535: = 4 NOON state without the need for postselection or zero photon detections, and has the same success probability of 3/64 as the more complicated circuit of Kok et al. Cable and Dowling proposed a method that has polynomial scaling in the success probability, which can therefore be called efficient.
530:
proposed the first general method based on post-selection via photodetection. The down-side of this method was its exponential scaling of the success probability of the protocol. Pryde and White subsequently introduced a simplified method using intensity-symmetric multiport beam splitters, single
565:
Super-resolution has previously been used as indicator of NOON state production, in 2005 Resch et al. showed that it could equally well be prepared by classical interferometry. They showed that only phase super-sensitivity is an unambiguous indicator of a NOON state; furthermore they introduced
186:
493:
1352:
Boto, Agedi N.; Kok, Pieter; Abrams, Daniel S.; Braunstein, Samuel L.; Williams, Colin P.; Dowling, Jonathan P. (2000). "Quantum
Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit".
1153:
Slussarenko, Sergei; Weston, Morgan M.; Chrzanowski, Helen M.; Shalm, Lynden K.; Verma, Varun B.; Nam, Sae Woo; Pryde, Geoff J. (2017). "Unconditional violation of the shot-noise limit in photonic quantum metrology".
330:
43:
550:. Three- and four-photon NOON states cannot be created deterministically from single-photon states, but they have been created probabilistically via post-selection using
558:
and a classical laser beam on a 50:50 beam splitter, was used by I. Afek, O. Ambar, and Y. Silberberg to experimentally demonstrate the production of NOON states up to
1084:
Resch, K. J.; Pregnell, K. L.; Prevedel, R.; Gilchrist, A.; Pryde, G. J.; O’Brien, J. L.; White, A. G. (2007). "Time-Reversal and Super-Resolving Phase
Measurements".
826:
Walther, Philip; Pan, Jian-Wei; Aspelmeyer, Markus; Ursin, Rupert; Gasparoni, Sara; Zeilinger, Anton (2004). "De
Broglie wavelength of a non-local four-photon state".
409:
373:
401:
353:
555:
551:
181:{\displaystyle |\psi _{\text{NOON}}\rangle ={\frac {|N\rangle _{a}|0\rangle _{b}+e^{iN\theta }|{0}\rangle _{a}|{N}\rangle _{b}}{\sqrt {2}}},\,}
757:
Cable, Hugo; Dowling, Jonathan P. (2007). "Efficient
Generation of Large Number-Path Entanglement Using Only Linear Optics and Feed-Forward".
566:
criteria for determining if it has been achieved based on the observed visibility and efficiency. Phase super sensitivity of NOON states with
1225:
Nagata, T.; Okamoto, R.; O'Brien, J. L.; Sasaki, K.; Takeuchi, S. (2007). "Beating the
Standard Quantum Limit with Four-Entangled Photons".
237:
1489:
635:
Kok, Pieter; Lee, Hwang; Dowling, Jonathan P. (2002). "Creation of large-photon-number path entanglement conditioned on photodetection".
1023:
Israel, Y.; Afek, I.; Rosen, S.; Ambar, O.; Silberberg, Y. (2012). "Experimental tomography of NOON states with large photon numbers".
570: = 2 was demonstrated and super resolution, but not super sensitivity as the efficiency was too low, of NOON states up to
511:
895:
Mitchell, M. W.; Lundeen, J. S.; Steinberg, A. M. (2004). "Super-resolving phase measurements with a multiphoton entangled state".
543:
531:
photon inputs, and either heralded or conditional measurement. Their method, for example, allows heralded production of the
696:
Pryde, G. J.; White, A. G. (2003). "Creation of maximally entangled photon-number states using optical fiber multiports".
542: = 2, can be created deterministically from two identical photons and a 50:50 beam splitter. This is called the
1494:
964:
Afek, I.; Ambar, O.; Silberberg, Y. (2010). "High-NOON States by Mixing
Quantum and Classical Light".
583:
1441:
1372:
1310:
1244:
1173:
1103:
1042:
973:
914:
845:
776:
715:
654:
34:
1422:
Lee, Hwang; Kok, Pieter; Dowling, Jonathan P. (2002). "A quantum
Rosetta stone for interferometry".
