geometric:1 differentiating:2 averaging:1 von:1 thus:22 non:1 according:1 ii:7 itself:2 curved:3 discarded:1 vanish:2 result:1 confirms:1 verified:1 rotators:1 etc:1 generic:7 s2k:3 make:2 same:2 any:9 quant:3 wavepacket:3 modification:1 finite:1 breaks:1 difficult:1 used:3 trivially:2 i0:5 trajectories:12 upon:1 possible:1 running:1 moving:8 potentials:6 infinite:3 nl:4 centred:1 lower:2 inital:1 schr:1 reflection:1 band:1 onedimensional:2 colour:1 no:4 well:14 analysis:1 bohr:1 patterns:5 quantitative:1 plotted:5 arising:2 whereas:1 realised:1 reconstruction:1 just:2 less:4 being:1 when:12 starting:2 effects:1 press:1 shape:3 predicts:4 immediately:3 alternative:1 speed:3 yet:1 multiples:3 previous:1 adding:1 hills:1 density:14 5v:2 except:1 iψ:3 extends:1 location:1 grating:11 rost:1 scully:1 remaining:1 momentum:7 sˆk:4 real:4 australia:1 depends:1 evaluate:3 showing:1 sums:2 term:14 period:5 dark:3 increases:3 makes:1 background:6 confined:5 integer:12 part:2 intersection:1 mod:7 semiclassical:1 necessary:1 replacing:1 particle:13 follows:11 velocities:2 shapes:6 yields:6 either:4 integrals:1 arbitrary:4 translated:2 kinzel:1 probabilty:1 grouping:1 pertaining:2 valleys:1 wavepackets:9 classical:4 successfully:2 some:10 understood:2 strongest:1 examples:7 respect:2 multiple:1 extended:3 matching:3 eiα:1 provided:1 lead:2 bottom:2 broad:3 per:6 contributing:2 quantenphysik:1 does:3 decomposition:17 provides:9 leftmost:1 propagating:4 bessel:1 limitations:2 measures:1 run:1 power:1 bl:1 s4:1 equivalent:2 wavefunctions:12 obtain:4 agreement:2 constructive:3 abteilung:1 eiφ:8 plots:1 normalisation:1 properties:11 neighbourhood:1 analysing:1 integers:1 about:8 extension:1 gratings:2 discussed:3 dependence:4 o:4 2i:3 addition:1 range:3 sinusoidal:1 plus:2 greatly:1 act:1 definition:2 equally:2 localised:15 suppression:1 previously:5 pergamon:1 into:9 within:3 integral:1 negative:4 down:2 included:2 because:2 references:1 δk0:1 iπn:1 t76:1 performing:1 acknowledgements:1 ridge:23 ψk:18 normalised:1 assumed:1 support:1 initial:40 approximate:5 generation:1 accordingly:1 quadratic:1 low:2 way:1 2m:5 slopes:6 valley:1 was:5 eg:1 naturally:1 function:25 complete:1 form:7 energies:1 δkl:1 differences:4 lane:1 but:2 hoped:2 hk:1 link:1 delta:1 line:10 partially:1 wφ:5 arranged:1 whether:1 2πk:2 smooth:2 up:1 ur:1 below:3 fluctuations:3 distribution:26 quantised:3 similar:3 called:2 detailed:2 required:1 constant:5 defined:10 paraxial:2 abstract:1 orbit:1 influence:1 deep:5 general:11 single:1 right:3 dθ:1 marklof:1 πx0:2 physical:1 again:3 functions:22 paradox:1 entirely:1 dotted:1 variety:1 dashed:4 discerned:1 wavefunction:29 generally:4 vanishes:9 nx:3 other:2 details:2 suppress:1 test:1 out:2 picture:1 briefly:2 superposition:5 pronounced:1 generated:2 important:1 bounded:2 ridges:3 variable:1 birula:2 structure:46 independently:1 kx:2 implies:4 using:3 typically:4 interval:6 resolving:1 δx:4 rule:1 superpositions:1 depth:4 mass:3 lying:1 time:9 n2:1 requires:2
|
quant-ph9906108.txt |@word ibid:1 limited:2 concept:2 arrives:1 consider:6 ceases:1 saying:4 gupta:1 rev:4 equalities:2 varying:2 results:3 existing:2 leads:3 obstruction:1 quadrature:1 commute:2 consists:1 follow:1 localized:1 equivalences:1 compact:1 whose:3 certainly:1 const:1 rest:1 disposal:1 equivalence:3 including:2 removal:1 charge:17 ny:1 preserved:2 excluded:1 under:2 tg:4 include:2 presentation:1 magnetic:1 ingredient:1 p2:1 g3:3 g2:28 abelian:11 g0:4 far:1 rise:1 translations:2 springer:3 choice:4 every:2 stays:1 redefinition:2 infrared:3 deformations:1 condition:11 presented:3 did:1 positions:4 erratum:1 list:1 solution:1 leave:2 admissible:1 vector:1 irreducibly:2 section:3 small:1 gauge:9 equation:7 configurations:5 smaller:1 says:2 variables:5 direct:3 maintain:1 approximation:1 go:1 imply:1 cost:1 tangential:1 rigorous:2 further:2 fapp:2 contingent:1 even:2 trick:2 what:10 plays:1 appear:2 iterating:1 incompatible:1 specification:1 localization:1 expressed:2 d3:2 henceforth:1 consistently:1 issues:1 subspaces:1 basic:1 new:11 boost:1 contrast:1 satisfy:4 kijowski:1 justification:1 notions:1 degree:6 excludes:1 multipole:5 respectively:1 component:1 residual:1 here:11 highly:2 met:2 objects:1 possibility:1 groups:2 relaxation:1 represented:1 causality:2 along:4 standard:3 equations:10 appears:1 galilei:12 obtained:2 translate:1 glm:1 rigorously:1 technical:2 leaves:1 losses:1 allows:1 reason:3 amount:2 products:1 definitively:1 permutation:1 usually:7 makes:2 cancellation:1 involves:1 formulated:1 useful:1 projection:1 extra:1 requiring:1 merely:1 explained:1 replace:1 ask:1 support:1 glance:1 total:7 causal:1 unit:1 readily:1 derivatives:1 superpositions:3 would:12 commun:2 distinct:1 contains:3 quasi:1 next:1 calculation:1 helv:3 derivation:1 call:4 therefore:6 criteria:3 taken:3 zorn:1 more:11 introducing:1 formally:1 ambiguity:1 relevant:3 becomes:2 operators:10 apparent:6 odinger:7 validity:1 aware:2 berlin:3 labelled:1 particular:9 known:5 projective:1 hold:4 potential:5 must:9 involve:2 none:1 valued:2 room:1 sphere:1 recall:1 points:4 pretend:1 mi:12 modified:2 λj:1 obvious:5 following:6 vt:2 my:3 example:8 proof:3 control:1 compare:2 weaker:1 give:2 process:3 discussed:3 preserving:1 purposes:1 states:34 contradicts:1 sense:9 r12:1 tions:1 conversely:1 occur:1 charged:4 practical:1 scalar:4 rays:5 domenico:8 g1:23 turn:1 rather:7 verify:1 discussion:4 acts:6 feature:1 regions:1 maps:3 criterion:1 pure:4 significance:1 answer:1 instead:1 ordinary:4 parameter:1 simplicity:1 continues:1 constraint:1 description:1 algebra:14 may:6 after:2 mapping:1 minkowski:1 consequence:1 wrong:2 redundancy:1 physik:1 multiplication:5 requirements:1 law:4 constants:2 criticize:1 natural:3 dynamical:29 moments:4 sr:1 spectra:1 lines:1 correspond:2 redundant:1 projectors:4 ones:2 so:14 realizes:1 allow:3 suggest:2 representation:11 bleuler:1 looking:1 order:4 operations:1 restriction:3 holds:1 interpretation:4 help:1 considerations:1 giulini:13 indeed:1 over:1 fall:1 enlarge:1 furnishes:1 course:3 xi:14 through:1 statistical:1 argued:1 existence:5 poincar:1 its:10 environmentally:1 buchholz:1 supplemented:2 group:24 how:4 chosen:1 masses:5 relativity:1 coordinates:2 actually:2 destroyed:1 degrees:6 choose:2 fade:1 potentially:1 might:4 setting:1 outside:1 maximal:8 eventually:2 them:2 thereby:2 delocalization:1 integral:3 processes:1 functional:2 often:2 framework:7 walls:2 hamilton:1 they:12 acta:3 suffice:1 rotation:1 now:15 discuss:2 nor:1 possess:1 down:1 term:5 finite:2 dirac:6 fully:3 hamiltonian:9 identified:1 d3n:1 realistic:1 iff:5 l2:4 each:6 2m:1 universit:1 difficult:1 characterized:1 mean:1 subset:1 adjointness:2 formulate:1 map:3 hard:3 reduce:1 idea:1 elementary:1 literature:1 obtains:2 entering:1 measure:1 quantum:23 our:7 beyond:1 special:1 out:2 shown:1 fundamentally:1 space:28 restricted:1 nuovo:1 since:11 crucial:1 projected:1 denotes:1 particles:3 re:1 contained:3 strocchi:1 nontrivially:1 wick:2 induced:1 cause:1 occurs:1 math:5 shows:5 theory:9 assured:1 written:1 mechanisms:1 little:1 free:2 quite:1 completely:1 complicated:1 element:2 put:2 subalgebras:1 inconsistent:1 definition:3 pairs:1 r1:5 language:1 agree:1 via:3 times:2 motion:8 introduction:1 maximality:3 place:1 qualification:1 hence:20 subgroup:4 onto:5 think:1 first:4 xj:1 δh:2 already:5 xn:1 rooted:1 symmetry:12 bijection:1 relate:1 critique:1 theoretische:1 restrict:2 done:1 least:4 r2:3 representations:6 stated:1 precisely:1 light:1 illustrate:1 given:20 necessarily:1 rewritten:1 strict:1 bears:1 adjoint:1 system:12 relations:2 their:9 assumption:1 ug1:7 too:3 statement:4 molecular:1 structures:1 exponents:9 observations:1 commutativity:1 superselected:2 allegedly:1 tuple:1 asymmetric:1 distribution:1 serve:1 putting:1 simply:3 x2:1 off:1 translation:2 x1:1 representing:1 than:4 specify:1 localizations:1 perfectly:1 sectors:1 require:6 cimento:1 namely:1 modelled:1 project:1 classes:1 contrary:2 represents:1 were:3 similar:1 r3n:4 fashion:1 false:1 generality:2 footnote:1 electrodynamics:6 unchanged:1 mind:1 argument:5 curves:4 discussions:1 say:3 parameterized:1 conjugate:6 need:4 seen:2 seem:4 constrained:1 apparently:1 any:9 ray:15 lie:4 issue:1 jour:2 der:1 describe:1 convenient:3 self:3 responsible:3 able:1 ideas:1 admittance:1 converges:1 note:8 lifts:1 generalized:2 neither:1 coincide:1 canonical:4 apply:3 unless:2 fundamental:4 clash:1 opposite:1 object:1 reach:1 systems:2 joos:3 most:2 detect:1 connected:1 gauss:1 nothing:1 extremely:1 why:3 xµ:1 relates:1 treats:1 environmental:1 considered:5 partition:1 lattice:1 properly:2 nucl:1 principle:7 exp:9 sorts:1 velocity:1 effect:1 usual:2 notion:1 fact:5 laws:2 precise:3 impression:1 phenomenon:1 idealisation:1 show:2 violation:1 variational:2 labels:1 converge:1 purely:1 attempts:1 spaces:5 relation:3 solutions:10 wigner:4 trivial:7 find:2 current:1 based:1 just:2 kiefer:2 implementation:2 explain:3 behind:1 universal:1 should:14 lemma:1 only:17 quickest:1 removable:1 factor:1 local:10 zeh:2 meant:2 do:6 his:1 above:1 writing:2 means:6 dependent:2 xdn:1 express:1 overall:6 preferred:1 truly:1 cannot:8 legitimate:1 words:1 combinations:1 ug2:5 symmetries:16 2mi:1 boundary:12 evolution:1 initial:4 fields:3 arxiv:1 wightman:6 investigate:3 intervals:1 contain:1 switzerland:1 identify:2 raghunathan:1 fixed:1 setup:3 view:1 asked:1 requirement:5 set:8 motions:2 exists:2 achieved:1 physically:7 frame:1 proc:1 closures:1 relative:2 mentioned:1 depends:1 radius:2 truncating:1 misra:2 fail:1 inequivalent:2 λi:9 concern:1 lost:1 said:6 exponent:3 consistency:1 review:1 ranged:2 label:1 symmetric:1 state:8 smallest:1 various:1 boosts:1 closed:2 between:4 invariant:4 electric:3 conditions:9 preserve:1 ends:1 terms:5 spatially:1 adding:1 modify:1 complement:1 weak:2 however:3 implementing:1 vanishing:3 rapid:1 φlm:3 multiplier:13 analyzed:1 configuration:2 problem:1 topology:1 suggested:2 observable:2 essentially:1 realizable:1 last:1 2n:1 stationary:2 region:2 elm:4 equal:1 presentations:1 quantization:2 odds:1 admit:1 mildly:1 distinction:2 contribution:2 argue:2 whole:1 regarded:1 comes:2 flm:8 among:1 presumably:1 ch:1 characterization:1 reasons:1 had:2 corresponds:1 insist:1 dimensional:3 ab:1 anti:2 lagrange:3 moreover:2 superselection:51 stamatescu:1 forms:1 strong:1 transformations:3 second:1 source:1 addition:1 associativity:1 locally:3 chirality:1 due:5 been:2 rˆole:3 clashes:1 ph:16 algebras:1 ann:1 define:3 tg2:2 direction:1 tg1:4 general:8 unavoidable:1 commutes:3 quantities:3 sufficient:2 coherence:3 subspace:1 modelling:1 remarks:1 lift:1 understand:1 derivative:1 careful:1 irrelevant:3 those:6 case:11 multi:1 look:1 subsets:1 gervais:1 kupsch:1 quantenmechanik:1 commutant:3 appearance:1 discrete:1 remaining:1 will:15 invoking:1 suppose:3 momentum:1 applies:1 situation:1 property:3 couplings:1 procedure:1 vb:2 unitary:8 rescaled:1 almost:1 characteristics:1 von:9 thus:1 non:12 surface:5 ii:1 characterize:2 reads:1 itself:1 rij:2 against:2 rid:1 vanish:2 bargmann:6 containing:2 formalism:1 verified:1 combination:1 anymore:2 il:1 insofar:1 make:2 intrinsic:1 same:4 clearly:6 read:2 complex:2 quant:1 arguments:3 modification:1 resulting:2 defines:6 subalgebra:2 conflict:1 higher:2 independent:1 used:2 infinity:1 see:14 trivially:3 i2:1 upon:3 mutual:1 hand:2 action:23 urich:2 infinite:1 invariance:2 identity:1 task:1 schr:7 center:6 charges:1 expression:2 no:7 well:4 analysis:1 obviously:4 thought:1 concrete:1 mathematische:1 without:7 solve:1 components:2 sets:1 coordinate:1 model:2 latter:3 left:2 distances:1 world:1 rudolph:1 proposed:1 less:1 being:2 when:1 obtain:1 actions:3 underlying:2 cease:1 questions:1 immediately:2 localize:2 momenta:3 inversion:1 multiples:1 previous:3 zwanziger:3 heuristic:2 intersection:1 field:7 similarities:1 admission:1 point:6 seems:2 parametrization:1 mirrored:1 mathematically:3 simple:4 priori:2 lett:3 easy:3 theorem:2 input:1 formal:1 transformation:4 euler:1 take:1 real:1 iθ:1 iξ:3 rules:20 big:1 iγ:1 possible:3 molecules:1 λlm:8 pair:1 necessary:1 part:1 accepted:1 mod:3 loss:3 phenomena:1 imposed:2 like:1 particle:3 follows:4 reduces:2 serves:1 ignore:1 flux:3 continue:2 unstable:2 either:1 integrals:2 always:3 become:2 works:1 soft:3 topologically:1 δa:2 mathematical:6 parity:1 shed:1 because:3 old:3 qed:6 classical:7 sequence:1 interact:1 some:15 galindo:1 examples:1 b2:4 respect:9 proper:3 extended:4 proofs:1 matching:1 generates:3 happens:1 canonically:2 slice:1 represent:2 lead:1 unreduced:1 exhausts:1 avoid:1 shall:2 integration:1 per:1 get:1 everything:2 does:6 erich:1 expressing:1 grundlagen:1 stressed:1 straightforward:1 survive:1 inserting:2 ba:1 convincing:2 equivalent:11 broken:1 winterthurerstrasse:1 pascual:1 although:4 instability:1 refers:1 hilbert:9 asymptotic:2 chapter:2 about:2 kinematical:4 central:3 extension:6 algebraic:2 freedom:12 oc:7 factors:2 o:68 essential:1 compatible:1 union:1 range:1 a2:3 extensions:1 act:6 r4n:1 constraints:1 slightly:2 other:6 allowing:1 accessible:2 statements:1 inclusion:2 h2:1 maxwell:2 into:5 within:9 definitely:1 isomorphic:1 notoriously:1 suppl:1 accommodate:1 phase:6 appropriate:2 references:1 raises:1 formidable:1 operator:8 pointless:1 neumann:9 relativistic:1 additional:1 removing:2 strictly:1 there:9 question:7 approximate:2 long:2 class:4 start:2 restricts:4 conservation:1 pi:2 regarding:1 way:3 delocalized:1 was:3 naturally:1 function:4 arise:1 complete:2 form:4 laboratory:3 converse:2 jun:1 but:27 principles:1 volume:2 hi:4 gain:1 solved:1 larger:1 hb:1 subsidiary:1 level:1 true:3 observation:1 made:2 coulomb:2 intuitive:1 whether:1 wish:4 access:1 up:2 differentiable:1 different:6 below:1 limit:1 ug:8 jauch:10 called:10 b1:2 mechanics:12 sometimes:3 associated:2 defined:1 certain:9 abstract:3 sketched:1 am:1 textbook:2 denote:2 supersymmetries:2 exist:7 together:4 formulation:4 work:1 commuting:2 check:1 physical:28 again:3 functions:4 locality:4 generally:3 detail:1 application:1 disjoint:1 valid:3 dt:2 normal:3 spatial:4 test:2 really:2 concerning:1 conclusion:1 picture:1 elements:10 superposition:5 separate:1 necessity:3 inescapable:1 a1:2 generated:5 important:3 bounded:4 6n:1 vectors:1 variable:2 qψ:1 f00:1 existent:1 structure:5 matrix:3 rxi:1 lm:4 implies:8 using:1 dω:3 values:2 measurements:1 required:1 rule:18 equivalently:2 mass:15 time:11 observables:21 decoherence:11 quantity:1 requires:1 original:1 once:2
|
