99:
than separable states. Families of bound entangled states known analytically even for high dimension that outperform separable states for metrology. For large dimensions they approach asymptotically the maximal precision achievable by bipartite quantum states. There are bipartite bound entangled
94:
While no singlets can be distilled from bound entangled state, they can be still useful for some quantum information processing applications. Bound entanglement can be activated. Any entangled state can enhance the teleportation power of some other state. This holds even if the state is bound
84:
It has been shown that bipartite bound entangled states with a positive partial transpose exist in symmetric systems. It has also been shown that in symmetric systems multipartite bound entangled states exists for which all partial transposes are non-negative.
60:
There are also multipartite entangled states that have a negative partial transpose with respect to some bipartitions, while they have a positive partial transpose to the other partitions, nevertheless, they are undistillable.
91:
conjectured that bipartite bound entangled states with positive partial transpose cannot violate a Bell inequality. After a long search for counterexamples, the conjecture turned out to be false.
450:
DiVincenzo, David P.; Shor, Peter W.; Smolin, John A.; Terhal, Barbara M.; Thapliyal, Ashish V. (17 May 2000). "Evidence for bound entangled states with negative partial transpose".
715:
Tura, J.; Augusiak, R.; Hyllus, P.; KuĹ›, M.; Samsonowicz, J.; Lewenstein, M. (22 June 2012). "Four-qubit entangled symmetric states with positive partial transpositions".
344:
Piani, Marco; Mora, Caterina E. (4 January 2007). "Class of positive-partial-transpose bound entangled states associated with almost any set of pure entangled states".
100:
states that are not more useful than separable states, but if an auxiliary qubit is added to one of the subsystems then they outperform separable states in metrology.
78:
Bipartite bound entangled states with a positive partial transpose are useless for teleportation, as they cannot lead to a larger fidelity than the classical limit.
117:
Horodecki, Michał; Horodecki, Paweł; Horodecki, Ryszard (15 June 1998). "Mixed-State
Entanglement and Distillation: Is there a "Bound" Entanglement in Nature?".
548:
Horodecki, Michał; Horodecki, Paweł; Horodecki, Ryszard (1 September 1999). "General teleportation channel, singlet fraction, and quasidistillation".
503:
Horodecki, Pawel; Smolin, John A; Terhal, Barbara M; Thapliyal, Ashish V (January 2003). "Rank two bipartite bound entangled states do not exist".
53:
are all bound-entangled. Moreover, a particular quantum state for 2x4 systems has been presented. Such states are not detected by the
57:
as entangled, thus other entanglement criteria are needed for their detection. There are a number of examples for such states.
601:
Chen, Lin; Tang, Wai-Shing (2 February 2017). "Schmidt number of bipartite and multipartite states under local projections".
64:
The possible existence of bipartite bound entangled states with a negative partial transpose is still under intensive study.
1167:
223:
Bennett, Charles H.; DiVincenzo, David P.; Mor, Tal; Shor, Peter W.; Smolin, John A.; Terhal, Barbara M. (28 June 1999).
870:
Horodecki, Paweł; Horodecki, Michał; Horodecki, Ryszard (1 February 1999). "Bound
Entanglement Can Be Activated".
50:
923:
Masanes, LluĂs (17 April 2006). "All
Bipartite Entangled States Are Useful for Information Processing".
170:
BruĂź, Dagmar; Peres, Asher (4 February 2000). "Construction of quantum states with bound entanglement".
54:
27:
95:
entangled. Bipartite entangled states with a non-negative partial transpose can be more useful for
283:
Breuer, Heinz-Peter (22 August 2006). "Optimal
Entanglement Criterion for Mixed Quantum States".
81:
Bound entangled states with a positive partial transpose in 3x3 systems have a
Schmidt number 2.
1125:
1074:
1007:
942:
889:
826:
734:
673:
620:
567:
469:
416:
363:
302:
249:
189:
136:
23:
72:
Bipartite bound entangled states do not exist in 2x2 or 2x3 systems, only in larger ones.
8:
67:
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38:
1115:
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1033:
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905:
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152:
126:
526:
42:
1143:
1087:
1052:
1037:
1025:
958:
909:
844:
805:"Disproving the Peres conjecture by showing Bell nonlocality from bound entanglement"
754:
689:
587:
436:
318:
156:
96:
46:
970:
701:
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TĂłth, GĂ©za; GĂĽhne, Otfried (1 May 2009). "Entanglement and
Permutational Symmetry".
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534:
489:
383:
330:
269:
1138:
1133:
1103:
1082:
1020:
1015:
985:
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834:
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742:
685:
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628:
575:
522:
477:
424:
371:
310:
257:
209:
197:
144:
954:
397:
Smolin, John A. (9 February 2001). "Four-party unlockable bound entangled state".
314:
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Tóth, Géza; Vértesi, Tamás; Horodecki, Paweł; Horodecki, Ryszard (7 July 2020).