603:
595:
587:
1295:
1465:
1431:
1404:
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1207:
1163:
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1066:
1032:
1005:
946:
904:
877:
835:
808:
766:
739:
705:
678:
644:
606:. The term "NOON state" first appeared in print as a footnote in a paper published by Hwang Lee,
591:
507:
488:{\displaystyle \Delta \theta ={\frac {\Delta A}{|d\langle A\rangle /d\theta |}}={\frac {1}{N}}.}
1457:
1396:
1388:
1334:
1326:
1268:
1260:
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997:
989:
938:
930:
869:
861:
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792:
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220:
358:
1449:
1380:
1318:
1252:
1189:
1181:
1111:
1050:
981:
922:
853:
784:
723:
662:
611:
527:
499:
378:
224:
1296:"Quantum dynamics of the nonlinear rotator and the effects of continual spin measurement"
1445:
1376:
1314:
1248:
1177:
1107:
1046:
977:
918:
849:
780:
719:
658:
547:
338:
228:
22:
1483:
1070:
1009:
682:
554:. A different approach, involving the interference of non-classical light created by
503:
208:
1469:
1280:
1211:
812:
743:
1408:
1139:
950:
881:
1115:
788:
522:
There have been several theoretical proposals for creating photonic NOON states.
1453:
1384:
1054:
727:
666:
227:
for their ability to make precision phase measurements when used in an optical
1185:
607:
523:
1461:
1392:
1330:
1322:
1264:
1203:
1123:
1062:
993:
934:
865:
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735:
674:
1256:
985:
1400:
1272:
1131:
1001:
942:
873:
804:
1338:
1436:
1367:
1098:
909:
840:
710:
649:
1194:
926:
857:
325:{\displaystyle A=|N,0\rangle \langle 0,N|+|0,N\rangle \langle N,0|.\,}
204:
1168:
355:
for a system in a NOON state switches between +1 and −1 when
1239:
1037:
771:
599:
574: = 4 photons was also demonstrated experimentally.
594:
states. They were independently rediscovered in 2000 by
618:, where it was spelled N00N, with zeros instead of Os.
403:. Moreover, the error in the phase measurement becomes
602:, who introduced them as the basis for the concept of
412:
381:
361:
341:
240:
46:
487:
395:
367:
347:
324:
180:
502:, and gives a quadratic improvement over the
203:, and vice versa. Usually, the particles are
8:
447:
441:
301:
298:
264:
261:
157:
137:
98:
80:
62:
16:Quantum-mechanical many-body entangled state
1435:
1366:
1238:
1193:
1167:
1097:
1036:
908:
839:
770:
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648:
472:
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114:
101:
89:
83:
71:
68:
56:
47:
45:
219:NOON states are an important concept in
627:
231:. For example, consider the observable
556:spontaneous parametric down-conversion
552:spontaneous parametric down-conversion
582:NOON states were first introduced by
506:. NOON states are closely related to
7:
191:which represents a superposition of
425:
413:
33:is a quantum-mechanical many-body
14:
518:Towards experimental realization
538:Two-photon NOON states, where
462:
434:
314:
285:
277:
248:
147:
127:
90:
72:
48:
1:
1116:10.1103/PhysRevLett.98.223601
789:10.1103/PhysRevLett.99.163604
514:, and are extremely fragile.
199:with zero particles in mode
1490:Quantum information science
1454:10.1080/0950034021000011536
1385:10.1103/PhysRevLett.85.2733
586:in the context of studying
1511:
1294:Sanders, Barry C. (1989).
1055:10.1103/PhysRevA.85.022115
728:10.1103/PhysRevA.68.052315
667:10.1103/PhysRevA.65.052104
1186:10.1038/s41566-017-0011-5
335:The expectation value of
211:can support NOON states.
1424:Journal of Modern Optics
1323:10.1103/PhysRevA.40.2417
1355:Physical Review Letters
1257:10.1126/science.1138007
1086:Physical Review Letters
986:10.1126/science.1188172
759:Physical Review Letters
578:History and terminology
368:{\displaystyle \theta }
207:, but in principle any
504:standard quantum limit
498:This is the so-called
489:
397:
396:{\displaystyle \pi /N}
369:
349:
326:
182:
544:Hong–Ou–Mandel effect
490:
398:
370:
350:
327:
183:
1430:(14–15): 2325–2338.
410:
379:
359:
339:
238:
44:
1446:2002JMOp...49.2325L
1377:2000PhRvL..85.2733B
1315:1989PhRvA..40.2417S
1249:2007Sci...316..726N
1178:2017NaPho..11..700S
1108:2007PhRvL..98v3601R
1047:2012PhRvA..85b2115I
978:2010Sci...328..879A
927:10.1038/nature02493
919:2004Natur.429..161M
858:10.1038/nature02552
850:2004Natur.429..158W
781:2007PhRvL..99p3604C
720:2003PhRvA..68e2315P
659:2002PhRvA..65e2104K
604:quantum lithography
596:Jonathan P. Dowling
588:quantum decoherence
485:
393:
375:changes from 0 to
365:
345:
322:
195:particles in mode
178:
1361:(13): 2733–2736.
1303:Physical Review A
1233:(5825): 726–729.