quant-ph9906109.txt |@word represent:2 now:2 consider:3 caused:1 magnetic:8 separates:1 results:6 four:20 eds:2 yamamoto:1 computation:13 issues:2 calculate:4 leung:1 re:10 alamos:3 equivalence:1 does:1 those:1 under:4 include:1 division:2 r12:6 r13:6 r10:2 r11:6 frequencies:10 hughes:1 wave:6 electron:2 figs:6 polytechnic:1 resonant:35 experimentally:1 difference:1 matrices:1 condition:4 rotating:4 level:1 positions:1 t2:1 solution:1 large:1 small:6 eigenvalues:1 der:1 degeneracy:1 measuring:1 smaller:1 destroys:1 pulse:38 feasibility:2 second:3 design:1 dynamics:33 implemented:7 even:1 index:1 errors:1 sub:2 section:6 analogously:1 3j:6 experiment:2 fortschritte:1 above:3 berman:2 new:4 acknowledgments:1 component:1 here:2 understanding:1 desired:3 selective:3 separation:1 relaxation:1 active:1 consideration:2 equations:1 change:1 obtained:1 involved:1 study:5 studied:4 allows:1 knill:2 action:4 resonance:1 implement:1 changes:1 involves:1 plenum:1 highly:1 apply:1 unit:1 eiωt:1 conventional:1 takes:1 working:1 positive:1 laflamme:3 negative:1 process:1 call:1 m0:1 taken:1 associated:2 type:1 theoretical:2 today:2 more:2 separated:1 formally:1 gyromagnetic:1 initial:31 company:1 particular:2 foundations:1 iii:3 must:3 high:2 springer:1 room:12 science:8 equation:6 work:2 modified:1 london:2 reviews:1 labeled:1 grover:4 values:11 following:10 strategies:1 example:6 control:5 computers:1 figure:1 calculation:1 bennett:2 neglected:1 states:10 numbers:2 degenerate:2 allowed:1 exclude:1 r23:7 r22:6 r21:1 axis:2 end:5 varied:1 eng:1 provide:2 utilize:1 delay:2 sate:1 pure:9 instead:1 r20:1 importance:2 sin:1 brassard:1 express:1 transforming:1 after:2 different:2 plane:1 physik:1 summarize:1 rdm:9 constants:1 realized:3 dynamical:1 liquid:3 register:5 relation:2 correspond:1 perform:1 negligible:1 order:2 se:1 operations:5 restriction:1 gershenfeld:3 least:1 indeed:1 satisfied:3 thermal:1 paper:5 through:3 same:7 mentioned:1 captions:1 still:1 excitations:2 its:1 regions:2 derive:1 iαx:3 energies:1 coordinates:4 isica:1 systems:2 rabi:4 non:32 rotations:1 fig:22 introduce:5 steane:2 effects:28 they:3 gate:41 accumulate:1 rotation:3 sixteen:1 discuss:1 bigger:1 finite:1 parameter:4 university:1 hamiltonian:10 ensemble:12 2e:1 l0:3 each:5 found:1 side:2 2j:3 significantly:3 ek:7 mesoscopic:1 energy:1 kane:1 idea:2 related:1 society:2 books:1 expect:1 measurement:1 quantum:83 laboratory:2 operation:4 transitions:4 special:1 divincenzo:3 shown:4 matrix:32 space:1 rep:1 rev:6 holevo:1 cancels:1 attracted:1 rn:1 induced:2 shows:2 earlier:1 interactions:3 diagonal:3 departamento:1 8e:1 indices:2 reason:1 advantages:1 york:1 besides:1 e1:5 e0:5 interaction:11 ion:1 could:4 transition:7 times:1 motion:1 american:1 δij:3 universidad:1 first:6 already:1 upper:1 opez:1 omitted:1 timeindependent:1 lond:1 multiplying:1 simplified:1 relations:1 compared:1 given:5 temperature:12 their:3 introduction:2 interact:4 insignificant:1 system:23 approximately:2 indicate:1 calculations:10 1j:2 bits:2 national:3 williams:1 gives:1 completed:1 transistor:1 part:3 eliminated:1 korotkov:1 than:5 coefficients:1 iωt:2 polarized:1 target:2 see:6 final:1 individual:1 amplitude:2 were:6 letters:1 function:6 correction:1 case:6 close:1 any:3 strength:1 convenient:3 agency:1 note:3 k1:3 take:1 destroy:2 coincide:1 techniques:2 europhysics:1 accuracy:1 pqrs:3 shall:5 molecule:5 most:1 brooklyn:1 significant:6 r30:1 class:1 r32:2 exico:1 kb:3 deviations:1 kk:1 average:1 proceedings:1 verlag:1 exp:3 levinson:1 physics:4 dot:1 shor:3 show:4 supported:1 dependences:4 discovered:1 aleiner:1 radio:1 lloyd:2 ωcr:2 cnls:2 ground:3 slow:3 ratio:2 parameters:20 implementation:4 state:24 should:4 only:6 subsection:1 molecules:12 equilibrium:1 do:2 notation:1 wide:1 dependent:4 zurek:3 de:2 cannot:1 despite:1 meir:1 evolution:4 precession:1 transversal:1 arxiv:1 investigate:2 pulses:7 fixed:1 ignored:1 requirement:1 set:2 reference:1 frame:1 j0:3 j1:2 j2:5 up:1 differs:1 depends:1 computer:8 r00:6 us:1 terms:3 ieee:1 subject:1 phases:4 yamaguchi:1 interacting:2 nuclear:10 ωk:18 label:2 initially:1 written:1 between:8 caves:1 conditions:20 knowing:1 recently:2 nature:2 qubits:11 attention:1 implementing:2 δj3:2 uω:3 extent:1 carbon:3 thank:1 suggested:2 both:3 cos:1 region:4 annual:1 according:3 zeeman:2 chosen:5 logic:6 0j:2 qubit:10 hρ:3 expression:1 experimental:1 load:1 cn:46 corresponds:5 proton:4 dimensional:1 decreases:1 cr:1 described:3 transformations:1 leads:1 basis:1 create:1 due:3 been:1 much:2 complicated:1 basic:1 expected:2 ph:3 choose:2 direction:2 corresponding:3 6e:1 sufficient:1 coherence:1 photon:1 external:2 c1:2 c0:2 spin:34 mcr:5 present:2 applied:2 inhibit:1 solid:2 value:9 transformation:2 will:1 error:1 35th:1 amplitudes:2 rnk:4 unitary:3 examines:1 orientation:2 00e:15 mexico:1 im:10 thus:1 ii:3 ih:1 ik:1 ij:5 rij:5 contract:1 rii:6 φij:1 ic:4 containing:1 verified:1 circularly:1 guadalajara:2 iα:3 complex:1 quant:3 pauli:1 defines:1 independent:1 used:7 i0:8 i3:4 numerical:9 usually:3 levels:1 uses:1 doolen:2 hospitality:1 normalization:1 recent:1 center:1 well:1 materials:1 solve:1 components:2 left:2 r01:6 gates:2 r03:6 r02:6 less:1 when:1 world:1 rotates:2 macroscopic:1 eigenstates:2 previous:1 loading:1 density:22 royal:1 realize:1 lett:3 excited:2 chuang:4 build:1 identical:1 around:2 read:1 decomposed:1 possible:1 ρkk:1 increases:1 press:2 using:6 excluding:1 follows:4 wingreen:1 mhz:2 james:1 become:2 security:1 conclusion:2 stationary:1 decimal:1 spins:12 therein:1 right:3 classical:2 sequence:3 some:4 duration:4 describing:1 confirm:1 cavity:1 electromagnetic:3 gurvitz:3 critical:4 prog:1 δj:2 proc:3 demonstrated:1 limitations:1 presented:3 varying:1 nmr:4 scientific:2 sixth:1 journal:1 use:5 eiπ:1 step:2 mainieri:1 imaginary:1 includes:1 simpler:1 chapter:1 about:3 works:1 central:1 discussed:1 dependence:4 o:1 reduced:1 kwiat:1 range:1 neighbor:1 consequently:1 soc:2 real:1 publishing:1 presence:1 communication:1 into:2 within:1 numerically:6 jα:6 three:1 because:4 references:2 determine:1 operator:2 proportional:1 prepare:1 assumed:1 there:1 approximate:1 fast:3 r31:1 los:3 appl:1 series:1 r33:6 was:8 hz:1 complete:2 form:3 jun:1 but:2 atom:1 rji:1 made:1 applying:1 places:1 characteristic:3 ωt:2 devices:1 placed:1 below:6 frequency:19 exploration:1 demonstrate:1 similar:1 calculated:1 constant:7 computing:1 defined:3 abstract:1 contribute:1 influence:16 oscillations:1 single:23 exist:1 our:6 regime:1 functions:1 codes:1 jcr:3 generally:1 field:7 other:9 becomes:3 department:2 mathematics:1 ny:1 deviation:4 symposium:1 elements:10 excitation:1 separate:1 hirota:1 problems:1 prepared:2 important:1 ising:6 stodolsky:1 algorithm:2 assume:7 required:2 resolving:1 fact:1 time:18 n1:1 decoherence:2 4e:1 requires:2
|
quant-ph9906110.txt |@word consider:5 illustrates:1 magnetic:1 results:2 four:4 computation:2 consists:2 depend:2 finally:1 th:1 amplitudes:1 orthogonal:1 wave:10 print:8 mattle:1 experimentally:2 matrices:1 condition:4 swapping:1 presented:10 turns:1 solution:1 large:1 vector:1 optics:1 lloyd:1 second:2 further:1 established:1 what:1 section:4 version:1 above:2 consisting:2 contrast:2 simultaneously:1 teleportation:27 here:3 atoms:1 iσy:5 others:1 change:1 obtained:5 sender:2 vectors:9 allows:2 resonance:1 bob:15 composed:1 named:1 useful:1 projection:8 classification:2 logical:2 outcomes:8 hardy:1 total:1 unit:2 use:3 would:2 contains:1 cory:1 noting:1 ψn:3 therefore:1 themselves:1 more:2 separated:3 share:4 operators:6 cases:2 hold:1 involve:1 science:1 equation:1 work:2 oscillator:1 following:4 example:2 control:1 boschi:1 figure:3 process:2 expanding:1 bennett:1 organized:1 states:13 tag:1 teleport:2 needs:7 end:1 acts:1 feature:1 instead:1 parameter:1 brassard:1 product:1 may:1 after:1 bourennane:1 choice:1 realized:2 light:4 ghz:13 element:2 claire:10 so:3 martini:1 operations:5 horne:4 produces:1 indeed:3 over:1 flips:1 experiments:1 looks:1 affect:2 its:1 before:1 teleporting:4 chosen:1 choose:2 communication:1 main:4 them:2 introduce:1 they:1 half:2 now:1 easily:1 level:1 magnitude:1 mode:1 each:6 found:1 2n:6 polzik:3 series:2 measurement:13 quantum:8 our:3 operation:1 ep:7 out:2 shown:1 accomplish:3 network:4 space:4 rev:8 projected:1 bennet:1 particles:18 acting:2 performs:4 c35:1 c34:1 ref:1 linear:3 retrieved:1 transfer:1 reason:2 base:1 imagine:1 put:1 ore:1 jozsa:1 molotkov:1 pairs:1 chiral:1 counterpart:2 πk:8 first:3 initial:11 features:1 variables:1 number:3 parkins:1 another:1 impossible:1 message:1 lidar:1 given:2 rewritten:1 similarly:1 introduction:1 unknown:15 system:4 their:2 realization:1 scheme:3 recovered:2 continuous:1 optical:2 than:1 polarized:1 target:1 fuchs:1 transferred:1 crepeau:1 outcome:4 projections:2 generality:1 turned:1 say:2 greenberger:4 recover:5 demonstration:1 any:2 conversion:1 traditionally:1 built:1 zero:2 general:1 gorbachev:1 note:2 instance:2 take:1 transmit:1 channel:2 shall:1 who:2 eight:4 nothing:3 observation:1 considered:4 braunstein:3 h2n:1 exp:1 fact:1 particularly:1 ψghz:2 loock:1 find:2 popescu:1 written:1 should:1 only:8 bases:1 local:1 do:3 his:5 means:2 dependent:1 de:1 joint:13 arxiv:1 motion:1 common:1 qn:4 set:18 ψep:8 achieved:1 depends:1 result:4 ways:1 nuclear:1 receivers:10 ralph:1 qubits:12 state:35 between:3 triplet:9 terms:2 nature:3 initially:1 however:6 both:7 equal:3 σz:1 σx:5 receiver:1 qubit:19 expression:1 experimental:1 among:1 point:2 wootters:1 pp:1 basis:25 three:12 been:5 combined:4 ph:9 pn:4 fig:3 cerf:1 generating:1 controlled:1 sorensen:2 sufficient:1 photon:2 zeilinger:5 coherent:1 maximally:17 case:3 kimble:3 value:1 will:3 while:1 suppose:1 situation:1 procedure:4 unitary:10 non:1 ij:1 different:3 weinfurter:2 perform:2 unity:1 quant:9 pauli:2 pan:2 independent:3 used:3 i5:3 i4:2 moment:1 harris:1 entanglement:18 identity:2 task:4 epr:27 vaidman:1 without:1 solve:2 sets:2 parametric:1 usual:1 protocol:4 proposed:1 being:1 distant:1 spatially:3 density:5 bell:3 iϕ:1 source:1 lett:6 c12:2 transformation:9 generalized:2 decomposed:1 possible:2 entangled:22 using:11 unique:1 loss:1 rotate:1 necessary:2 like:1 particle:22 follows:2 alice:14 separately:3 inter:1 reduced:2 adami:1 because:1 classical:1 sends:4 ijk:1 describing:1 broadband:1 affects:1 does:7 demonstrated:1 measuring:3 expansion:2 hadamard:2 rus:1 includes:3 hilbert:3 discussed:2 furusawa:1 obeys:1 connected:3 introduced:2 projectors:2 presence:2 h2:1 h3:2 into:3 h1:3 h4:1 h5:1 down:1 pair:27 references:1 parties:3 operator:5 van:1 u8:1 her:4 u5:2 u4:2 u7:1 there:2 u1:3 u3:2 u2:2 daniell:1 way:1 function:9 complete:5 form:10 differences:1 jun:1 but:1 hn:1 atom:1 true:1 consist:2 versions:1 uk:5 problem:3 similar:1 called:1 inclusive:1 defined:4 abstract:1 denote:1 peres:1 single:5 corresponding:3 physical:1 bouwmeester:2 field:1 other:1 branca:1 elements:3 superposition:3 u6:1 reached:1 prepared:2 important:1 prepares:1 structure:2 matrix:3 correlated:2 required:4 together:1 teleported:1 nelson:1 original:1
|
quant-ph9906111.txt |@word 1st:2 limited:1 logarithms:1 japan:1 consider:10 remarkable:4 illustrates:1 informally:1 desirable:1 results:4 extends:2 executing:1 abelian:1 widely:1 computation:17 consists:1 query:55 research:3 worked:1 issues:1 relationships:1 whose:7 c0:4 depend:2 ozawa:1 gcd:3 concerned:1 deterministic:7 vs:1 factoring:12 tn:1 rightmost:1 asking:1 indicate:1 those:2 under:2 alberta:1 nodes:1 include:2 alternations:2 traditionally:1 resources:2 adleman:1 alternating:2 applied:3 updated:1 labels:1 amplitudes:4 string:10 straightforward:4 very:3 reversibility:1 tends:2 subject:1 choice:1 implicit:1 coprime:1 additional:1 summarized:1 application:2 affect:2 exact:7 høyer:4 condition:1 ibm:1 groups:1 randomness:1 induced:1 subsets:1 solves:15 level:3 transmission:1 turns:5 who:3 list:1 solution:2 fewer:1 negates:1 large:6 solved:1 convenience:1 vector:3 phase:1 math:1 section:4 small:8 intersection:4 upper:3 approximately:4 version:5 deutsch:8 quantifiers:2 dealing:1 estimates:1 factorization:2 goldreich:1 outcomes:4 second:3 cost:3 design:1 evaluated:1 follow:1 notwithstanding:1 initialized:3 implemented:4 odd:1 machines:3 linear:3 even:11 aim:1 what:4 xor:2 power:2 richard:1 t2n:1 performs:3 specification:7 interpolation:1 supplied:1 uniform:9 access:1 errorcorrecting:1 fortschritte:1 above:11 polylogarithmic:2 net:1 ever:1 consisting:6 stabilizer:1 pictorially:1 margolus:1 full:1 degree:2 exchange:1 a400:1 respectively:1 error:11 modify:1 here:7 refinement:1 simon:10 compressed:1 separation:1 situation:1 represented:5 consideration:2 standard:2 directions:1 appears:2 change:1 knowledge:1 obtained:2 sending:3 search:9 accomplishes:1 eiπ:1 technical:2 involved:2 leaves:1 larger:2 completely:1 later:2 council:1 accomplished:2 symp:10 resulting:3 pomerance:3 usually:4 complicated:2 implement:1 suitable:1 changes:1 involves:1 amplification:1 composed:1 boykin:1 via:2 useful:3 family:23 extra:2 distributed:2 merely:2 explained:3 engineering:1 root:1 highly:2 mor:1 boolean:2 send:3 issue:1 δn:1 total:5 establish:2 unit:1 solovay:3 holevo:1 use:4 asymptotic:1 uniformity:6 prove:2 recalling:1 positive:2 lengthened:1 coins:2 toffoli:4 chooses:1 next:4 scenarios:3 few:1 noting:1 call:1 therefore:6 memory:1 taken:4 kremer:1 associated:4 25th:1 msc:1 entails:3 diagrams:1 more:22 possession:3 bennett:3 formally:2 fortnow:1 buhrman:5 started:1 outputs:3 operators:1 adjacency:1 about:2 discovering:1 reversible:14 varying:1 known:15 foundations:3 cases:5 hold:1 td:1 must:11 logarithm:1 md:4 springer:3 bernstein:2 anything:1 err:2 erratum:1 science:8 der:1 work:5 london:4 worth:1 remain:1 grover:9 values:7 norm:1 evolved:2 determining:1 following:3 making:4 converse:1 example:18 proof:5 control:1 employs:1 figure:11 give:1 process:2 beals:1 allowed:1 zeroes:1 purposes:1 implementations:1 states:8 unbiased:1 2nd:1 minimum:2 something:1 want:1 sense:12 every:1 tolerant:5 absolute:1 information:20 counting:2 end:1 advantage:3 turn:1 rather:5 discussion:1 holds:2 feature:1 machine:2 maps:8 nontrivial:2 adapted:1 pure:1 significance:1 answer:3 gate:58 strong:1 parameter:2 priori:1 brassard:4 inputs:11 product:6 proc:20 description:2 capture:1 may:3 turing:6 fz:8 after:5 mapping:5 ball:1 reflect:1 consequence:1 produce:3 physik:1 existential:4 date:2 erroneously:1 inconceivable:1 meaningful:3 response:1 constants:1 efficiently:2 proceeds:1 short:2 natural:10 third:1 whenever:1 slightly:2 goal:12 explicit:3 provide:1 complexity:84 algorithms:29 allow:2 farhi:1 definitions:2 imply:1 order:10 