901:
261:
148:
746:
481:
428:
375:
201:
781:
632:
1161:
579:
1147:
1029:
986:"Quantum States with a Positive Partial Transpose are Useful for Metrology"
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131:
88:
1051:
Pál, Károly F.; Tóth, Géza; Bene, Erika; Vértesi, Tamás (10 May 2021).
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804:
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Properties of bound entangled states with a positive partial transpose
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615:
821:
729:
668:
502:
1101:
1053:"Bound entangled singlet-like states for quantum metrology"
869:
547:
116:
31:
449:
222:
49:. Bipartite entangled states that have a non-negative
714:
225:"Unextendible Product Bases and Bound Entanglement"
30:
with local operations and classical communication (
1050:
803:Vértesi, Tamás; Brunner, Nicolas (December 2014).
768:Peres, Asher (1999). "All the Bell Inequalities".
1159:
984:Tóth, Géza; Vértesi, Tamás (12 January 2018).
802:
75:Rank-2 bound entangled states do not exist.
1104:"Activating Hidden Metrological Usefulness"
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37:Bound entanglement was discovered by
13:
14:
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16:Weak form of quantum entanglement
1088:10.1103/PhysRevResearch.3.023101
26:, from which no singlets can be
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647:
594:
1139:10.1103/PhysRevLett.125.020402
1021:10.1103/PhysRevLett.120.020506
686:10.1103/PhysRevLett.102.170503
603:Quantum Information Processing
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1:
955:10.1103/PhysRevLett.96.150501
527:10.1016/S0304-3975(01)00376-0
315:10.1103/PhysRevLett.97.080501
103:
505:Theoretical Computer Science
7:
1168:Quantum information science
902:10.1103/PhysRevLett.82.1056
262:10.1103/PhysRevLett.82.5385
149:10.1103/PhysRevLett.80.5239
10:
1184:
747:10.1103/PhysRevA.85.060302
482:10.1103/PhysRevA.61.062312
429:10.1103/PhysRevA.63.032306
376:10.1103/PhysRevA.75.012305
202:10.1103/PhysRevA.61.030301
633:10.1007/s11128-016-1501-y
55:Peres-Horodecki criterion
1057:Physical Review Research
580:10.1103/PhysRevA.60.1888
1108:Physical Review Letters
990:Physical Review Letters
925:Physical Review Letters
872:Physical Review Letters
782:10.1023/A:1018816310000
656:Physical Review Letters
285:Physical Review Letters
232:Physical Review Letters
119:Physical Review Letters
770:Foundations of Physics
809:Nature Communications
24:quantum entanglement
1130:2020PhRvL.125b0402T
1079:2021PhRvR...3b3101P
1012:2018PhRvL.120b0506T
947:2006PhRvL..96o0501M
894:1999PhRvL..82.1056H
831:2014NatCo...5.5297V
739:2012PhRvA..85f0302T
678:2009PhRvL.102q0503T
625:2017QuIP...16...75C
572:1999PhRvA..60.1888H
474:2000PhRvA..61f2312D
421:2001PhRvA..63c2306S
368:2007PhRvA..75a2305P
307:2006PhRvL..97h0501B
254:1999PhRvL..82.5385B
194:2000PhRvA..61c0301B
141:1998PhRvL..80.5239H
840:10.1038/ncomms6297
22:is a weak form of
20:Bound entanglement
717:Physical Review A
550:Physical Review A
452:Physical Review A
399:Physical Review A
346:Physical Review A
238:(26): 5385–5388.
172:Physical Review A
125:(24): 5239–5242.
97:quantum metrology
51:partial transpose
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938:quant-ph/0508071
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885:quant-ph/9806058
878:(5): 1056–1059.
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556:(3): 1888–1898.
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17:
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1094:
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931:(15): 150501.
915:
862:
795:
776:(4): 589–614.
760:
707:
662:(17): 170503.
646:
593:
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511:(3): 589–596.
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1080:
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1066:
1063:(2): 023101.
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1027:
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723:(6): 060302.
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458:(6): 062312.
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405:(3): 032306.
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352:(1): 012305.
351:
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291:(8): 080501.
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178:(3): 030301.
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47:R. Horodecki
43:P. Horodecki
39:M. Horodecki
36:
19:
18:
815:(1): 5297.
89:Asher Peres
1121:1911.02592
1070:2002.12409
1003:1709.03995
616:1609.05100
609:(75): 75.
104:References
1038:206306250
910:119390324
822:1405.4502
755:118386611
730:1203.3711
669:0812.4453
588:119532807
437:119474939
157:111379972
28:distilled
1162:Category
1148:32701319
1030:29376687
971:10914899
963:16712136
849:25370352
702:43527866
694:19518768
641:34893860
535:43737866
490:37213011
384:55900164
331:14406014
323:17026285
270:14688979
1126:Bibcode
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857:5135148
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790:9697993
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