1025:Physical Review A
972:(5980): 879–881.
903:(6988): 161–164.
834:(6988): 158–161.
698:Physical Review A
637:Physical Review A
616:quantum metrology
526:, Hwang Lee, and
480:
467:
348:{\displaystyle A}
221:quantum metrology
172:
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59:
1502:
1474:
1473:
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1437:quant-ph/0202133
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1368:quant-ph/9912052
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1309:(5): 2417–2427.
1300:
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1197:
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1156:Nature Photonics
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711:quant-ph/0304135
693:
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650:quant-ph/0112002
632:
612:Jonathan Dowling
584:Barry C. Sanders
562: = 5.
528:Jonathan Dowling
500:Heisenberg limit
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1162:(11): 700–703.
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35:entangled state
17:
12:
11:
5:
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1495:Quantum states
1492:
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1344:
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1217:
1145:
1092:(22): 223601.
1076:
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956:
887:
818:
765:(16): 163604.
749:
688:
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623:
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579:
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548:quantum optics
519:
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23:quantum optics
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1031:(2): 022115.
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704:(5): 052315.
703:
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672:
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664:
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656:
651:
646:
643:(5): 052104.
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209:bosonic field
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1195:10072/369032
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640:
636:
630:
598:'s group at
581:
571:
567:
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559:
539:
537:
532:
521:
497:
334:
218:
215:Applications
200:
196:
192:
190:
30:
26:
20:
18:
510:states and
1484:Categories
1169:1707.08977
622:References
608:Pieter Kok
524:Pieter Kok
512:GHZ states
31:N00N state
27:NOON state
1462:0950-0340
1393:0031-9007
1331:0556-2791
1265:0036-8075
1240:0708.1385
1204:1749-4885
1124:0031-9007
1071:118485412
1063:1050-2947
1038:1112.4371
1010:206525962
994:0036-8075
935:0028-0836
866:0028-0836
797:0031-9007
772:0704.0678
736:1050-2947
683:118995886
675:1050-2947
459:θ
448:⟩
442:⟨
426:Δ
417:θ
414:Δ
383:π
363:θ
302:⟨
299:⟩
265:⟨
262:⟩
158:⟩
138:⟩
122:θ
99:⟩
81:⟩
63:⟩
54:ψ
1470:38966183
1401:10991220
1281:14597941
1273:17478715
1212:51684888
1132:17677842
1002:20466927
943:15141206
874:15141205
813:18816777
805:17995252
744:53981408
1442:Bibcode
1409:7373285
1373:Bibcode
1339:9902422
1311:Bibcode
1245:Bibcode
1227:Science
1174:Bibcode
1140:6923254
1104:Bibcode
1043:Bibcode
974:Bibcode
966:Science
951:4303598
915:Bibcode
882:4354232
846:Bibcode
777:Bibcode
716:Bibcode
655:Bibcode
205:photons
1468:
1460:
1407:
1399:
1391:
1337:
1329:
1279:
1271:
1263:
1210:
1202:
1138:
1130:
1122:
1069:
1061:
1008:
1000:
992:
949:
941:
933:
897:Nature
880:
872:
864:
828:Nature
811:
803:
795:
742:
734:
681:
673:
610:, and
1466:S2CID
1432:arXiv
1405:S2CID
1363:arXiv
1299:(PDF)
1277:S2CID
1235:arXiv
1208:S2CID
1164:arXiv
1136:S2CID
1094:arXiv
1067:S2CID
1033:arXiv
1006:S2CID
947:S2CID
905:arXiv
878:S2CID
836:arXiv
809:S2CID
767:arXiv
740:S2CID
706:arXiv
679:S2CID
645:arXiv
1458:ISSN
1397:PMID
1389:ISSN
1335:PMID
1327:ISSN
1269:PMID
1261:ISSN
1200:ISSN
1128:PMID
1120:ISSN
1059:ISSN
998:PMID
990:ISSN
939:PMID
931:ISSN
870:PMID
862:ISSN
801:PMID
793:ISSN
732:ISSN
671:ISSN
223:and
58:NOON
25:, a
1450:doi
1381:doi
1319:doi
1253:doi
1231:316
1190:hdl
1182:doi
1112:doi
1051:doi
982:doi
970:328
923:doi
901:429
854:doi
832:429
785:doi
724:doi
663:doi
614:on
600:JPL
590:in
546:in
29:or
21:In
1486::
1464:.
1456:.
1448:.
1440:.
1428:49
1426:.
1403:.
1395:.
1387:.
1379:.
1371:.
1359:85
1357:.
1333:.
1325:.
1317:.
1307:40
1305:.
1301:.
1275:.
1267:.
1259:.
1251:.
1243:.
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