nearly:1 operations:27 exclusive:3 executed:1 aforementioned:2 noteworthy:1 numbers:3 over:3 vary:2 satisfied:1 produced:1 held:1 computational:38 through:2 twoqubit:2 thesis:1 differs:2 existence:1 still:1 ieee:4 its:12 earlier:3 perfect:2 sciences:1 thank:1 how:3 chosen:1 interesting:8 xm:3 translation:1 methodology:1 actually:4 destroyed:1 willing:1 fig:14 intl:2 hidden:1 main:1 might:2 setting:4 outperform:1 freeman:1 them:6 affected:1 greater:1 thereby:1 yn:5 press:1 dam:3 vectors:1 practice:2 30th:1 regarding:1 introduce:2 disregarded:1 they:6 optimal:3 resource:3 now:9 nor:1 structural:1 channels:1 several:3 stated:2 name:1 2s:10 always:3 university:4 presented:1 annals:1 identified:1 distributive:1 sufficiently:1 ussr:1 transmitted:1 parameters:1 reasonable:4 each:26 inherent:1 2n:29 polynomially:9 macchiavello:1 notes:3 mean:1 subset:1 ann:9 domain:2 schemes:3 directly:1 doing:1 series:1 approximates:2 related:7 conventions:1 constitute:1 errs:6 logd:6 extended:1 interplay:1 refinements:1 encodings:2 quantum:154 our:2 operation:16 t1:3 eq:13 event:2 special:3 out:6 canada:2 try:2 ultimately:2 accomplish:1 lenstra:1 matrix:6 3rd:1 factors:5 restricted:2 since:12 rev:4 unknown:2 denotes:1 fx:31 adapt:1 precision:2 reader:3 denoted:2 lecture:3 get:1 illustrate:1 suffices:3 correct:2 indicating:1 shows:2 1n4:1 weaknesses:1 log2:4 theory:16 recently:1 found:2 rumely:1 surveys:1 quite:4 vazirani:3 reason:1 base:1 advantages:1 ask:2 beginning:1 inevitable:1 encode:1 definition:1 fa:10 starts:1 could:3 computers:1 messages:1 βy:3 times:1 ordering:1 length:3 exponentially:4 circuit:127 assumed:3 hence:3 quadratically:3 broken:2 generalizations:1 think:2 first:10 xk:7 initial:3 xn:13 features:1 probability:27 encoding:12 bijection:1 mistakenly:1 number:28 restrict:2 instances:1 xy:1 done:1 least:3 another:7 frequently:2 impossible:2 message:1 precisely:1 zalka:2 occurred:1 size:29 idea:1 given:5 necessarily:1 smaller:3 their:3 introduction:2 data:5 top:1 29th:1 system:12 construct:4 pinned:1 needed:1 convention:1 siam:6 scheme:6 bits:30 final:8 speaking:1 back:1 implements:1 relationship:2 derandomization:1 ownership:1 johnson:1 continuous:1 esoteric:1 agree:1 padding:1 technique:1 part:2 incur:1 extensions:2 somewhat:3 x2:4 x0:27 x1:25 representing:2 than:21 specify:1 royal:4 finitely:2 distance:1 kind:2 translate:1 critically:1 nonreversible:1 collectively:1 approximations:1 database:1 tree:2 computes:11 preparation:1 matter:1 individual:1 kth:1 store:2 amplitude:5 were:1 accessed:1 outcome:1 result:8 popescu:1 m2:1 specifiable:1 comput:2 ran:1 lines:2 michele:1 reduction:1 measure:2 argument:1 bitwise:1 randomly:1 already:1 say:10 manner:2 conjugate:1 need:2 aharonov:1 seem:1 weinfurter:2 apparently:1 any:36 seminar:1 helpful:1 conversion:2 constructions:1 depending:1 efficient:11 convenient:2 latter:2 responsible:1 able:2 aside:1 spiller:1 note:23 instance:7 concerns:1 take:1 5th:1 finding:7 so:11 techniques:2 switching:1 accuracy:9 calculus:1 formulas:1 begin:4 exactly:3 entanglement:3 fundamental:2 test:1 shall:2 jun:1 informatsii:1 technicality:2 systems:3 most:16 involving:3 encodes:5 significant:1 preliminary:1 pair:1 coin:2 measured:4 why:3 appear:2 invertible:2 consequences:1 31st:1 considered:3 clear:2 sometimes:3 flow:2 countable:1 sources:3 principle:2 inaccuracies:2 mechanical:1 usual:1 typically:1 notion:1 fact:13 quantity:1 precise:1 shor:5 simulate:7 show:2 0n:3 random:7 converge:1 discovered:7 russian:1 mfcs:1 relation:1 expressed:3 threshold:1 subtle:1 determined:3 trivial:1 find:6 substituting:1 help:1 current:1 partially:1 based:4 simulating:3 spite:1 similarity:1 produces:3 inserted:1 behind:1 supported:1 should:2 penalty:1 only:13 explicitly:2 black:1 semantics:2 factor:5 employed:1 amplify:1 local:6 interested:1 do:2 his:1 dominant:1 intersect:1 notation:6 means:3 dependent:1 uncountable:1 zurek:1 de:2 designated:2 flips:1 methods:2 joint:1 cannot:3 legitimate:1 words:2 despite:1 combinations:1 during:2 quantifier:1 conjunction:1 procedures:1 him:1 stoc:6 prime:4 acm:6 evolution:1 multiplying:1 nisan:1 settings:1 shy:1 arxiv:1 yield:3 acknowledgments:1 whether:10 paper:1 common:1 queries:49 garey:1 including:1 fortunately:1 fixed:1 explanations:2 require:1 mosca:5 searching:3 reveals:1 requirement:1 set:19 decides:1 computed:2 exists:17 edited:1 physically:1 generally:1 testing:8 lett:2 flip:3 relative:1 y1:4 see:13 computer:11 introduced:1 usefulness:1 y0:4 primality:10 unaltered:1 11th:1 flavor:1 best:7 wonder:1 sequences:1 israeli:1 satisfying:1 tensor:2 multiparty:1 ways:2 αx:9 review:1 currently:8 icalp:1 state:29 smallest:4 various:2 permutes:1 correctly:1 between:11 neither:1 approach:2 email:1 discovery:1 available:2 notice:1 attention:1 terms:9 tapp:4 extend:2 complementary:1 qubits:22 weak:1 suppresses:1 transpose:1 however:1 efficiency:3 subgroup:1 sleator:2 distribution:3 34th:1 both:11 essentially:3 nishimura:1 hebrew:1 many:1 according:1 called:4 sensitive:2 involve:1 context:6 lo:1 qubit:39 estimation:1 expression:1 boyer:1 otherwise:2 arbitrarily:1 among:3 english:1 cn:10 point:3 simple:8 overview:1 ca:1 combinatorica:1 unitary:23 corresponds:3 cd:2 dimensional:1 alone:1 carlo:1 simply:1 xi:2 church:1 polynomial:11 respect:4 cook:1 writing:1 appeared:3 society:4 pr:1 wigderson:1 pp:37 applies:1 described:2 transformations:2 basis:8 2k:11 px:11 py:7 he:2 three:5 been:5 quickly:1 cient:1 much:2 combined:2 interest:3 basic:10 applying:5 ph:10 abstract:3 define:7 box:1 graphical:1 arises:1 corresponding:5 versa:2 mind:1 sufficient:2 further:1 cambridge:1 correction:1 realizable:1 understand:1 kitaev:2 modulo:1 c3:1 c2:4 c1:13 general:5 wolf:2 protocols:5 case:17 13th:1 exponential:4 defining:1 henceforth:2 harder:1 twenty:1 value:16 choices:1 will:7 euclidean:1 suppose:6 bounds:5 behavior:2 freely:1 associating:1 revisited:1 property:5 limitations:1 guide:1 procedure:1 yi:2 would:3 qxk:1 park:1 ip:10 von:2 simulations:1 thus:5 non:6 discrepancy:1 itself:1 equality:1 communicating:1 conf:4 ax:1 claimed:2 ignoring:1 interacts:1 coefficients:1 nielsen:1 binary:13 different:8 perhaps:1 develop:1 combining:1 perform:10 raz:2 make:6 amount:2 same:4 clearly:2 complex:2 quant:10 virtually:1 established:1 evaluate:3 avoids:1 survey:1 finite:8 composition:1 difficult:2 development:1 independent:2 used:8 receives:1 barenco:1 lie:1 yao:3 effect:3 counterparts:2 hand:4 running:1 nk:3 uses:3 kushilevitz:1 never:1 infinite:1 changing:2 randomized:1 bob:35 identity:1 simulates:1 lower:6 scenario:9 possibly:1 nevertheless:1 makes:7 well:6 analysis:1 thought:7 incorporated:2 solve:6 sets:9 marked:1 model:36 ekert:2 left:2 gates:68 world:1 protocol:21 37th:1 just:5 less:3 being:4 when:17 networks:1 obtain:2 actions:1 unary:2 λb:1 transforms:2 questions:3 integer:1 regardless:1 alternative:1 speed:1 ams:1 sampled:1 execution:2 preprint:12 extracted:1 conclude:1 seems:3 except:1 exploits:1 reasons:1 operator:1 other:11 transformed:1 treatment:1 easy:3 theorem:23 usage:1 input:35 extensive:1 unitarity:1 transformation:7 ought:1 nasa:2 identical:1 satisfiability:11 depends:4 eigenvalue:1 big:1 measurement:5 possible:8 np:3 game:1 completeness:1 five:2 logical:1 quasirandom:1 confined:1 using:18 bit:21 unique:1 moreover:3 mod:6 39th:1 strengths:1 necessary:5 like:4 follows:8 alice:25 translates:1 specific:3 communications:2 true:1 examine:1 yields:4 sparse:1 arbitrary:5 multiplicative:3 output:17 fault:5 fy:31 preskill:1 specifies:1 parity:21 exceed:1 right:1 laflamme:1 neumann:2 classical:52 discrete:4 sends:3 conditional:1 some:36 somehow:3 global:1 understood:1 convey:1 specified:2 distinct:1 peter:1 embodied:1 vol:26 scale:3 primary:1 bottom:1 demonstrates:1 measurements:2 comments:2 does:2 linearly:1 distinguishing:1 assuming:2 ucalgary:1 steps:1 closely:1 tk:3 refer:1 measuring:1 particular:1 replaced:1 scientific:1 indicated:1 intimate:1 performed:1 uniformly:1 equivalent:1 processing:1 ben:1 translated:1 substituted:3 polynomials:4 although:9 2m:3 hadamard:4 relating:1 obscured:1 permitted:4 cnot:1 takes:5 integers:1 acquire:2 actual:1 working:1 extension:1 commutator:1 tracing:1 certainty:1 discussed:2 peredachi:1 o:61 simulation:5 practical:1 strassen:2 chor:1 plus:2 vatan:1 monte:1 ti:2 referred:3 consequently:1 individually:1 own:2 simulated:5 gutmann:1 communication:50 into:10 within:6 bound:8 due:2 down:1 included:1 appropriate:1 square:2 references:2 raises:1 determine:6 parties:3 elementary:2 accumulated:1 refined:1 rounds:1 theoretically:1 technically:1 sipser:1 van:3 log:43 her:1 roychowdhury:1 probabilistic:23 strictly:1 there:52 question:2 approximate:4 fast:4 rigorous:2 contrapositive:2 workshop:1 lov:2 inner:4 way:6 overhead:1 conceivable:1 instead:1 was:5 function:25 considerably:1 himself:1 complete:1 form:9 enough:1 proving:1 smolin:1 differences:1 denoting:2 but:14 sophisticated:1 calgary:3 construction:1 gain:1 knill:2 encoded:1 goldstone:1 irreversible:1 themselves:1 auxiliary:4 made:2 compute:6 rogers:1 consist:1 versions:1 circuits:22 logic:1 variations:2 up:6 us:4 until:1 assume:2 below:1 converted:3 limit:1 verification:1 observation:1 highlight:1 problem:90 similar:7 emit:1 eigenvector:1 obtains:3 detailed:2 bearing:1 predicate:1 required:6 constant:21 28th:1 computing:20 defined:17 stronger:1 universal:16 describe:2 linearity:2 generating:1 proven:2 denote:2 single:3 ar:3 exist:2 promised:1 field:5 families:10 formalism:1 quantph:3 approximated:1 defines:1 vertical:1 functions:5 codes:1 receive:1 no:18 computations:1 whereas:1 nd:2 composite:3 valid:1 compares:1 details:3 quantities:2 department:2 mathematics:1 satisfiable:3 applications:1 arithmetic:2 recursive:2 elements:5 tight:1 problemy:1 divincenzo:2 models:3 become:1 problems:18 shown:11 inherently:1 subsume:2 cleve:9 generated:1 important:2 bounded:13 studied:1 variable:1 formal:1 focs:5 intuitively:1 n2:8 structure:3 independently:1 implies:2 faster:1 algorithm:54 vice:2 controlled:11 n4:3 proposed:1 space:4 mask:2 together:1 original:4 4n:1 portion:1 implied:1 personal:1 4k:1 time:4 far:3 n1:5 decoherence:1 n3:1 requires:6 strings:4
|
quant-ph9906112.txt |@word limited:4 sci:1 consider:2 rev:5 results:4 generalize:1 subclass:1 computation:14 query:3 expressions:1 denotes:3 causes:1 relationships:1 inverse:1 const:2 leung:2 knill:2 equivalence:2 tr:1 tq:3 program:1 indicate:1 those:1 under:2 dramatically:1 resources:1 henderson:1 case:2 supported:1 far:1 stipulate:1 tradeoffs:2 worst:2 decide:1 experimentally:1 difference:1 continued:1 condition:9 entire:1 solves:1 large:1 solved:2 small:1 eigenvalues:2 lloyd:1 abbreviated:1 unexpected:1 verifiable:1 deutsch:4 demonstrations:1 second:3 cost:1 further:1 implemented:1 amplified:1 machines:2 theory:2 even:3 what:1 errors:3 above:1 mosca:5 new:2 increasing:2 method:1 contrast:2 satisfy:4 led:1 error:3 here:1 desired:2 amplification:1 operating:2 σxi:1 represented:1 along:1 imperfections:1 obtained:1 ultra:1 provably:1 study:2 typically:1 products:1 suggestion:1 bob:7 fourier:1 changes:1 involves:1 deterministic:5 depart:2 projection:1 summations:1 outcomes:2 analyzing:1 apply:2 total:1 post:1 alamitos:1 confidence:1 would:4 prove:2 classically:1 therefore:5 criteria:1 taken:1 type:1 more:3 hqa:14 successful:1 outputs:2 factor:1 surprisingly:1 accept:1 particular:1 known:3 cases:2 states:12 ibm:1 2yi:2 science:3 originally:1 work:4 modified:1 grover:1 ρu:1 believed:1 hansen:1 averages:1 example:1 proof:2 omit:1 thermally:1 allowed:1 implementations:3 high:1 minimum:2 performed:3 arise:1 simulation:1 distinguishable:1 occur:1 information:4 carriers:1 hoi:1 how:1 hot:4 pure:8 answer:6 symposium:1 ensemble:6 inputs:5 product:1 paramount:1 may:4 max:1 constraint:1 applications:1 produce:2 parallel:1 types:1 efficiently:2 effective:1 following:9 register:3 σzk:1 complexity:4 σzi:5 algorithms:24 allow:1 operations:3 restriction:1 gershenfeld:3 ith:5 produces:1 indeed:1 over:6 insight:1 held:1 thermal:9 through:2 affect:1 existence:2 satisfies:3 suffer:1 ieee:2 before:1 thank:2 interesting:1 imperfection:1 better:1 degrees:1 systems:1 isaac:1 might:2 yi:4 them:1 good:1 return:1 practice:1 operator:2 they:4 half:1 now:3 represents:1 february:1 several:1 2q:1 james:1 university:2 2x:1 realistic:3 each:3 found:4 2n:13 polynomially:13 macchiavello:2 ei:19 significantly:1 simplicity:1 doing:1 reduce:1 related:5 slowdown:1 elementary:1 obtains:2 measurement:5 quantum:37 our:3 operation:5 eq:8 out:3 shown:3 fundamentally:1 space:1 furthermore:2 since:7 crucial:2 research:1 looking:1 similarly:1 performs:1 ancilla:6 print:2 correct:1 shows:1 linear:1 standard:3 vazirani:1 difficulty:1 advantages:1 term:2 jozsa:4 starts:1 computers:4 feasible:1 place:1 exponentially:2 assumed:1 hence:2 retain:1 qn:1 onto:1 unmodified:1 first:4 separable:1 ability:1 initial:11 probability:3 powerful:2 number:5 oracles:1 lond:3 clear:2 least:3 directly:1 robust:1 impossible:1 xq:3 open:1 size:1 given:5 long:1 become:1 unknown:2 eqs:1 πi:1 system:3 construct:2 needed:2 chem:1 observations:1 realization:2 final:3 gives:1 imperfect:1 relationship:1 observable:1 proving:1 part:1 lieven:1 than:6 havel:1 achieves:1 determines:1 fahmy:1 require:1 likely:1 determined:1 providing:1 distinguished:1 entail:1 correction:1 affirmative:1 randomly:1 seem:1 demonstration:1 any:2 viewed:1 strength:2 min:3 efficient:1 convenient:1 able:1 zq:1 note:3 k2:1 ideal:3 generalized:5 begin:1 exactly:1 fundamental:1 shall:2 most:2 involving:1 letter:1 phase:1 measured:1 class:4 constructed:1 surprising:2 average:4 kn:2 zhou1:1 points:1 principle:1 physics:2 fact:5 shor:1 show:2 his:1 vandersypen:2 random:1 chuang:6 solutions:1 substituting:1 trivial:1 find:1 q1:1 implementation:1 entangling:1 distributed:1 written:1 only:13 developed:1 employed:1 pointed:1 do:3 mixture:1 dj:14 establishes:1 notation:1 meanwhile:1 df:4 expectation:1 words:1 despite:1 dr:1 prime:1 reveal:1 resolve:1 arxiv:1 expansions:1 she:1 queries:6 qi:5 bal:6 view:1 modulo:1 exists:2 higher:1 ary:1 signs:1 flip:4 relative:2 computer:9 result:5 discussions:2 simultaneously:1 uncorrelated:3 techniques:2 fails:1 still:1 capacity:1 ways:1 away:1 definite:1 yet:1 initially:1 state:23 between:3 caves:1 conditions:2 discovery:1 creating:1 nature:2 qubits:6 darpa:1 however:6 implementing:3 distribution:1 both:3 realizable:2 improved:1 many:1 annual:1 against:1 σz:3 σx:1 qubit:16 experimental:2 otherwise:2 ci:7 afterwards:1 point:1 simple:1 ca:5 initiative:1 polynomial:2 san:1 pr:3 ensures:1 described:1 basis:3 addition:1 computing:1 