Maximally entangled set of multipartite quantum states

Physical Review Letters

Volumn 111, Issue 11, 2013, Pages

  De Vicente, J I ^a   Spee, C ^b   Kraus, B ^b  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^b UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL COMMUNICATION; ENTANGLEMENT MANIPULATION; LOCAL OPERATIONS; MAXIMALLY ENTANGLED STATE; N-PARTITE; QUANTUM INFORMATION THEORY; QUANTUM STATE;

QUANTUM COMPUTERS; QUANTUM ELECTRONICS;

QUANTUM ENTANGLEMENT;

EID: 84884277244     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.111.110502     Document Type: Article

References (33)

1. D. Gottesman, Ph.D. thesis, California Institute of Technology, 1997, arXiv:quant-ph/9705052.
2. R. Raussendorf and H. J. Briegel, Phys. Rev. Lett. 86, 5188 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.5188
3. For a review on multipartite systems, see for instance L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008) and references therein. RMPHAT 0034-6861 10.1103/RevModPhys.80.517
4. See, e.g., the reviews of M. B. Plenio and S. Virmani, Quantum Inf. Comput. 7, 1 (2007); QICUAW 1533-7146
5. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009). RMPHAT 0034-6861 10.1103/RevModPhys.81.865
6. M. A. Nielsen, Phys. Rev. Lett. 83, 436 (1999). PRLTAO 0031-9007 10.1103/PhysRevLett.83.436
7. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.70.1895
8. A. K. Ekert, Phys. Rev. Lett. 67, 661 (1991). PRLTAO 0031-9007 10.1103/PhysRevLett.67.661
9. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996). PLRAAN 1050-2947 10.1103/PhysRevA.53.2046
10. See, e.g., M. J. Donald, M. Horodecki, and O. Rudolph, J. Math. Phys. (N.Y.) 43, 4252 (2002); JMAPAQ 0022-2488 10.1063/1.1495917
11. E. Chitambar, Phys. Rev. Lett. 107, 190502 (2011); PRLTAO 0031-9007 10.1103/PhysRevLett.107.190502
12. E. Chitambar, W. Cui, and H.-K. Lo, Phys. Rev. Lett. 108, 240504 (2012); PRLTAO 0031-9007 10.1103/PhysRevLett.108.240504
13. E. Chitambar, D. Leung, L. Mancinska, M. Ozols, and A. Winter, arXiv:1210.4583v1.
14. S. Turgut, Y. Gül, and N. K. Pak, Phys. Rev. A 81, 012317 (2010); PLRAAN 1050-2947 10.1103/PhysRevA.81.012317
15. S. Kintas and S. Turgut, J. Math. Phys. (N.Y.) 51, 092202 (2010). JMAPAQ 0022-2488 10.1063/1.3481573
16. B. Kraus, Phys. Rev. Lett. 104, 020504 (2010); PRLTAO 0031-9007 10.1103/PhysRevLett.104.020504
17. B. Kraus Phys. Rev. A 82, 032121 (2010). PLRAAN 1050-2947 10.1103/PhysRevA.82.032121
18. W. Dür, G. Vidal, and J. I. Cirac, Phys. Rev. A 62, 062314 (2000). PLRAAN 1050-2947 10.1103/PhysRevA.62.062314
19. F. Verstraete, J. Dehaene, B. De Moor, and H. Verschelde, Phys. Rev. A 65, 052112 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.65.052112
20. G. Gour and N. R. Wallach, New J. Phys. 13, 073013 (2011). NJOPFM 1367-2630 10.1088/1367-2630/13/7/073013
21. C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 59, 1070 (1999). PLRAAN 1050-2947 10.1103/PhysRevA.59.1070
22. E. Chitambar and R. Duan, Phys. Rev. Lett. 103, 110502 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.110502
23. See, e.g., P. Facchi, G. Florio, G. Parisi, and S. Pascazio, Phys. Rev. A 77, 060304(R) (2008); PLRAAN 1050-2947 10.1103/PhysRevA.77.060304
24. G. Gour and N. R. Wallach, J. Math. Phys. (N.Y.) 51, 112201 (2010) and references therein. JMAPAQ 0022-2488 10.1063/1.3511477
25. This can be easily seen by noting that the bipartite entanglement between a single qubit and the rest cannot be increased via LOCC, and in C. H. Bennett, S. Popescu, D. Rohrlich, J. A. Smolin, and A. V. Thapliyal, Phys. Rev. A 63, 012307 (2000), it has been shown that two states, which have the same local entropies, are either LU equivalent or LOCC incomparable. PLRAAN 1050-2947 10.1103/PhysRevA.63.012307
26. F. Verstraete, J. Dehaene, and B. De Moor, Phys. Rev. A 65, 032308 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.65.032308
27. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.111.110502 for fully detailed proofs of theorems 1, 2, and 3.
28. J. I. de Vicente, T. Carle, C. Streitberger, and B. Kraus, Phys. Rev. Lett. 108, 060501 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.060501
29. N. Linden and S. Popescu, Fortschr. Phys. 46, 567 (1998). FPYKA6 0015-8208 10.1002/(SICI)1521-3978(199806)46:4/5<567::AID-PROP567>3.0.CO;2- H
30. D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999). PRLTAO 0031-9007 10.1103/PhysRevLett.83.3566
31. G. Vidal, Phys. Rev. Lett. 83, 1046 (1999). PRLTAO 0031-9007 10.1103/PhysRevLett.83.1046
32. G. Vidal, Phys. Rev. A 62, 062315 (2000). PLRAAN 1050-2947 10.1103/PhysRevA.62.062315
33. J. I. de Vicente, C. Spee, and B. Kraus (to be published).