three:1 been:3 reduction:3 interest:1 erases:1 expected:1 pk:12 ph:3 ann:2 define:1 wants:1 arises:1 corresponding:1 restrictions:1 sufficient:1 requires:1 bulk:4 fung:1 deep:1 importance:1 present:2 applied:2 look:1 exponential:2 value:2 will:4 while:1 replaced:1 pressed:1 applies:1 evaluates:1 σxk:9 35th:2 procedure:2 unitary:4 laflamme:2 thus:4 non:3 contract:1 different:3 perform:1 make:1 same:3 another:1 quant:3 pauli:1 finite:1 difficult:1 independent:8 used:3 initialization:1 effect:1 counterparts:1 harris:1 necessity:1 changing:1 conveniently:1 normalization:1 recent:1 prescribed:1 lower:2 center:1 nevertheless:1 well:2 without:2 solve:2 comes:2 model:24 usual:1 stringent:1 stores:1 less:2 being:3 generally:1 schack:1 transforms:1 facts:1 useful:1 yamamoto:1 speed:1 eigenstates:1 previous:2 jose:1 k1:2 capabilities:1 signals:1 spread:1 lett:3 natl:1 input:8 solvable:1 transformation:1 usable:1 motivating:1 easily:1 possible:3 possibly:1 press:2 using:6 bit:5 highly:2 projects:1 helpful:1 loss:3 modifications:2 concretely:1 like:1 systematically:1 follows:3 signal:7 alice:4 translates:1 steps:1 either:3 output:4 accessible:2 parity:2 acad:1 classical:9 discrete:1 sends:2 some:2 back:1 understood:1 2qi:5 provided:2 scale:1 dimensions:1 lead:2 support:1 though:2 overly:1 overlap:1 does:4 provides:1 prof:1 proc:7 refer:1 limitations:4 power:2 equivalent:10 bk:2 restrictive:2 symp:2 although:1 inherent:1 hadamard:1 relating:2 includes:2 cory:1 schulman:1 usa:1 extension:1 simplify:2 freedom:1 o:3 nontrivial:1 practical:2 mixed:3 comp:2 considerations:2 soc:5 computational:3 presence:1 acm:1 into:4 obtaining:1 due:2 modifying:1 sqc:14 determine:2 balanced:7 proportional:1 prepare:1 few:1 probabilistic:2 strictly:1 there:3 question:5 transform:1 fast:1 why:1 los:2 detectable:1 inner:2 fraction:1 was:1 debbie:1 function:6 jun:1 but:7 31st:1 lows:1 collapses:1 he:1 applying:1 stanford:4 whether:4 robustness:1 maximum:1 us:1 limit:1 problem:10 uf:2 similar:1 ki:9 ex:1 promises:1 lanl:1 constant:12 up:1 defined:4 certain:1 measure:1 proven:1 general:4 single:1 implement:2 chau:1 ing:1 physical:3 ni:1 functions:2 compared:1 ideally:1 no:3 ekert:2 commutes:2 when:9 reality:1 other:6 department:2 conclusion:2 kinds:1 superposition:1 zhou:1 models:5 nonclassical:1 prepared:4 important:2 bounded:3 prepares:1 qi1:1 jones:3 simon:5 implies:1 algorithm:26 resolution:1 required:2 together:1 original:3 equivalently:1 time:2 cleve:2 observables:1 n2:4 starting:1 having:1
|
quant-ph9906113.txt |@word longer:4 selection:2 help:1 just:1 show:1 rosen:1 forbidden:6 leads:2 experiments:2 relation:1 thanks:1 aspect:1 determined:4 causes:1 before:1 based:7 symmetry:1 yu:1 relativity:3 nonlocal:28 should:1 simple:1 only:2 experiment:5 about:7 theorem:3 he:3 achieve:1 gave:1 boris:1 fax:1 his:3 impacts:1 get:1 breaks:2 kind:1 preferred:10 nonzero:1 weakens:1 effects:1 now:1 dr:1 realize:2 helpful:1 down:1 like:1 settings:1 always:1 suarez:5 arxiv:1 acknowledgments:1 roger:1 demonstrated:1 each:1 podolsky:1 either:1 domain:1 didn:1 tel:1 exists:5 people:2 frame:12 some:1 related:1 elegant:1 namely:2 owing:1 result:4 measurement:2 quantum:47 special:3 even:1 iqm:1 still:1 describing:2 lead:2 space:3 demonstrates:1 review:1 since:3 relate:1 academia:1 consistently:2 does:3 above:1 between:3 net:1 cause:1 email:1 relations:2 refer:1 philosophy:1 simultaneously:2 theory:8 indicated:2 validity:1 however:1 here:1 reason:2 china:1 extent:1 causality:2 along:2 observing:1 generate:1 transformations:1 limitation:2 last:1 derivation:1 institute:2 sinica:1 certainty:1 cosmic:1 according:2 contradiction:1 called:1 inputs:1 simultaneous:6 hopeless:1 discussions:1 argue:1 experimental:3 first:4 rev:2 regardless:1 although:1 probability:1 bell:7 orders:4 communication:14 assumptions:1 presupposed:1 logical:2 peculiarity:2 hardy:4 exclusively:2 directly:1 einstein:1 frames:6 causal:16 classical:3 district:1 rejects:1 come:1 there:5 predictions:1 been:1 permitted:1 their:3 assumption:1 forward:1 ph:5 simpler:1 consistent:1 opens:1 more:2 nuovo:1 direction:2 himself:1 door:1 collapse:1 clearly:1 thus:4 albert:1 essentially:2 jul:1 gao:1 demonstrations:1 proceed:2 undoubtedly:1 peculiar:1 present:4 must:4 inhibit:1 john:1 nathan:1 look:1 evident:1 permits:1 double:2 inertial:5 cimento:1 different:2 will:12 lorentz:12 contrary:2 theoretical:1 those:1 demonstrate:1 percival:4 naturally:1 agree:1 loop:6 proof:2 mechanics:2 beijing:1 links:1 give:1 process:5 describe:1 influence:19 systems:2 states:1 loops:6 say:1 itself:4 exist:4 demonstration:1 any:4 physical:2 again:1 confirmed:1 strength:1 dalibard:1 no:8 when:1 lett:5 evidently:2 other:4 quant:5 influences:2 outputs:1 correlating:4 ordinary:1 happens:2 shan:1 events:5 conclusion:3 independent:4 extended:1 description:5 superluminal:10 may:2 after:1 june:1 needs:3 hand:2 involving:1 but:3 possible:1 manifested:1 building:1 dynamical:2 assume:1 physics:2 clear:1 eberhard:1 center:1 analysis:1 concrete:1 devise:1 definitely:1 asserts:1 time:5 backward:2 requires:1 order:2 fact:4
|
quant-ph9906114.txt |@word code:37 consider:5 results:1 four:1 computation:4 consists:1 research:2 payoff:1 whose:3 c0m:2 knill:3 environment:3 those:1 under:7 analogous:2 must:6 worth:2 r12:1 straightforward:1 orthogonal:11 wave:6 non:2 electron:3 nesting:1 word:3 matrices:4 condition:2 cmn:3 info:1 hamiltonian:3 irreducible:2 occurs:1 try:1 vector:5 small:1 c01:1 zj:2 zk:14 dealing:2 consistent:1 estimates:1 sign:5 second:2 implemented:1 linear:1 even:2 what:2 errors:54 advantageous:2 incompatible:1 sum:3 brief:2 3n:4 above:2 net:1 increasing:1 satisfy:8 advantageously:1 full:3 simultaneously:1 exchange:35 respectively:5 component:1 here:1 z8:1 represented:2 appears:1 z2:2 obtained:1 involved:1 leaves:1 vectors:4 orthogonalization:1 suggests:3 products:3 permit:1 usually:1 makes:1 involves:1 corrects:1 regardless:1 9n:2 replace:1 analyzing:1 apply:1 total:1 use:3 additive:1 usa:1 codewords:1 probabilities:1 positive:2 negative:2 few:1 type:2 today:1 more:4 bennett:1 duality:1 concatenation:2 known:2 cases:1 circumstances:1 include:2 ma:1 science:1 challenge:1 labeled:2 itself:1 cab:8 trans:1 example:2 proof:1 weaker:1 indicated:2 give:1 process:1 permutations:9 implementations:2 states:7 professor:3 sense:1 νi:1 occur:2 νk:2 guarantee:1 redundancy:1 quantph:1 mutually:3 rather:2 s2:3 s1:3 holds:1 write:1 pure:1 answer:1 instead:3 simplicity:1 product:3 blocks:1 flip:4 may:10 after:2 fa:12 fb:9 designed:1 representations:1 fm:5 fn:4 natural:2 imply:1 grant:2 explicit:1 yielding:2 sk:2 so:8 sn:3 representation:3 r112:1 order:3 zℓ:3 least:1 dx:4 office:1 indeed:1 over:2 exchanges:1 expects:1 already:1 including:1 differs:2 ieee:1 its:3 group:3 exclusion:1 computers:1 coordinates:2 better:1 absence:1 drawback:1 systems:1 lx:1 lowell:2 them:2 yj:2 impervious:1 dab:8 number:2 steane:1 effects:1 they:4 identically:1 now:3 discuss:1 easily:1 february:1 several:2 equality:1 2q:2 lies:1 always:2 university:1 identified:1 orthonormal:1 realistic:1 theory:2 l2:2 reasonable:1 each:5 xℓ:5 2n:9 side:1 mean:1 subset:2 schemes:3 independent:2 hard:2 related:1 extended:1 dfs:1 expect:2 measurement:4 quantum:13 our:4 eq:3 event:1 special:2 leave:1 matrix:6 space:7 types:1 since:7 rev:7 denotes:4 particles:9 acting:6 denoted:1 rn:1 cause:2 correct:12 rk:1 foundation:1 earlier:1 ruskai:1 interactions:4 diagonal:1 free:2 reason:2 term:5 e0:1 shortest:1 pairs:1 interaction:4 r1:16 r2:16 r3:2 could:1 similarly:1 tolerant:3 length:1 δij:3 hence:6 retain:2 onto:1 first:5 xj:3 xk:14 initial:1 xn:2 symmetry:4 coding:2 primary:1 iht:2 restrict:1 simplified:1 long:1 another:2 compared:1 open:1 size:1 given:2 necessarily:3 anyons:1 needed:2 system:2 approximately:1 their:2 assumption:3 fortuitous:1 fermions:1 realization:1 normalization:1 bits:7 gives:1 exploring:1 discussion:1 exactly:2 encouraging:1 optical:2 x2:2 x1:2 than:6 king:1 impractical:1 require:4 zero:6 determined:1 contrary:1 r3n:1 7b:1 7a:1 rewrite:1 correction:6 kitaev:1 miquel:1 dms:1 need:3 seem:3 seek:2 any:6 permutational:5 symmetrized:2 lie:1 smallest:1 depending:1 general:2 convenient:1 latter:1 able:4 isolated:1 mechanism:3 note:1 potential:1 multiple:4 opposite:1 bounds:1 most:2 involving:1 pleasure:1 phase:5 beth:1 class:1 clear:1 sometimes:1 δmm:1 hierarchical:1 electrons:6 principle:3 mechanical:1 χk:2 fact:1 precise:1 optimal:1 shor:5 supported:1 merit:1 carlen:1 minimizing:1 find:2 d0:9 d1:4 based:3 proposed:7 implementation:3 written:1 should:1 only:10 bases:1 exchanged:1 do:2 handle:4 notation:1 familiar:1 zurek:1 flips:3 cannot:2 dz:4 words:10 dy:4 combinations:1 lattices:2 parlance:1 aκ:2 hardin:1 dpq:4 approach:2 arxiv:1 yield:4 common:1 contain:1 coefficient:2 set:5 physically:1 national:1 up:3 see:6 computer:4 result:2 discussions:2 terms:6 best:1 c2q:2 subsequent:1 label:1 symmetric:9 importance:1 state:11 converted:1 µi:1 µk:2 between:3 invariant:6 justified:1 conditions:1 notice:1 triplet:1 triples:1 nature:1 qubits:8 attention:2 however:10 distinguish:1 thank:1 both:7 last:1 many:1 equal:4 σz:1 σy:1 σx:1 qubit:20 σp:2 finds:1 experimental:1 comment:1 cj:2 ci:30 bell:1 simple:5 corresponds:4 dimensional:6 cirac:1 anti:4 moreover:2 considering:2 transformations:1 basis:2 addition:3 three:2 been:2 describes:1 treat:1 basic:3 ph:5 mary:1 isolating:1 corresponding:3 restrictions:1 sufficient:1 subspace:3 requires:2 external:1 c2:1 c1:26 c0:30 spin:14 present:2 case:6 multi:2 solid:1 expanded:1 calarco:1 δkℓ:1 will:12 while:1 replaced:1 probability:5 reliably:1 error:17 investigating:1 property:1 couplings:1 unitary:1 satisfying:1 laflamme:4 thus:5 yk:8 exchanging:1 ik:1 ij:1 different:4 cjm:1 paz:1 lett:4 same:5 clearly:1 shorter:1 complex:1 quant:5 arguments:1 pauli:21 φk:2 higher:1 development:1 evolve:1 used:2 permutation:2 effect:3 action:1 codes:20 chris:1 invariance:1 contribution:1 identity:2 changes:2 variety:1 well:3 analysis:3 dkk:1 efficient:1 severe:1 without:1 components:4 model:1 dimension:6 charged:1 gates:1 calderbank:1 just:1 less:1 permutationally:1 half:2 identify:1 useful:1 permute:1 preprint:5 zoller:1 photons:1 had:1 reasons:1 5n:1 attractive:1 δpq:1 c11:1 identical:4 big:1 possible:3 lanl:4 possibly:1 grid:1 entangled:2 background:1 press:1 using:3 bit:34 correcting:3 helpful:1 necessary:2 excluding:1 particle:4 exploiting:1 ignore:1 wooters:1 yields:5 either:2 sloane:2 fault:3 reduced:1 preskill:1 because:5 theorists:1 often:2 sequence:1 some:10 understood:1 happens:1 describing:1 comments:1 does:2 provides:1 minimal:1 inserting:1 rank:1 noise:1 11a:1 11b:1 equivalent:1 although:3 hilbert:1 actual:1 would:4 extension:1 army:1 c1m:2 briegel:2 range:1 done:1 block:1 considerations:1 viola:1 into:1 within:3 isomorphic:1 down:2 a9:2 references:1 operator:1 additional:3 combinatorics:1 there:6 question:2 specifically:1 lidar:1 bosons:1 inner:2 way:1 triplets:1 was:1 function:5 complete:1 form:11 concatenated:1 smolin:1 jun:1 but:4 change:1 neutral:1 construction:4 hn:1 larger:2 proposal:1 partially:1 count:1 places:1 whether:5 dmm:1 dmn:3 projecting:1 simplifying:1 boldface:1 problem:1 similar:1 called:1 detailed:1 required:1 computing:2 certain:1 describe:1 denote:4 single:13 exist:2 eric:1 jaksch:1 physical:1 physics:1 functions:4 e34:6 cim:1 drafts:1 no:2 rains:2 when:13 detail:1 ep:4 other:4 spatial:3 department:1 mathematics:1 nonzero:2 elements:3 superposition:1 divincenzo:1 models:1 june:1 includes:3 a0:2 a3:2 important:2 massachusetts:1 a6:2 included:1 n2:1 structure:1 acknowledgment:1 implies:4 coulomb:1 typically:1 ejk:3 time:2 serious:1 nuclei:1 once:1 4b:1 4a:1
|
quant-ph9906115.txt |@word consider:4 magnetic:1 results:2 leads:2 contributions:1 whose:1 inverse:1 γt:2 γn:4 under:3 analogous:2 supported:1 very:4 frequencies:2 tends:1 springer:1 puzzles:1 resonant:1 experimentally:6 difference:2 condition:3 randomness:3 vibrational:3 hamiltonian:9 turns:1 t2:3 damped:4 large:2 small:3 eigenvalues:1 dip:2 configurations:1 smaller:1 pragmatic:1 oscillation:3 consistent:1 measurable:1 pulse:8 rate:3 estimated:1 leakage:3 theory:1 even:3 established:1 plays:1 trapping:2 sum:1 selected:2 while:1 consistently:1 experiment:5 above:3 fractional:1 woodbury:1 increasing:2 satisfy:1 edited:1 vitali:1 exchange:1 error:1 here:2 diagonal:3 identifications:1 relaxation:2 along:1 table:1 appears:1 logarithmic:1 obtained:3 delle:1 shift:2 study:1 studied:4 approaches:2 suggests:1 characterizing:1 tτ1:1 appropriately:1 via:2 depart:1 stray:1 transit:1 explained:2 private:2 coinciding:1 apply:1 counts:1 unit:2 use:4 takes:1 would:2 remains:1 positive:3 negative:1 therefore:4 theoretical:4 today:1 more:5 becomes:2 berlin:1 normalized:2 known:1 cases:5 must:5 logarithm:1 high:5 account:1 quantized:1 equation:8 averaged:2 remain:1 fock:1 values:5 evolved:1 following:3 example:3 control:1 νt:1 give:1 process:1 states:5 assumptions:1 performed:1 sense:1 times:1 lamb:3 motion:1 celoria:1 requirements:1 varied:2 destroying:3 verify:1 get:1 write:1 instead:4 mysteries:1 parameter:7 priori:1 circular:2 description:2 derived:4 mapping:1 stefano:1 tries:1 inst:1 designed:1 verified:1 law:5 data:1 concerns:1 realized:1 waist:1 effective:2 schneider:1 acknowledged:1 yielding:1 provide:1 so:9 fundamental:1 decreasing:1 representation:2 order:4 typical:1 interpretation:1 feedback:1 over:1 mainly:1 satisfied:1 experiments:8 through:1 statistical:3 satisfies:1 still:3 jaynes:2 its:5 derive:3 decay:11 interesting:1 degrees:2 differently:1 rabi:23 non:6 good:1 investigated:1 scaling:4 walls:1 dap:1 effects:1 they:4 now:4 easily:3 february:1 gets:1 characterizes:2 level:1 sideband:1 ryzhik:1 sufficiently:2 vibrations:3 mode:4 reasonable:2 each:3 found:1 universit:2 higher:1 characterized:1 mean:4 subsystem:1 schemes:1 significantly:1 there:2 energy:6 idea:1 frequency:16 obtains:1 quantum:3 our:4 approximated:2 recognizable:1 eq:26 out:4 tombesi:1 matrix:6 driving:1 res:1 nuovo:1 since:3 rev:7 denotes:1 collisions:1 rb:1 print:1 induced:2 ref:15 shows:1 linear:1 fluctuates:1 mechanisms:2 fisica:2 free:1 completely:1 estimate:4 beginning:1 milburn:3 interaction:20 optics:1 transition:2 david:1 counterpart:1 place:1 hence:2 adjoint:1 first:1 origin:2 already:2 probability:7 laguerre:1 rydberg:6 variables:1 number:1 ond:1 clear:1 another:1 bonifacio:2 given:3 checked:1 rewritten:1 unknown:1 eqs:2 2ωr:4 system:3 2ωn:1 assumption:2 master:8 πw:2 rates:3 white:1 ranging:1 trapped:2 explanation:2 prediction:3 environmental:2 larger:1 authors:1 than:1 population:3 cimento:1 intensity:3 iωz:1 annihilation:1 determined:2 contrary:1 were:1 sec:2 perturbative:1 raman:7 fluctuation:2 argument:1 tτ:1 recover:1 strength:3 depending:2 self:1 responsible:2 able:2 milano:3 note:2 fitting:2 potential:1 generalized:4 analogy:1 coincide:1 blue:1 trace:1 though:2 most:1 connected:1 cummings:2 gradshteyn:1 phase:6 measured:2 considered:3 average:1 adopt:1 detectors:1 accounted:1 exp:5 velocity:6 fact:15 particularly:1 phenomenon:2 random:11 implying:1 individuated:1 ωz:2 find:1 paradoxes:1 just:1 parameters:3 situations:3 explain:2 should:1 only:9 stand:1 candidates:1 ien:1 constant:2 oct:1 do:2 mixture:1 di:5 beams:1 zurek:1 infm:2 soon:1 cannot:4 preparing:1 despite:2 dt:3 differentiating:1 evolution:9 progressive:1 fields:1 arxiv:1 tuned:1 pulses:2 valid:3 view:1 lasers:3 observes:1 imposing:1 comparable:2 observed:9 see:5 injecting:1 discussions:1 limiting:1 ieee:1 phases:3 excitations:1 knight:1 definite:2 state:8 between:8 intensities:2 approach:7 brune:2 notice:3 terms:5 nature:2 however:7 suggested:3 both:4 cos:4 ila:2 many:3 taking:1 uncertainty:4 according:1 attributed:2 agree:1 ilt:3 raimond:2 variance:1 whole:1 finds:1 experimental:11 unitarily:1 mechanics:1 jitter:1 cm:1 point:1 simple:5 asymptotically:1 corresponds:1 polynomial:1 moreover:2 ae:1 considers:1 considering:1 described:4 second:2 basis:3 due:4 been:13 detuning:1 much:2 damping:2 expected:1 ph:2 choose:1 direction:2 controlled:1 suppress:1 coherence:1 photon:3 essentially:2 coherent:1 observe:1 understand:1 presented:1 present:4 case:14 traced:1 laser:7 exponential:1 voltage:1 aip:1 value:7 transformation:1 will:1 dephasing:1 replaced:3 behavior:2 applies:1 situation:1 property:2 procedure:2 unitary:2 coupled:1 averaging:3 refs:2 t1:3 ii:1 reads:1 il:1 madonna:1 different:5 italy:2 make:1 quadratic:1 same:6 archive:1 quant:2 pag:2 dimensionless:1 finite:1 murst:1 difficult:1 independent:4 used:2 numerical:1 effect:1 driven:1 ion:5 levels:2 potentials:1 changing:2 identity:1 recent:2 lower:1 supports:1 off:2 center:1 expression:2 well:6 analysis:1 academic:1 quantitative:1 model:4 usual:6 unified:1 µsec:5 proposed:2 generally:1 sources:2 underlying:1 atomic:4 predicts:2 immediately:1 eigenstates:1 previous:1 monitored:1 timescale:1 density:7 similarities:2 character:2 dicke:3 arctg:1 internal:5 lett:4 easy:1 natl:1 semigroup:3 excited:1 fluctuating:2 lacking:2 couple:1 possible:3 dark:1 background:1 vacuum:1 using:6 δv:2 δt:2 velocities:1 camerino:2 specific:1 yields:1 sezione:1 become:1 therein:1 because:6 often:1 classical:1 orlando:1 some:3 back:1 examples:1 respect:2 oscillations:15 matching:1 provided:1 describing:1 cavity:14 shall:3 microwave:3 unavoidably:1 peg:5 proc:1 trap:1 measuring:2 integrals:1 power:4 coincides:1 agreement:1 expansion:2 properties:2 rodolfo:1 origins:1 freedom:2 introduces:1 dependence:6 l1n:1 greatly:1 importantly:1 wineland:3 communication:2 into:2 within:2 integral:1 predictions:2 en:1 references:1 operator:7 proportional:2 theoretically:1 qed:1 log:2 area:6 initial:3 describes:1 way:1 series:1 was:1 eg:2 assumes:2 function:5 considerably:1 complete:1 form:3 totic:1 but:5 gaussian:7 murao:1 properly:1 matematica:1 atom:8 dissipative:5 infn:1 paolo:1 made:2 evident:1 characteristic:1 ωr:7 ωt:1 us:2 work:1 limit:5 verification:1 ωn:6 fluctuations:11 distribution:4 called:1 originating:1 khz:3 lanl:1 associated:2 defined:1 steady:1 describe:2 linearity:1 general:5 duration:2 laboratory:1 corresponding:6 formalism:4 check:1 physical:5 again:4 no:4 whereas:1 when:3 meekhof:1 conditions:1 role:1 test:1 conclusion:1 picture:2 elements:4 superposition:1 gas:1 durations:1 prepared:1 a2:1 technol:1 variable:4 implies:1 faster:1 assume:1 interval:2 mass:1 fitted:3 time:31 decoherence:20 expands:1 having:1
|
quant-ph9906116.txt |@word secondly:2 precondition:1 consider:2 founder:2 results:1 eds:2 certainly:1 deterministic:2 nonlocal:8 environment:1 device:4 stochastic:2 fax:1 presently:1 outside:1 very:2 wave:5 difference:3 condition:6 differentiated:1 did:1 settle:1 minimal:1 perceptual:2 optics:2 prevent:1 smaller:1 tel:1 demonstrations:1 subtle:1 further:1 dynamics:1 theory:18 even:5 aim:1 what:1 nonlinear:3 hide:1 appear:1 apparatus:1 deeply:2 section:1 availability:2 experiment:4 above:11 new:3 net:1 acknowledgments:1 satisfy:2 respectively:1 here:1 objects:4 china:1 strong:1 appears:1 extreme:1 obtained:1 institute:2 spontaneous:2 study:1 changed:2 resulting:2 permit:2 action:2 surely:1 pearle:2 useful:1 projection:4 discontinuous:1 explained:1 trained:2 apply:1 causal:2 use:2 eye:2 takes:1 distinct:1 predictions:1 call:1 mysterious:1 scope:2 theoretical:2 more:4 separated:1 validity:4 visual:3 hold:1 iii:1 must:6 involve:1 eberhard:1 room:1 equation:4 theories:1 values:1 concepts:2 following:3 endow:1 beijing:1 process:17 accept:1 states:12 lorentz:1 grassi:1 exclude:1 evidently:2 absolute:1 needs:1 requirements:1 polchinski:1 turn:2 discussion:1 ghirardi:2 how:2 reject:2 answer:1 description:2 superluminal:24 may:12 after:1 spot:2 confirmed:1 coming:3 realized:1 natural:15 dynamical:6 conscious:34 formidable:1 so:1 representation:1 order:4 interpretation:1 help:1 indeed:3 mainly:2 satisfied:2 including:5 existence:4 still:1 its:9 before:3 relativity:20 resort:1 compelling:1 systems:1 might:1 weber:1 eventually:1 them:1 nonorthogonal:5 oxford:2 now:1 yu:1 realize:3 juncture:1 always:1 university:1 transmitted:1 reasonable:3 found:1 beneath:1 identifier:1 reactions:2 domain:1 revised:6 owing:2 measurement:9 quantum:61 our:7 beyond:1 special:9 out:1 shown:1 space:2 furthermore:1 since:8 rev:6 particles:1 vector:2 adapt:1 rel:1 denoted:1 formula:1 disclose:1 foundation:3 perception:5 linear:4 localization:1 little:2 possibility:7 reason:2 confirmations:1 advantages:1 intermediate:1 sinica:1 correctness:1 feasible:2 motion:3 thing:2 invalidity:1 think:1 first:6 origin:1 number:1 feet:1 carry:1 impossible:2 precisely:1 affords:2 size:3 given:1 observer:7 district:1 rejects:2 introduction:1 system:2 assumption:1 brevity:1 too:1 postulate:3 sensitivity:1 speaking:2 collapse:13 completed:3 continuous:3 albert:1 part:4 undoubtedly:4 than:4 kind:3 penrose:5 require:1 cimento:1 contrary:1 were:1 tackled:1 rimini:2 nuovo:1 electrodynamics:1 correction:2 modern:1 mind:1 say:4 need:5 any:8 self:1 able:1 gravity:3 take:3 creatures:1 towards:2 though:3 object:19 most:1 involving:1 propagate:1 jul:1 nothing:2 measured:3 especially:1 surprising:1 formation:1 principle:15 left:1 physics:4 incomplete:1 stones:1 selection:3 show:2 earth:1 find:1 completion:1 based:1 knowledge:1 situations:2 enough:3 only:8 essence:2 isham:2 achieve:4 his:5 hit:2 means:4 perceive:1 preferred:1 during:2 dr:1 gen:1 evolution:6 fields:1 irrational:2 arxiv:1 grav:1 predicted:1 contain:1 worries:1 limitations:1 view:2 ignored:1 requirement:1 exists:4 achieved:1 frame:1 observed:2 namely:3 result:3 discussions:1 terms:1 luminous:2 satisfying:1 definite:8 propagates:1 state:18 bunch:1 email:1 recently:1 nature:3 fluctuations:1 distinguish:1 originates:1 both:2 essentially:1 perceptions:1 last:2 many:1 region:2 according:3 admit:1 became:2 whole:1 experimental:3 point:1 reasons:1 analyzed:1 applicability:1 bizarre:1 considering:1 capable:1 due:1 been:2 reduction:6 trigger:4 microscopic:1 ph:3 territory:1 wants:1 corresponding:3 deeper:1 reaction:1 sufficient:1 photon:2 gao:4 observe:2 general:1 present:12 case:4 exception:1 originate:1 will:18 while:4 replaced:2 situation:2 loop:2 seven:1 studied:1 ripe:1 vi:1 thus:6 iv:1 ii:1 itself:1 technology:1 different:7 realizing:1 same:1 shorter:5 quant:3 finite:1 shan:4 difficult:1 development:1 independent:1 weinberg:1 effect:2 hand:7 opportunity:2 recent:1 task:1 kept:1 disappears:1 analysis:2 concrete:2 academia:1 revising:2 model:1 possesses:1 entangled:2 unified:1 just:4 being:4 generally:1 identify:2 thanks:1 human:7 world:3 spatially:1 macroscopic:2 yet:1 previous:1 conclusions:1 photons:5 simple:1 other:9 lett:3 input:1 real:3 easily:1 know:2 press:3 using:3 phenomena:13 helpful:2 particle:1 imposes:1 either:1 become:1 essential:3 classical:10 some:5 confirm:1 normal:2 does:5 provides:1 demonstrated:2 measuring:4 who:1 june:1 clarendon:2 diosi:1 although:1 notorious:1 relating:1 properties:1 about:3 concretely:2 insufficient:1 emperor:1 revise:3 considerations:1 communication:24 within:1 negative:1 lies:1 einstein:4 there:5 question:2 long:3 way:1 analyze:2 function:5 himself:1 complete:1 unsettled:1 retina:2 but:3 true:3 evident:2 distinguishability:4 iqm:1 limit:3 demonstrate:1 problem:2 similar:1 gisin:1 mechanics:9 veiling:1 certain:2 universal:2 combining:1 influence:10 evidence:1 single:5 exist:4 physical:3 again:1 no:10 when:3 reality:1 valid:1 role:1 conclusion:2 permitting:1 superposition:6 models:2 problems:1 prepared:1 important:1 building:1 longer:2 spacelike:1 assume:2 required:2 inescapable:1 having:1 mass:3 fact:4 time:15 inaccuracy:1 requires:1 original:1 once:1
|
quant-ph9906117.txt |@word replacing:2 discards:1 footing:1 partial:5 consider:10 chain:1 exponentiation:1 informally:1 results:2 produce:1 existing:2 leads:1 obstruction:9 scalar:2 commute:1 generalize:1 computation:1 types:1 gn:1 remarkably:1 gk:8 spacetime:1 tenable:1 gh:1 ıq:4 particles:33 preserves:1 inverse:2 depend:6 calculate:1 re:10 tv:6 tw:1 acting:4 uniqueness:3 rg:1 those:6 th:1 ıf:12 breach:1 government:1 deducing:1 champagne:1 case:20 supported:1 amplitudes:1 kφ:15 straightforward:4 very:3 γi2:2 implicitly:1 kψ:2 translations:1 conditions:8 wave:8 reinterpret:1 corollary:5 untenable:1 putting:2 gℓ:4 condition:5 treating:1 differentiated:2 obvious:3 disregarding:1 immediately:1 level:1 did:1 positions:3 t2:4 solution:12 fewer:1 t1:4 solved:3 vector:5 subscript:1 indices:27 rk:2 inertial:1 hnr:2 application:1 abbreviated:1 smaller:1 says:2 version:5 construed:2 dealing:4 direct:1 literature:1 maintain:1 consists:1 zero:7 perspective:1 go:1 concludes:1 further:2 defines:1 theories:19 expressions:1 substitute:2 bold:1 bilinear:1 established:1 what:10 fℓ:2 adds:1 pg:8 invertible:3 kφ1:2 jxi:1 decisions:1 section:6 symbolically:1 expressed:3 paragraph:10 backtracking:1 above:11 capital:1 new:21 construction:1 rd:5 consisting:1 contrast:2 satisfy:3 rτ:2 justification:1 jnj:1 notions:1 degree:4 whose:2 deduces:3 respectively:11 observable:1 never:1 component:1 here:3 understanding:2 τl:4 canonically:4 explore:1 olica:1 possibility:4 separation:12 gnk:1 indexed:1 germs:1 along:2 equations:42 interpret:4 differential:10 obtained:3 spite:1 difficulty:1 involved:2 study:1 generator:15 meet:1 typically:1 ignoring:1 prior:1 theoretic:1 calculations:2 resulting:3 professor:1 permutation:5 domains:2 hospitality:1 conveniently:1 studies:2 hn2:2 uniquely:4 appropriately:2 spatially:1 family:5 ii2:1 differentiating:1 requiring:1 merely:2 explained:3 exercise:1 logarithmic:28 remnant:1 sgn:1 apply:4 ıp:4 comprised:1 discuss:1 use:6 takes:1 would:16 prove:4 covariant:1 contains:1 finally:2 next:2 ψj:2 comparing:1 going:2 call:6 opposed:1 themselves:1 iteratively:1 type:13 theoretical:1 reflects:1 more:6 introducing:2 ıg:4 ii1:1 becomes:1 operators:55 apparent:1 odinger:4 deserve:1 needed:1 particular:13 known:3 cases:6 producing:2 iik:1 must:16 logarithm:2 states:2 account:1 valued:3 word:1 r2:1 thanks:2 deformed:3 equation:31 rθ:1 modified:2 cat:1 infinitesimal:30 values:4 following:6 under:15 abandon:1 arrive:2 example:1 proof:11 f1:1 ready:1 indicated:3 stated:2 calculation:3 preserving:1 table:3 purposes:1 desenvolvimento:1 high:1 indicates:1 caution:1 numbers:11 want:2 allowed:1 dj:14 distinguishable:2 species:12 information:1 respective:2 ib:6 end:3 dh:1 provide:3 ideas:1 s1:1 acts:5 negation:1 write:9 maps:3 pair:3 behave:1 brazilian:1 familiar:1 simplifies:1 instead:1 ordinary:1 constraints:5 parameter:9 isotropic:1 simplicity:1 fr:4 express:1 algebra:16 may:10 designated:1 dηi:1 after:4 derived:1 φr:24 therefore:2 reflect:2 applications:2 independent:5 plane:1 multiplication:1 requirements:1 fj:1 choice:3 data:3 fm:6 constants:2 opted:1 changes:1 xnj:2 natural:4 third:3 whenever:3 explicit:2 parameterized:5 element:1 diffeomorphism:1 greek:2 switch:1 cannot:1 so:18 sn:1 sl:1 challenge:1 parameterizes:1 first:16 sg:1 order:8 operations:1 restriction:1 innocuous:1 holds:3 interpretation:1 exponentiated:2 hierarchy:48 developed:1 pointed:1 choose:1 interpreted:1 course:9 during:1 paper:5 through:6 graph:3 omitting:1 mentioned:2 existence:4 satisfies:16 its:11 boosts:2 member:1 s2:1 x1j:1 derive:1 group:14 probability:4 ln:31 gerald:1 affine:1 translation:1 conjugation:3 ds:3 forms:3 parts:2 degrees:19 systems:9 persist:1 jacobi:1 derivative:11 olver:1 freely:1 defining:2 deformation:2 renaming:1 ηh:1 pursue:2 non:23 good:1 motivated:1 greater:5 janeiro:1 gets:2 runs:1 introduce:7 functional:1 break:1 mention:2 φˆj:2 they:7 identically:1 front:1 rotation:4 now:38 φj:6 maintaining:2 densities:2 easily:4 february:1 finite:4 equality:1 instances:1 always:6 university:1 drop:1 labeling:1 gnr:1 theory:2 2b:1 each:25 found:3 repeating:1 side:17 associative:1 mean:8 homogeneous:27 lifted:5 square:1 directly:1 arbitrariness:1 map:3 series:1 energy:2 ea:4 product:16 abuse:1 conventions:1 constitute:1 inhomogeneous:1 fs:3 isospin:1 obtains:1 multiparticle:1 our:9 adequately:1 special:2 out:2 ultimately:1 precisely:1 exponential:8 factors:5 restricted:1 furthermore:6 since:15 semi:1 research:1 increase:1 obstructions:12 contained:1 investigation:2 ra:1 denoted:1 formula:4 get:3 cause:1 occurs:2 shows:5 exactly:1 earlier:1 linear:46 interchange:1 rely:1 departamento:1 quite:4 atica:1 ıfico:1 necessarily:4 besides:1 ask:2 simplifying:3 obstructing:1 axioms:1 care:2 r4:1 definition:21 pairs:4 derivation:13 language:1 argument:6 could:5 impose:2 times:1 counterpart:1 thing:1 fc:1 place:2 derivations:6 assumed:1 consequence:2 experimenter:1 supplemented:1 generalizations:1 frequent:1 heuristically:2 xj:7 xk:2 verifies:1 there:9 xn:24 symmetry:61 xm:2 variables:5 number:41 rank:2 transform:4 clear:1 specified:2 done:1 relations:2 another:7 xr:1 distributive:1 clarity:2 george:1 idea:1 svetlichny:3 given:25 cartesian:2 exists:2 likely:1 indicate:2 introduction:2 tecnologia:1 system:3 adopted:1 their:7 echet:4 assumption:4 inversion:4 lifting:16 linearities:1 restrictions:1 πx:1 doebner:1 recovered:1 πw:1 preserved:2 statement:4 relationship:1 tuple:6 continuous:1 immediate:1 employ:1 short:3 universally:1 differentiate:1 x2:1 off:1 x0:6 x1:12 undoubtedly:1 than:5 lim:1 determines:1 require:1 second:9 inversely:1 matter:3 computer:2 sct:1 speaking:1 amplitude:1 were:2 tion:1 providing:1 treated:1 minus:1 exhibit:1 questionable:1 before:1 enumerated:1 symmetries:59 generality:2 separations:1 matem:1 generalization:2 needs:1 say:13 acknowledgment:1 manner:3 need:3 seen:6 seem:2 idempotents:1 any:31 viewed:1 lie:16 traditionally:1 reciprocally:1 smallest:1 depending:1 convenient:3 self:1 able:1 si:2 produces:1 note:8 k2:2 k1:2 internal:22 take:2 jacobian:1 finding:1 envisage:1 canonical:17 modulus:2 ciˆencia:1 said:1 even:8 begin:2 added:1 unless:4 though:6 versa:1 cnpq:1 γi1:2 designates:2 extending:4 satisfying:4 ıcia:1 letter:2 representation:2 phase:1 subset:1 why:1 tensor:28 jx1:3 deny:2 γi:2 constructed:2 especially:2 surprising:1 considered:8 kj:6 chosen:2 adopt:2 cover:1 kn:5 km:1 face:3 traditional:1 kr:1 bracket:13 kw:1 principle:7 multiplicative:1 left:3 physics:3 sum:4 fact:6 reserve:1 automatically:2 naively:1 tempered:1 show:5 labels:3 fβ:1 least:1 focusing:2 spaces:4 relation:1 solutions:6 saying:1 threshold:14 substituting:3 careful:1 find:3 dilation:1 d1:5 pick:1 based:1 knowledge:3 parameters:4 situations:2 less:2 distributed:1 written:4 start:1 should:5 only:28 explicitly:4 generators:19 ambiguity:1 factor:1 integrable:1 over:5 achieve:2 nj:2 meant:1 do:6 dl:1 his:1 handle:1 dk:1 notation:10 means:5 df:11 dg:7 pontif:1 de:5 overall:1 xdj:1 truly:2 joint:1 ones:3 instance:1 legitimate:2 words:1 altogether:1 dv:1 compute:1 dt:3 homogeneity:9 dr:2 thresholds:7 dp:1 evolution:38 increasing:5 φi:2 φk:1 fields:3 arxiv:1 quantities:1 rotationally:1 whether:1 investigate:2 financially:1 common:3 qg:8 qf:7 identify:1 kℓ:4 fixed:3 discussing:1 λf:9 set:24 modulo:3 reference:3 notational:3 generally:8 frame:3 respect:9 j1:5 arrives:2 maximum:1 relative:1 differs:1 see:6 individual:1 rf:1 result:3 w1:1 arg:10 discussions:1 drawing:1 uncorrelated:1 analog:1 subject:3 brazil:1 gφ:1 fails:1 αr:2 interacting:2 fn1:2 ostensibly:1 xj1:2 review:3 exchange:1 justifies:1 label:2 symmetric:7 enough:1 difficulties:1 identification:1 expedite:2 closed:1 between:3 understood:1 invariant:1 bears:1 αj:1 approach:3 αl:1 law:3 gives:2 various:1 terms:6 ability:1 extend:1 nature:1 distinct:3 wn:1 attention:1 however:8 agencies:1 jn:1 cut:1 answers:1 separately:1 configuration:2 distribution:1 τk:4 both:9 essentially:1 last:2 fnr:1 tractable:1 powers:4 taking:1 postulate:1 equal:4 abstraction:1 sφ1:1 etc:2 admit:2 objects:2 purely:3 context:7 γik:2 expression:6 finds:2 referring:1 otherwise:3 mechanics:1 presumably:1 relativity:1 groups:3 point:10 simple:1 continuation:1 rη:6 motivation:1 dimensional:3 maintained:1 simply:1 coordinates:3 xi:7 dependent:4 proved:3 nacional:1 considers:1 lies:1 considering:3 claims:1 described:1 transformations:6 basis:1 simplification:2 invert:2 locally:1 due:2 rest:1 transformed:3 cient:1 tuples:4 pf:7 treat:2 interest:1 basic:2 corollaries:2 ph:1 abstract:1 empty:1 define:11 direction:1 rather:1 corresponding:11 deeper:1 commutes:1 suppress:2 sufficient:1 else:1 assert:2 lift:3 understand:1 covered:2 instant:3 general:20 spin:4 present:4 goldin:3 applied:2 multi:12 subsets:1 restrictive:1 value:5 choices:2 will:13 euclidean:1 while:3 rutgers:1 suppose:6 evaluating:2 applies:1 gnj:1 situation:2 property:23 procedure:1 remembering:1 opt:1 dfn:1 changed:1 ve:7 iq:3 ip:1 thus:19 yk:1 vn:3 according:1 ii:3 rio:1 ik:1 itself:4 im:9 fn:22 affected:2 tecnol:1 vanish:9 id:1 different:6 recover:1 develop:1 author:2 perform:1 φy:2 make:2 belong:1 roman:1 same:19 jℓ:3 liftings:4 tensorial:1 complex:25 quant:1 products:2 hierarchies:11 several:1 subalgebra:1 composition:5 higher:3 evolve:2 compositions:1 used:3 trivially:1 i1:2 i2:1 upon:2 effect:5 hand:16 action:2 investigates:1 solubility:1 necessity:2 infinite:2 changing:2 invariance:7 identity:3 ks:1 lower:2 schr:4 reflection:1 sees:2 nevertheless:2 makes:2 substantially:1 xjn:2 well:3 lℓ:2 obviously:3 transformational:1 without:7 solve:3 extensible:1 components:3 sets:2 coordinate:1 position:4 grounds:1 dimension:2 usual:10 composed:1 ia:1 construct:4 just:10 examining:1 being:12 reiθ:1 fα:2 obtain:2 effects:2 isolated:1 abbreviation:1 underlying:2 λg:7 transforms:3 questions:3 using:16 ogico:1 useful:7 flavor:1 multipliers:1 yet:1 previous:6 discipline:1 adding:1 unique:5 secondly:1 integer:1 density:1 conclude:2 shortcut:1 mathematically:1 leibnitz:2 add:1 priori:3 extends:2 association:1 easy:3 theorem:40 occurring:1 transformation:10 euler:2 generalized:2 real:35 iλ:1 aspects:1 depends:2 acute:1 iα:4 evaluate:3 showing:1 term:18 iη:1 interior:1 similarly:1 world:1 part:3 poses:1 usually:1 formal:4 loss:1 necessary:4 like:1 particle:89 systematically:2 follows:5 reduces:2 isomorphism:1 isotropy:1 barring:2 modify:1 specific:2 communications:1 misled:1 continue:4 indication:2 either:7 arbitrary:2 evolutions:2 anti:1 jxn:3 mathematical:6 right:15 old:2 often:4 deal:5 some:38 back:1 exposes:1 cancel:1 deduce:5 evaluated:1 escape:1 proper:3 small:1 happens:2 endomorphisms:1 scale:2 proceeding:1 vanishes:10 eiθ:1 avoid:1 shall:19 whole:2 ubiquity:1 everything:1 does:9 decomposition:3 provides:3 assuming:4 confusion:1 conselho:1 refer:1 deciding:1 claimed:1 object:2 run:1 obey:1 power:11 derivatives:1 performed:1 equivalent:1 pose:1 conventional:2 expansion:1 likewise:2 broken:4 rξ:1 although:2 relating:1 stay:1 dictated:1 properties:12 simpler:1 compose:2 about:5 trivialization:1 actual:1 extension:2 most:9 freedom:22 theorems:5 introduces:1 dependence:1 o:10 2i:1 practical:2 sake:1 2j:1 act:2 mixed:27 recourse:1 introduced:5 revise:1 enlightening:1 seeing:1 hypotheses:1 own:2 letters:2 significant:1 into:6 within:3 ηk:1 domain:3 ηi:2 three:4 down:1 multiply:1 appropriate:6 because:1 references:2 raises:1 determine:3 operator:66 versions:2 germ:2 mere:2 objective:1 additional:7 possible:3 combinatorics:1 topologies:1 strictly:8 initial:8 question:4 righthand:1 long:1 class:3 ordered:1 strict:1 accordingly:1 describes:3 classic:1 way:4 oneparticle:2 notices:1 analyze:1 was:3 ψr:1 function:27 arise:1 form:27 quantity:1 vanishing:1 phenomena:1 differences:1 jun:1 but:9 equa:1 change:3 state:1 hn:6 related:3 preceded:1 don:1 line:1 trying:1 true:10 considerable:2 kf:1 absent:1 made:4 applying:4 full:1 wπ:2 2πi:1 wish:1 metries:1 vice:1 up:1 us:4 below:2 exploration:1 verification:2 problem:9 called:9 expect:1 detailed:1 springer:1 ac:1 sometimes:2 associated:3 ad:2 item:3 defined:19 certain:6 universal:2 describe:2 linearity:1 determinant:1 covers:1 denote:7 quantum:4 single:5 exist:2 together:1 laboratory:1 journal:2 considerations:4 conversely:1 universidade:1 physical:9 effected:1 again:10 functions:30 therein:1 analyticity:1 no:7 amounts:2 index:3 separating:22 attacked:1 when:9 detail:2 envisaged:1 hn1:2 hn0:8 disjoint:1 other:10 helpful:1 branch:2 spatial:2 department:1 mathematics:1 nr:2 concerning:1 conclusion:1 polar:2 elements:6 calculating:1 separate:1 hereman:1 preceding:1 setting:2 problems:2 shown:2 includes:2 deriving:1 commutator:11 fnj:1 allowing:4 utterly:1 overdetermined:1 variable:2 sides:2 structure:5 matrix:1 algebraic:1 correlated:2 implies:5 imposes:3 practically:1 assume:7 starting:1 moved:1 space:31 rule:3 having:3 implied:1 dot:1 time:39 n0:3 n1:4 n2:3 laws:2 requires:1 original:2 once:5
|
quant-ph9906118.txt |@word represent:1 measurements:2 consider:10 remarkable:1 similarity:1 rev:6 magnetic:23 varying:1 splitting:2 eds:1 concept:1 entropy:18 computation:1 dϕ1:2 dϕ2:2 ahler:1 issues:1 whose:2 inverse:1 depend:3 catastrophe:1 deterministic:1 tr:4 b267:1 environment:5 finally:1 monotonically:1 preserved:1 th:1 under:1 stochastic:1 analogous:1 presentation:1 worth:2 applied:2 random:3 comm:1 performs:1 straightforward:1 orthogonal:1 far:1 frequencies:7 k02:2 results:4 tombesi:1 every:7 summarized:1 experimentally:2 emphasized:1 condition:1 called:3 turns:1 notes:1 fragile:1 kien:1 large:5 guarneri:1 optics:7 setup:1 unexpected:2 disordered:5 lecture:1 guidelines:1 sin2:1 hillery:1 aip:1 approximation:3 eith0:3 second:2 value:5 equal:1 incidentally:1 qualitatively:2 scientific:1 even:5 aim:1 what:1 voros:1 apparatus:1 xσ:1 section:7 expressed:2 uniform:2 experiment:1 above:2 new:1 increasing:7 pictorially:1 vitali:1 degree:4 respectively:3 aten:1 never:3 component:5 here:3 agreement:1 represented:1 path:1 along:2 strong:2 respect:1 change:2 obtained:7 great:3 waseda:1 difficulty:1 shift:18 leaves:1 larger:6 completely:1 commonly:1 periodic:2 resulting:3 condor:1 suitable:1 studies:1 plotted:2 composed:1 golden:3 technique:1 useful:3 ratios:1 marginal:1 namely:1 private:1 neutrons:6 austria:1 εint:1 gradshteyn:1 stern:1 apply:1 total:2 detecting:1 readily:6 use:3 quasi:1 would:5 analytic:1 beginning:1 h0:8 negative:2 hilbert:1 few:2 a53:1 noting:1 therefore:6 a57:1 associated:1 theoretical:2 possible:2 more:16 separated:1 elliptic:3 r5:1 becomes:8 naive:3 visibility:1 berlin:4 appendix:6 everywhere:1 normalized:4 particular:8 cases:8 aligned:1 iii:5 potential:1 high:1 account:1 crosses:4 brukner:1 ml:2 der:1 work:4 makino:1 values:13 concepts:2 following:1 making:2 ith0:4 averages:2 example:1 sinusoidal:1 f0:1 f1:1 bent:2 figure:14 process:1 choice:1 neglected:2 stressing:1 saito:2 states:9 purity:2 sense:2 provoke:2 axis:2 information:1 end:3 pure:1 rather:3 interacts:3 divided:1 di:5 recovers:1 very:5 varies:1 opposite:1 significance:1 simplifies:1 acta:1 ordinary:2 verlag:3 parameter:20 ensemble:9 a222:1 simplicity:1 irrational:1 undergoing:1 4k02:4 coined:1 after:4 orbits:1 consequence:1 fj:8 wave:20 parallel:2 stress:2 natural:1 light:1 generating:1 explicit:2 cosmology:1 so:7 fundamental:2 s2:1 representation:2 travel:1 displays:1 namiki:4 wigner:25 words:2 numbers:1 indeed:1 over:2 eqs:1 dα:2 years:3 top:1 paper:5 through:1 statistical:6 innovative:1 japan:1 kinetic:3 arrangement:2 its:21 perfect:1 ct96:1 longitudinal:1 thank:1 energies:1 interesting:3 randomization:1 decreases:2 recombines:1 better:1 fig:11 recombined:1 travelling:1 main:1 might:5 easier:1 non:3 h1:8 affected:2 greater:2 press:3 undergone:1 investigated:3 number:12 framework:2 b276:1 effects:3 they:2 half:1 oxford:3 grows:2 now:4 realize:1 easily:3 february:1 finite:4 always:2 delicate:1 hamiltonian:3 sin:11 realistic:1 le:1 magnitude:1 transmitted:1 l0:2 each:7 crossing:3 2m:1 universit:2 higher:2 2k:1 homogeneous:1 lectures:1 there:1 energy:5 idea:1 related:4 interferometer:12 literature:1 static:2 expect:2 measure:1 quantum:31 our:10 approximated:1 eq:6 event:1 shannon:1 out:3 shown:5 superposing:1 matrix:8 space:2 vch:1 rep:2 interference:5 chaos:4 denotes:1 looking:1 attracted:1 contained:1 investigation:1 gaussians:2 rational:5 istituto:2 formula:1 evaluation:4 correct:1 rj:12 shows:1 theory:3 fluctuates:3 divergence:3 fisica:3 free:6 standard:4 extraordinary:1 reason:1 complicated:2 term:2 estimate:1 akademie:1 monotonic:3 milburn:1 log:5 r4:1 definition:4 interaction:7 r1:1 r2:1 applications:2 could:1 motion:3 turn:2 length:8 exponentially:1 routes:3 scheme:1 undergo:2 think:3 speeds:1 first:8 initial:6 features:3 probability:5 reflected:1 reaches:3 echo:2 idempotency:1 intuitively:3 utilized:1 set:3 least:2 chopper:1 clarity:1 constructing:1 given:7 necessarily:1 smaller:1 b151:1 glauber:1 introduction:1 dipartimento:1 observes:1 amsterdam:1 system:6 approximately:1 their:1 appl:1 statement:1 realization:2 perfectly:1 final:2 speaking:1 ryzhik:1 mariano:1 continuous:1 realized:1 transverse:1 part:3 shifter:15 manipulation:1 x2:2 x0:16 than:3 distance:1 kind:2 polarized:7 holland:1 suda:3 double:14 require:1 see:9 tomographic:2 limiting:1 lim:2 quasistatic:1 future:1 supposed:1 amplitude:1 sec:3 treated:1 perspective:2 motivation:1 vector:2 san:1 giulini:1 fibonacci:7 fluctuation:3 ann:1 turned:1 defect:1 peculiar:1 say:2 substantial:1 ozorio:1 4k0:3 unaltered:1 seen:1 clearly:1 convenient:2 latter:3 b241:1 instance:1 k0:23 take:1 analogy:1 acquires:4 channel:3 formulas:1 play:1 towards:2 trace:1 shall:4 trρ:5 measures:1 systems:1 most:2 experiences:1 quantitative:5 phase:31 analytically:2 fluctuate:3 treats:1 ϕj:2 considered:1 behaves:1 calculated:1 coincides:1 physica:4 order:4 feynman:1 optical:1 exp:40 mechanical:8 north:1 typically:1 naively:3 fact:2 quantity:2 precise:1 arnol:1 selection:1 somewhat:1 show:1 probe:2 relation:1 gerlach:1 trρ2:5 find:2 lessons:1 slov:1 slow:1 ratio:3 just:1 parameters:3 series:1 situations:4 distributed:4 should:6 jan:1 being:1 only:8 going:1 subsection:2 integrate:1 integrable:5 hamiltonians:1 preliminaries:1 achieve:1 do:2 dk:6 means:2 dependent:1 dg:1 de:1 expectation:4 methods:1 beam:10 cannot:1 dx:6 progress:1 during:3 dt:5 ds:1 evolution:5 bar:1 wavenumber:1 arxiv:1 european:1 network:1 investigate:2 experiments:1 analytical:1 fixed:1 mezei:2 ik0:1 computed:7 achieved:2 physically:2 undergoes:3 correlations:1 outgoing:1 packet:9 maximum:4 observed:1 intensity:4 injecting:1 result:4 bari:3 recently:3 uncorrelated:1 techniques:2 ergodicity:1 practice:1 suffer:1 interacting:3 crystal:1 pattern:1 a44:2 tend:1 state:10 ωj:2 closed:1 conceptual:1 probably:1 erbfmrx:1 conditions:1 checks:1 law:7 available:1 publishers:1 notice:13 loose:1 terms:6 statistically:1 nature:1 wm:8 attention:1 focus:1 however:6 york:1 concentrate:1 hypothesis:1 magn:2 analyzed:3 suppressed:1 problem:1 both:12 cos:11 last:2 2n:1 irregular:1 many:3 region:3 conclusions:2 according:11 against:1 agree:4 fulfilled:1 iv:1 berry:2 context:2 introduce:1 variance:2 mean:4 expression:4 finds:1 experimental:13 grounds:1 comment:1 among:1 relevant:1 conclude:1 period:1 environments:1 dimensional:2 werner:1 simply:2 comprehension:2 proved:1 endeavor:1 schleich:1 considering:2 ps:4 sine:1 described:1 challenging:1 wien:1 due:5 been:3 quickly:1 defined:6 cosine:2 slowly:1 logarithmic:1 interest:2 expected:1 marginals:6 ph:1 nakazato:2 direction:5 flight:2 ωt:6 arcsin:1 quantities:1 coherence:18 remark:1 zeilinger:2 coherent:3 observe:6 understand:1 maximally:1 spin:15 former:1 those:1 matter:1 case:20 k2:1 p0:1 eit:4 unlike:1 pacs:1 appearance:1 single:9 evaluated:2 will:13 while:4 suppose:2 behavior:7 involved:1 situation:4 study:1 real:1 studied:1 vogel:1 played:1 characteristics:1 keller:1 surprisingly:1 encountered:1 ii:3 reads:7 vs:6 zeeman:1 claimed:1 motivated:1 ic:1 quantization:1 technology:1 different:19 italy:1 divergences:6 same:6 any:3 shifts:9 unity:4 quant:1 split:1 widely:1 accumulating:1 products:1 several:1 events:1 neutron:57 difficult:3 independent:2 used:2 schiller:1 singapore:1 welsh:1 numerical:7 effect:2 hand:3 v0:3 average:19 moment:1 purpose:1 normalization:2 nucleare:2 changes:3 well:3 analysis:7 obviously:2 academic:1 without:3 components:1 studying:1 position:7 bottom:1 routinely:1 proposed:2 less:4 increasingly:4 accurate:1 obtain:3 torus:3 underlying:1 world:2 previous:5 enters:1 preprint:1 ρint:4 density:10 badurek:2 except:1 spread:3 lett:3 easy:1 theorem:2 momentum:10 generalized:1 identical:1 fluctuating:7 around:1 depends:4 represents:3 quasidistribution:1 measurement:1 integrals:2 possibly:1 increases:6 know:1 confined:1 using:1 moreover:1 like:2 loss:8 facchi:2 counterintuitive:1 lost:1 particle:2 windings:1 university:3 δt:1 δl:2 yields:6 δk:1 sezione:1 smooth:2 become:2 disorder:3 collective:1 italian:1 mathematical:1 shed:1 because:2 wavepackets:1 classical:6 sequence:5 interact:1 some:11 springer:3 understood:1 b0:4 b1:1 choosing:1 table:3 golub:1 entropic:1 projection:1 dimensions:1 prolific:1 sufficiently:1 though:4 comments:1 ubiquity:1 mlynek:1 does:8 assuming:1 compute:1 displayed:1 either:3 noise:5 run:3 ba:1 tabor:1 performed:2 oscillating:3 perpendicular:3 clarendon:1 although:4 post:1 refers:1 properties:6 bz:1 noisy:1 diego:1 working:1 extension:1 algebraic:1 δb:2 am:1 prove:1 discussed:6 dependence:2 practical:1 mutually:2 trajectory:1 mixed:2 introduced:2 slightly:1 considerations:1 cambridge:2 almeida:1 communication:1 into:1 within:2 integral:3 ikξ:1 down:1 operator:1 proportional:1 conceptually:1 technically:1 acknowledgements:1 additional:4 interacted:3 measured:1 strictly:1 placing:1 r3:1 width:1 accordingly:2 much:1 pascazio:4 way:1 ed:1 analyze:1 was:6 interferometry:4 function:53 medium:3 deepened:1 phenomena:1 relaxed:1 differences:1 but:3 gaussian:27 idealized:1 properly:1 rauch:7 true:2 partially:2 infn:1 made:1 applying:2 qualitative:1 characteristic:1 robustness:1 up:3 us:3 entails:3 placed:2 below:3 frequency:2 limit:6 observation:1 fluctuations:8 distribution:19 similar:3 display:2 mechanics:2 b60:1 constant:5 2mδ:1 int:2 abstract:1 disclosing:1 influence:1 ergodic:3 general:6 dξ:1 conserved:2 proves:1 nazionale:2 balazs:1 distributions:1 check:2 physical:4 incorrect:2 again:6 functions:4 compared:1 no:2 index:2 when:9 vanishes:1 field:35 other:7 role:2 branch:1 spatial:1 deviation:4 picture:1 kinds:1 uniformly:2 tmr:1 meaning:2 important:2 suppression:2 variable:4 dense:1 pool:1 watanabe:2 ago:1 suffers:1 implies:1 lead:1 assume:5 physics:3 interval:6 packets:3 orbit:1 notion:3 4n:3 equivalently:1 4k:1 time:10 decoherence:37 dϕ:1 having:1 once:3
|
quant-ph9906119.txt |@word consider:1 springer:1 squared:1 results:16 existing:1 leads:4 francesco:1 consists:4 research:1 weakly:2 whose:1 inverse:2 collisions:1 technique:17 tr:1 tn:3 tl:2 compensate:1 tj:2 γm:16 ti:2 hermann:1 include:2 summarizes:1 case:14 amplitudes:1 outside:1 far:1 frequencies:1 rise:1 straße:1 account:1 wave:13 denoted:3 jack:1 ra1:1 resonant:3 experimentally:1 evaporation:1 exact:24 fakult:1 condition:6 solves:1 hamiltonian:8 evaluation:5 notes:1 t2:16 solution:25 t0:1 t1:25 large:1 integro:1 3b:1 markov:47 optics:4 employing:1 direct:2 approximation:49 go:1 rate:19 evaluated:2 concludes:1 savage:3 dynamics:8 odd:2 linear:1 spectral:4 arimitsu:1 t2k:1 adds:1 detuned:1 section:14 evaporative:2 43b:1 near:5 expressed:2 find:2 waiting:1 above:6 3c:1 new:5 3a:1 ground:10 contrast:2 3d:3 eω0:2 respectively:2 here:11 atoms:21 abandon:1 andrews:1 relaxation:2 ratio:7 strong:7 equations:5 appears:1 change:5 obtained:6 great:1 hωk:1 receive:1 shift:4 study:7 studied:1 allows:1 suggests:1 resulting:6 commutators:1 usually:3 resonance:1 interact:1 makes:1 involves:1 plotted:4 golden:3 via:1 projection:16 hres:2 scales:6 9a:3 9b:2 highly:1 apply:4 total:2 use:2 takes:1 would:2 failed:1 sake:1 positive:1 until:2 gj:1 next:1 depicted:2 tm:1 therefore:6 kl2:1 taken:2 survive:1 australian:1 theoretical:1 today:1 more:3 zeitschrift:1 operators:12 under:2 validity:2 long:4 normalized:6 known:2 hold:3 iii:3 must:3 couples:1 keeping:1 eiω1:1 eiω0:5 integrating:1 science:3 equation:32 dfg:1 45b:1 reproduce:1 remain:3 temperatures:1 following:3 making:2 history:1 asymptotic:1 compare:1 pushes:1 solved:2 process:1 boseeinstein:3 organized:1 naturally:1 larger:1 collision:3 assumptions:2 want:2 integrand:1 keep:1 absolute:1 lamb:4 end:1 varied:2 decaying:1 provide:1 discussion:4 holds:2 very:10 fourth:3 significant:1 verlag:1 parameter:16 sin:1 exponentially:1 oscillatory:1 simplicity:1 express:1 description:1 algebra:2 transforming:1 demonstrates:2 after:5 derived:2 different:2 hence:8 produce:1 differentialgleichungen:1 demonstrating:1 derives:2 realized:2 short:7 convolution:1 outline:1 effective:4 6th:10 counter:1 explicit:1 bloch:1 so:1 sm:3 correlation:5 hsys:6 order:37 pulsed:18 help:5 reservoir:26 over:6 eqs:8 satisfied:2 interpreted:3 thermal:3 paper:3 through:14 ρres:8 lasers:10 mentioned:2 japan:1 still:1 jaynes:1 its:1 before:1 perfect:1 derive:4 thank:1 decay:21 energies:1 solving:1 complex:1 exhibits:1 nonmarkovian:3 fig:15 superoperators:6 ra0:5 mail:4 main:1 non:11 good:2 greater:2 thereby:1 adiabatically:1 numerically:1 introduce:2 walls:1 effects:7 they:7 half:1 singularity:3 now:1 discuss:1 easily:5 february:1 always:1 university:1 traced:1 realistic:7 inequality:1 trap:32 reasonable:1 each:2 2m:3 universit:2 difficult:1 mean:2 differential:2 ei:2 energy:2 reduce:1 gaussian:2 t3:12 society:1 decays:1 obtains:4 measure:1 quantum:6 laboratory:1 transitions:7 eq:17 out:6 ketterle:1 leave:2 shown:10 matrix:3 space:2 bosonic:3 since:2 interference:4 concentrated:1 denotes:4 particles:2 may:1 daniel:1 ra:2 leaves:1 herder:1 lecture:1 get:6 ref:6 math:1 shows:5 theory:6 interactions:1 favored:1 pumping:3 free:2 standard:2 approaches:2 necessarily:1 esslinger:1 term:2 besides:1 beginning:2 faller:2 interaction:12 derivation:1 starts:1 transition:8 lout:6 times:10 motion:8 turn:1 length:3 4th:11 massive:2 freiburg:6 neglect:1 first:12 origin:1 fivefold:1 major:1 initial:2 physik:6 render:3 kernel:1 variables:1 number:32 restrict:1 heinz:1 simplified:2 fast:2 σk2:1 diagonal:2 open:1 given:16 perturbation:10 iω1:1 iω0:4 needed:2 introduction:1 leading:1 condensate:8 structured:1 system:19 relations:1 36a:3 their:1 cooling:3 intermediate:3 master:20 realization:1 dt3:3 dt2:5 dt1:9 scheme:2 final:1 gives:1 petruccione:4 collapse:2 continuous:12 albert:1 immediate:2 assumption:4 part:7 superoperator:3 45a:1 eliminated:1 45c:1 45d:1 than:4 coefficients:1 begins:1 wide:1 steady:1 determines:1 dtn:1 showed:1 bec:17 transferred:5 annihilation:6 future:1 assumes:1 were:3 tres:13 enables:2 powers:3 iωk:1 perturbative:9 function:9 sees:1 damped:2 spectrum:2 already:2 depleted:2 seen:2 occupied:5 clearly:6 heff:2 strength:31 built:2 lin:5 responsible:1 able:2 mechanism:9 note:4 k2:1 k0:4 build:2 essential:1 strengths:1 bernd:1 heisenberg:1 exactly:1 beyond:1 trace:1 any:1 replenished:1 enter:2 reach:1 systems:1 most:2 germany:1 cummings:1 kappler:3 successive:1 ludwigs:1 inserted:1 achievement:1 appear:1 peaked:1 cause:1 kg:1 especially:1 considered:2 later:2 stronger:1 kn:2 hagley:2 exp:3 physics:2 sum:1 quantity:2 show:1 agreed:2 dipole:10 relation:4 43a:1 agrees:3 occupation:22 slow:2 based:8 just:2 parameters:14 much:4 hope:4 pump:10 negligible:1 should:1 analytic:1 only:14 explicitly:1 summarizing:1 factor:5 local:2 achieve:2 do:2 mixture:1 dk:3 means:4 dependent:2 beams:1 de:4 expectation:4 supplies:1 during:1 dt:5 ds:1 becomes:1 holland:1 reveal:1 evolution:2 chronological:1 densities:2 conditions:2 arxiv:1 modern:1 shape:1 summary:2 investigate:3 mewes:2 breuer:4 including:1 transforms:2 reveals:1 k02:1 thesis:1 achieved:1 national:1 observed:1 depends:1 computer:1 result:2 fail:1 terms:13 uncorrelated:3 project:1 fails:7 commutation:1 federal:1 directional:1 liouville:1 importance:1 state:14 determined:2 closed:1 between:4 approach:5 αl:1 ωl:1 recently:4 reproduced:2 extend:2 initially:3 weak:2 ρsys:17 however:3 interfere:1 reproduces:1 bose:6 σk:3 cos:1 treated:5 taking:3 density:12 36b:2 according:1 laplace:2 chosen:5 uni:4 contribution:3 expression:1 experimental:2 strongly:3 relevant:1 afterwards:2 point:4 simple:3 corresponds:3 guzman:1 written:3 article:2 respect:1 cw:7 moore:3 broadening:1 described:3 second:14 addition:3 due:4 been:4 quickly:1 ansch:1 extraction:1 detuning:1 describes:6 slowly:3 basic:1 expected:2 ph:2 empty:5 define:2 suggested:1 enable:3 corresponding:5 constitutes:1 carmichael:1 photon:5 coincides:1 coherent:3 observe:1 systematic:1 stems:1 kicks:1 presented:1 present:3 applied:1 wiseman:1 laser:42 reliable:3 value:10 heidelberg:1 will:13 invoking:1 while:4 behavior:9 many:1 situation:1 hωj:1 property:1 couplings:1 a21:4 losses:1 coupled:4 almost:1 von:1 simulations:3 thus:4 iv:1 ii:12 coupler:8 reads:1 im:1 vanish:1 disappear:1 around:3 binary:2 containing:4 35b:2 35a:3 perform:1 suggest:1 lett:6 same:2 orders:2 parts:1 quant:1 emphasize:1 coworkers:1 survey:1 physical:2 consequence:1 higher:2 independent:2 used:1 infinity:1 see:8 numerical:7 upon:1 effect:2 depict:1 unpublished:1 cycle:1 suffices:2 off:1 modes:8 nevertheless:1 well:3 davis:1 obviously:1 without:1 solve:1 comes:1 model:13 rates:5 proposed:1 naraschewski:1 moments:1 resp:1 obtain:7 tcl:15 underlying:1 atomic:22 l0:5 previous:1 york:1 like:1 generator:1 hint:8 character:1 improvement:1 source:3 interested:2 treatment:2 easy:1 compares:1 formal:1 remaining:1 momentum:4 take:4 real:2 moy:6 increased:2 represents:1 iα:1 evaluate:2 couple:1 possible:4 harmonic:1 using:1 apart:1 loss:2 necessary:2 replacing:1 success:1 systematically:1 follows:2 performing:1 extremely:1 specific:1 integrals:3 output:28 stationary:6 reduced:3 because:9 neumann:1 namely:1 affects:1 creation:6 some:1 back:1 born:47 deduce:2 moreover:1 oscillations:14 peter:1 ourselves:1 ignore:2 scale:7 describing:3 lead:1 resonances:1 integration:2 does:3 provides:3 assuming:3 propagating:1 demonstrated:4 mode:28 ba:1 power:1 2µm:1 sixth:2 journal:2 aj:1 expansion:19 bk:6 step:1 departures:1 although:2 found:3 imaginary:1 simpler:1 comparison:2 about:5 energetically:1 2γm:1 algebraic:2 tuned:1 discussed:7 dependence:1 o:3 simulation:3 collett:2 financial:1 range:3 a2:1 introduced:1 other:2 rev:16 markovian:21 into:2 within:7 integral:6 bound:2 three:4 variable:1 appropriate:1 einstein:6 operator:25 proportional:1 nowadays:1 loc:5 assumed:3 support:1 there:6 tsys:11 ρtot:7 dispersion:3 width:3 anderson:1 conservation:1 low:3 way:1 analyze:1 was:8 convolutionless:12 kl1:1 raman:10 form:12 phenomena:1 jun:1 but:5 hi:10 atom:65 lindblad:5 highest:2 longer:2 commun:1 durfee:1 inside:4 us:1 ur:2 ωk:2 frequency:2 limit:3 pl:12 shibata:2 pumped:1 demonstrate:1 distribution:1 similar:3 agree:1 expect:1 detailed:2 diverges:3 constant:5 attenuating:1 defined:5 certain:2 describe:2 am:1 general:2 ap:2 single:3 reservoirs:5 rule:3 our:11 regime:14 again:2 functions:10 compared:3 no:4 whereas:4 mathematica:1 when:1 graduiertenkolleg:1 application:1 valid:8 republic:1 papers:1 deviation:1 picture:3 briefly:2 elements:1 provided:1 variation:1 includes:2 a1:21 a0:22 important:5 bounded:1 refrain:1 vectors:1 included:2 transfers:1 m18:1 acknowledgment:1 43c:1 condensation:1 insertions:2 coupling:61 algorithm:8 dω:2 assume:2 dτ:2 factors:1 berlin:1 together:1 investigated:2 mass:2 presenting:1 time:39 meystre:4 starting:2 chaturvedi:1
|
quant-ph9906120.txt |@word represent:1 concept:1 partial:1 consider:2 results:2 entropy:4 lian:1 retention:1 concerned:1 tr:4 factoring:1 environment:5 stochastic:3 analogous:1 far:2 every:1 matrices:1 transmission:1 tre:2 vector:2 eigenvalues:4 deutsch:1 consistent:1 discover:1 rate:1 enhancement:2 linear:1 what:2 errors:1 plays:1 while:5 new:1 satisfy:1 degree:1 exchange:1 teleportation:1 here:1 behaviour:1 ρy:2 objects:1 obtained:1 larger:1 reason:1 amount:3 schumacher:6 action:2 resonance:3 plotted:4 requiring:1 wij:1 a23:5 total:1 use:1 positive:2 vol:1 therefore:1 taken:1 today:2 more:2 benz:1 initial:4 berlin:1 particular:1 foundations:1 iii:1 springer:1 science:2 der:1 work:1 measures:1 theories:1 reviews:1 following:1 ρx:21 heart:1 transition:1 process:2 bennett:2 states:1 effectively:1 verlag:1 information:19 provide:1 how:1 pure:2 answer:1 symposium:1 parameter:1 brassard:1 product:1 mat:1 barnum:1 may:1 after:2 dietrich:1 explored:1 lay:1 mag:1 data:1 short:1 counter:1 lines:3 so:1 definitions:1 gershenfeld:1 developed:1 over:1 flips:3 paper:1 through:1 fidelity:11 still:1 ieee:1 before:1 fig:5 might:1 versus:3 them:1 material:1 evolution:1 number:1 effects:3 they:2 february:1 materialized:1 2x:9 transmitted:1 each:1 found:2 macchiavello:1 ed:1 elementary:1 quantum:23 our:2 operation:1 eq:3 really:1 divincenzo:1 matrix:11 furthermore:2 since:1 rev:7 particles:2 similarly:1 acting:1 induced:1 correct:1 log2:5 theory:3 possibility:1 completely:1 york:1 jozsa:1 depolarizing:2 interaction:2 could:1 computers:2 vulpiani:1 counterpart:1 length:1 hence:5 xi:1 probability:3 flipping:1 channels:11 hurdle:1 quality:1 aharonov:1 rewritten:1 their:3 introduction:1 system:3 needed:1 wootters:1 bits:2 relationship:1 cup:1 direct:1 environmental:1 part:1 than:1 submitted:1 amplitude:3 ia2:2 generality:1 julian:1 need:1 apparently:1 viewed:1 built:1 responsible:1 techniques:2 channel:36 trace:1 who:1 phase:3 nuisance:1 coded:2 why:1 considered:5 proceedings:1 physics:2 shor:2 spaces:1 relation:4 find:1 popescu:2 written:6 only:2 exchanged:1 do:1 cryptography:1 means:1 during:1 processes:1 resource:1 arxiv:1 burst:1 see:1 computer:3 enhanced:1 recently:1 concern:1 capacity:3 surmounted:1 symmetric:1 qubits:2 state:6 various:1 between:4 terms:2 initially:2 however:5 magn:1 both:1 annual:2 0e:3 qubit:4 com:1 whatever:1 non:1 considering:1 described:3 basis:1 three:4 ting:3 defined:3 ph:1 θi:3 corresponding:1 coherent:7 case:1 pacs:1 solid:1 quantenmechanik:1 will:2 stauffer:1 error:1 grundlagen:1 35th:1 a21:5 a22:5 unitary:2 played:1 almost:1 vi:1 von:3 coffee:1 iv:1 ii:1 characterize:1 cond:1 dual:1 binary:1 different:4 perhaps:3 same:2 unity:1 quant:1 pauli:11 development:2 used:3 entanglement:1 identity:1 mathematische:1 without:1 solve:1 model:1 parametric:1 know:2 just:1 less:1 storage:1 sources:1 world:6 λi:6 previous:3 preprint:1 density:7 had:1 except:1 lett:2 input:2 transformation:1 chuang:1 nielsen:3 read:3 possible:2 entangled:2 sanpera:1 press:1 using:3 aiming:1 correcting:1 loss:2 like:1 follows:1 signal:1 separately:1 always:2 become:3 works:1 page:1 preskill:1 because:3 methods:1 classical:10 people:4 describing:1 does:1 noise:17 nmr:1 scientific:1 equivalent:1 processing:1 output:2 plots:1 super:2 properties:1 noisy:1 freedom:1 bloch:1 software:1 computational:1 into:1 operator:5 neumann:3 log:1 there:4 question:1 long:1 noticed:1 smolin:1 jun:1 but:1 hk:1 aµ:1 trying:1 he:2 made:2 4x:3 consist:1 society:1 whether:1 flip:1 problem:2 mechanics:1 computing:1 ai:6 describe:2 influence:2 general:1 formulation:1 formalism:1 check:1 mutual:2 codes:1 completeness:1 no:3 dashed:2 ekert:1 claiming:1 interested:1 role:1 papers:2 conclusion:2 kinds:1 superposition:1 june:1 includes:1 a1:12 a3:9 a2:10 sides:1 longer:1 algorithm:1 time:1 decoherence:8
|
quant-ph9906121.txt |@word gs:1 gr:17 magnetic:7 decays:1 splitting:7 leads:2 grateful:1 partial:3 consider:3 simon:1 eˆ:1 ehfs:1 gatchina:1 charge:4 petersburg:4 th:2 include:1 cm2:1 far:1 shabaev:1 results:4 electron:11 formula:1 mixing:3 matrices:1 level:9 ref:3 large:2 vector:2 small:3 eigenvalues:1 upper:1 smaller:2 zf:1 direct:1 approximation:3 second:1 q1s:1 estimated:1 even:3 plays:1 rate:2 brackets:1 section:4 while:1 expressed:1 experiment:1 lifshitz:1 new:1 principal:1 method:2 coefficient:3 quenched:1 ibid:2 exchange:1 respectively:1 here:2 atoms:4 mev:1 isotope:1 based:1 along:2 quite:1 deduced:1 obtained:2 incoming:1 institute:1 shift:4 larger:1 prohibited:1 ne2:3 technique:1 projection:1 integrations:1 highly:5 total:8 unit:2 γj:1 probabilities:2 finally:1 vol:1 depicted:1 m1:3 therefore:1 ip:2 taken:2 theoretical:1 baur:1 gyromagnetic:1 becomes:1 operators:1 problem:2 1s1:3 transient:1 particular:1 known:1 me:1 high:1 mg:1 rotational:12 mm:1 work:1 protons:1 fock:1 values:1 mp:4 dunford:2 numbers:2 ions:20 indicated:2 give:1 process:1 relativistic:1 states:6 minimum:1 performed:3 arise:1 times:1 hydrogen:1 axis:1 lamb:3 huge:1 rather:1 s1:2 s0:6 length:2 bmin:2 pure:1 othnitzer:1 parameter:2 sis:1 fs:2 may:1 max:1 after:1 dietrich:4 protonic:1 physik:3 fits:1 wave:1 data:1 plank:1 e23:2 negligibly:1 hfs:16 spectra:1 lines:1 yielding:1 st:4 beyer:1 negligible:1 ohlker:1 order:1 typical:2 indebted:1 over:3 experiments:5 through:1 kinetic:1 still:1 its:1 systeme:2 decay:6 energies:2 exact:1 2e1:2 better:1 fig:4 constitutes:1 non:1 curtis:1 rotations:1 greiner:1 investigated:1 primary:1 band:5 multiconfigurational:1 eµ:4 rotation:1 now:2 discuss:1 represents:1 february:1 dirac:2 characterizes:1 university:1 drake:2 magnitude:1 radial:2 found:1 universit:2 2i:1 2j:1 homogeneous:1 darmstadt:2 int:1 ei:1 directly:2 energy:15 related:2 resolvable:1 literature:1 measurement:3 quantum:5 our:1 approximated:3 ev:10 eq:6 out:3 dominates:1 matrix:1 factors:1 rep:2 since:3 rev:14 denotes:5 collisions:1 coincidences:2 scheurer:2 m2e:2 induced:1 evaluation:1 ri:1 rj:1 benjamin:1 1s:1 possibility:3 standard:1 york:1 e1:5 e2:15 interaction:5 r2:2 r3:1 widths:1 transition:9 diminished:1 feasible:2 unexcited:2 technische:2 instrum:1 corrections:2 first:2 informations:1 already:1 probability:1 number:11 channels:1 employing:1 quadrupole:1 angular:4 size:1 given:4 theoretische:1 indicate:2 chem:1 calculations:4 dfg:2 scheme:2 bosch:2 aiche:1 behind:1 helpful:1 part:1 authors:1 than:3 maxplanck:1 target:1 double:1 fm2:1 intensity:2 future:1 supposed:1 were:1 powers:1 russia:2 lowest:1 correction:4 spectrum:1 emission:1 element:1 orders:1 ray:1 menzel:1 conversion:1 strength:1 zero:1 latter:3 polarization:2 liu:1 fitting:1 internal:1 channel:1 accuracy:3 electric:1 hydrogenlike:5 gsi:3 germany:3 but:1 sheets:1 measured:1 observation:2 metag:1 calculated:4 typeset:1 electrons:1 exp:1 velocity:1 physics:1 sum:1 lying:3 precise:1 1s2s:2 1s2p:5 charles:4 rotating:2 radii:1 determined:2 fine:1 ground:13 impact:1 ratio:1 knowledge:1 state:31 should:5 being:1 only:3 factor:6 chemin:2 adiabaticity:1 dominant:1 means:1 beam:5 cannot:2 dr:2 precession:1 lefebvre:1 komplexer:2 fields:1 e1s:1 arxiv:1 yield:1 acknowledgments:1 rotationally:9 paper:1 predicted:1 analytical:1 view:1 magneton:1 multiplying:1 exists:1 grosse:1 observed:1 see:1 bare:1 result:1 discussions:1 3mp:1 barn:1 revolution:1 ways:1 nuclear:19 away:1 αz:4 dipole:1 µm:1 written:1 µn:5 various:1 between:3 approach:1 isakov:1 hence:1 spectrometers:1 jv:1 however:3 efficiency:2 shortlived:1 kev:7 inertia:2 received:1 last:1 taking:2 uncertainty:1 according:2 etc:1 figures:1 indelicato:5 contribution:3 expression:3 finds:3 experimental:2 cm:1 point:4 ca:1 corresponds:4 proton:1 carbon:2 constant:5 mpi:2 ps:4 described:1 lyman:1 radiative:5 due:3 been:6 ai:1 cosine:1 pj:1 ph:1 arises:1 flight:1 both:1 photon:6 deter:1 determination:2 angles:2 spin:2 present:3 mcdf:2 case:2 p0:14 p1:8 pacs:1 appearance:1 empirical:3 value:8 will:1 near:1 involved:1 situation:1 region:1 ekin:1 binding:1 averaging:1 refs:2 thus:3 photonuclear:1 equal:1 reads:1 turns:1 briand:4 plunien:4 grant:1 radiation:1 cross:4 any:1 shifts:1 another:1 quant:1 emphasize:1 finite:2 higher:1 transitions:4 extended:1 effect:4 hand:1 ion:7 moment:6 levels:5 hospitality:1 landau:1 passing:1 recent:1 lower:1 framework:3 acknowledge:1 well:4 bohr:1 without:2 components:1 coordinate:1 self:1 charged:4 magnetization:1 just:1 moments:1 accurate:1 obtain:3 isoelectronic:1 oxford:1 nonrotating:1 atomic:5 uller:1 scattering:1 captured:1 parente:1 enters:1 density:1 absorption:1 photons:3 exclusively:1 lett:9 mottelson:1 excited:15 momentum:4 real:1 spinless:1 bands:1 forbidden:1 background:3 vacuum:1 press:1 using:2 p1s:1 loss:1 like:2 particle:1 follows:1 collective:1 performing:1 soff:6 yields:3 hyperfine:9 stationary:1 reduced:2 schwalm:1 right:1 qed:1 mohr:4 sequence:1 absolutely:1 church:1 rffi:1 supplementary:1 deduce:1 labzowsky:3 b2:1 quenching:1 esr:1 measurements:5 per:2 does:1 assuming:2 mined:1 dresden:4 bold:1 pionic:1 equivalent:3 habs:1 revtex:1 references:1 δ2p:1 about:4 most:1 bmbf:1 discussed:1 o:3 side:1 bertulani:1 characterized:1 conserving:1 facility:1 pergamon:1 into:1 within:4 obtaining:1 mansour:1 accounts:1 operator:1 financial:2 strasse:1 methods:1 grunberg:1 institut:3 additional:1 area:1 support:2 there:2 nucl:2 width:4 much:1 low:4 fraction:1 was:2 iˆ:2 function:1 daad:1 form:1 enough:1 metastable:2 jun:1 schwerionenforschung:1 expected:1 neutral:1 hc:1 line:1 utilizing:1 he:1 directed:2 absent:1 characteristic:1 inside:2 up:1 us:1 ur:4 converted:1 those:1 verification:1 gould:1 ωn:2 distribution:2 mechanics:1 gesellschaft:1 associated:2 af:1 defined:3 abstract:1 contribute:1 denote:1 laboratory:1 lifetime:9 dε:1 distributions:1 defines:1 moshammer:1 ni:3 compared:1 no:2 uranium:9 virtual:1 envisaged:1 role:1 spatial:1 nr:5 ns:2 deviation:1 clean:1 excitation:8 prepared:1 foil:10 important:1 nucleus:19 structure:5 steck:1 land:1 coulomb:1 proposed:1 required:1 together:1 mass:4 time:3 nuclei:10 resolution:1 4a:1
|
quant-ph9906122.txt |@word sch:4 switched:1 both:1 focus:1 illustrated:1 roy:1 scalar:3 entropy:2 consists:1 research:1 consider:1 increase:1 terms:6 calculate:1 tr:10 corrections:1 intensive:1 quasi:1 squeezing:12 present:1 under:4 robaschik:1 far:1 rise:2 results:1 condition:5 induced:8 hamiltonian:14 turns:1 eigenmodes:1 t1:1 large:3 discrete:1 vector:1 small:1 enhance:2 challenge:1 configurations:1 uµν:2 employing:1 force:4 oscillation:1 sinh2:2 sailer:1 measurable:1 pulse:1 approximation:6 second:3 enclosed:1 mitter:1 further:2 dynamics:2 canonical:3 even:4 appear:1 rate:2 sum:3 experiment:2 ˆi:1 lamoreaux:1 contributes:2 consisting:1 contrast:1 backreaction:3 gsi:1 respectively:4 here:1 behaviour:1 explore:1 relaxation:2 consideration:2 strong:2 z0:1 appears:1 change:4 deduced:2 obtained:3 dashed:2 antisymmetric:1 involved:3 leaves:1 larger:1 allows:2 vibrating:7 resulting:2 action:1 resonance:7 conveniently:1 studies:1 involves:2 via:1 addressed:1 claredon:1 aˆλ:1 apply:1 total:8 µa:2 asymptotic:1 would:1 intensively:1 remains:3 contains:1 visit:1 daad:1 jaekel:2 scenarios:1 linear:2 examination:1 taken:2 survive:1 associated:2 von:1 reflects:1 more:2 formally:1 initiated:1 comparison:1 becomes:2 operators:1 about:1 particular:2 known:1 cases:2 hold:1 sλλ:1 high:1 account:3 lengths:1 room:1 recall:1 equation:3 reviews:1 remain:1 fock:1 temperatures:6 ms:1 concepts:1 following:1 modifies:1 drops:1 numbers:2 indicated:1 mirrors:1 predict:1 neglected:2 states:1 indicates:1 performed:1 magnitudes:1 feasible:1 creates:1 goal:1 provide:1 verify:2 discussion:1 holds:1 utilize:1 occuring:1 pure:11 parameter:2 ensemble:3 exponentially:1 oscillatory:1 product:1 undergoing:1 may:6 after:4 derived:5 applications:2 physik:1 wave:4 data:1 parallel:1 dynamical:19 effective:5 explicit:2 ghz:1 trembling:1 rather:1 so:2 fundamental:5 ned:1 representation:1 looking:1 order:9 typical:2 s0:1 exploited:1 ature:1 over:3 satisfied:3 interpreted:1 produced:1 course:1 thermal:21 experiments:1 london:2 statistical:3 erot:1 existence:1 still:1 aλ:1 before:1 lc:1 ln:2 mohideen:2 production:2 microscopic:1 systems:2 covered:1 main:1 decades:1 maximal:1 non:2 cen:1 greiner:2 processes:4 anticipated:1 framework:1 effects:8 they:1 half:1 now:3 refering:1 represents:2 february:1 several:2 always:1 university:1 presented:2 barton:1 sin:2 financially:1 realistic:2 magnitude:2 mode:8 disregard:1 accounts:1 universit:1 assume:1 characterized:1 constraints:3 el:1 financial:1 generation:1 energy:7 ef:1 investigated:2 static:4 expect:2 measurement:1 quantum:13 our:3 eq:7 out:4 matrix:1 space:1 rep:1 singapore:1 rev:10 denotes:3 particles:9 investigation:1 dominate:1 ref:6 integrated:1 math:1 occurs:1 theory:4 diagonal:2 term:16 lajos:1 eigenvalues:1 estimate:1 temperature:22 definition:1 interaction:5 derivation:1 created:5 argument:1 could:6 hyperbolic:1 times:4 motion:7 turn:1 technische:1 derivations:1 vac:4 consequence:4 undergo:2 2ωt:3 first:3 major:1 initial:2 qˆµ:1 number:16 theoretische:1 restrict:1 another:1 shadowed:2 eberlein:1 size:4 given:5 perturbation:4 publication:1 similarly:1 ordering:2 leading:1 eqs:1 achieved:1 system:6 least:1 response:3 indicate:2 perturbations:1 master:1 calculations:1 convention:1 dt1:1 perfectly:1 gives:2 continuous:1 prediction:2 dfg:1 specify:1 kind:1 hopping:1 namely:1 annihilation:1 determined:3 supposed:1 amplitude:2 tion:1 enables:1 klimov:1 perturbative:2 lowest:5 acknowledged:1 correction:2 spectrum:2 generalization:1 vilenkin:2 need:1 constrained:3 occupied:1 orders:5 generalizes:1 zero:1 min:1 εt:1 latter:1 predominantly:1 note:3 internal:1 istv:1 negligible:1 eff:5 unperturbed:2 spectral:1 play:1 akad:1 allow:1 trace:1 normal:1 most:6 involving:1 experiences:1 letter:1 phase:2 analytically:1 kb:1 deviations:1 acknowledges:1 especially:1 consequences:1 considered:1 parametric:1 average:1 adopt:1 totic:1 physica:1 exp:4 velocity:9 left:1 pˆν:1 notion:1 fact:1 phenomenon:3 disturbances:1 timedependent:1 supported:1 rotating:3 hungary:1 ground:1 ratio:1 parameters:1 commutators:1 should:4 only:3 corresponds:2 factor:4 achieve:1 equilibrium:4 his:1 dominant:2 closed:4 quantph:1 means:1 dependent:3 expectation:5 cannot:1 during:4 dt:7 years:1 intensify:1 evolution:8 fields:3 arxiv:1 investigate:2 nλ:6 predicted:1 dodonov:2 lovas:1 fixed:1 view:2 requirement:1 ser:1 observes:1 up:1 see:6 result:3 enhanced:1 discussions:1 close:1 forthcoming:1 subject:1 preparation:1 satisfying:1 interacting:1 enlightening:1 resonantly:5 definite:1 fulling:2 its:4 µm:1 state:1 radiated:5 between:1 iω0:1 boundary:6 approach:3 law:2 available:3 n1s:1 recently:1 initially:3 neglection:1 however:3 gratefully:1 bose:1 configuration:1 wx:1 observable:2 essentially:1 last:1 mob:1 region:1 vibration:4 according:3 fulfilled:1 figures:1 context:1 casimir:23 variance:2 contribution:10 expression:2 experimental:7 relevant:2 cm:2 conclude:1 wall:2 address:1 cf:2 dimensional:2 variety:1 simply:1 respect:1 throughout:1 selfadjoint:1 sine:1 described:2 cavities:3 aˆ:6 addition:1 equations:2 three:1 been:5 basic:1 ph:1 ann:1 fig:2 generating:1 corresponding:3 ωt:2 photon:4 precision:1 gap:1 external:6 systematic:1 those:2 case:4 multi:1 utzhold:4 pacs:1 solid:2 might:1 single:2 value:9 will:9 while:3 replaced:1 theoretical:2 evaluating:1 promising:1 aid:1 gerhard:1 couplings:1 uncertainty:1 europhys:1 refs:1 thus:4 reads:1 confirms:1 plunien:6 considerable:1 generic:2 radiation:8 lett:7 any:4 shorter:1 noninteracting:1 quant:1 units:1 plates:1 dimensionless:2 finite:16 higher:1 independent:1 used:1 cubic:2 i3:1 upon:1 effect:35 moving:3 uˆ:4 generalize:1 recent:2 intermode:1 off:1 scenario:1 changes:4 lambrecht:3 well:2 davis:2 comes:1 easily:1 eigenmode:1 position:1 arising:2 possesses:1 usual:1 less:1 being:1 rest:1 shape:1 underlying:1 identify:1 sufficiently:1 uller:2 yet:2 preprint:1 generator:1 density:1 mµν:3 photons:9 point:1 seems:1 thermodynamics:2 attractive:1 wet:1 relevance:2 match:1 real:1 tests:2 aspects:1 depends:1 unter:1 situation:1 evaluate:1 possible:3 period:1 increases:2 background:5 vacuum:16 immediately:1 aiming:1 like:2 success:1 performing:1 soff:3 harmonically:1 yields:1 arbitrary:1 become:1 essential:1 therein:2 neumann:1 classical:1 creation:7 some:2 calculated:1 mirror:3 proper:1 neglecting:1 provided:3 scale:1 describing:1 dimensions:1 lead:1 confirm:1 cavity:18 measurements:2 integration:1 contributing:1 does:5 harmonic:1 assuming:1 ralf:1 proc:2 measuring:2 considering:2 dresden:2 scientific:1 oscillating:2 analysing:1 integers:1 conducting:1 world:1 dˆ:1 bmbf:1 dependence:4 o:4 ensure:1 germany:1 efforts:1 automatically:1 enhancement:2 soc:1 significant:2 presence:1 into:1 within:4 obtaining:1 device:1 references:3 operator:15 proportional:2 bosonic:2 choosen:1 institut:1 additional:2 area:2 reynaud:2 assumed:4 support:1 there:2 question:1 depicted:1 long:2 ordered:1 intention:1 accordingly:3 quadratic:2 low:1 way:1 perform:1 was:1 assumes:1 function:4 form:2 jun:1 but:1 ford:2 line:2 sµν:3 whether:3 characteristic:4 inside:2 particle:4 us:4 ur:1 placed:2 frequency:8 limit:1 verification:3 fluctuations:1 distribution:3 similar:1 called:1 obtains:3 detailed:1 later:1 constant:2 moore:1 coincides:1 abstract:1 contribute:2 influence:3 general:2 duration:2 examine:1 exist:1 together:2 formalism:3 bordag:1 compared:2 thermodynamical:1 no:3 cos:1 when:5 envisaged:1 field:7 conditions:7 role:1 details:2 investigations:1 department:1 massless:2 korn:1 stay:1 a1:2 important:1 fabry:1 variable:1 εmax:1 sνµ:1 gets:1 conclusive:1 implies:4 longer:1 perturbatively:1 physics:1 curve:2 governed:1 sˆ1:2 time:21 n1:6 having:1
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.