Optimal entanglement witnesses based on local orthogonal observables

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 1, 2007, Pages

  Zhang, Cheng Jie ^a   Zhang, Yong Sheng ^a   Zhang, Shun ^a   Guo, Guang Can ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; OPTIMAL SYSTEMS; OPTIMIZATION; PROBLEM SOLVING;

BIPARTITE HIGHER-DIMENSIONAL SYSTEMS; LOCAL ORTHOGONAL OBSERVABLES; OPTIMAL NONLINEAR WITNESSES;

NONLINEAR OPTICS;

EID: 34547583525     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.012334     Document Type: Article

References (44)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, U.K., 2000).
2. The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation and Quantum Computation, edited by, D. Bouwmeester, A. Ekert, and, A. Zeilinger, (Springer, New York, 2000).
3. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
4. D. Bruß, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1494474 43, 4237 (2002).
5. M. B. Plenio and S. Virmani, Quantum Inf. Comput. QICUAW 1533-7146 7, 1 (2007).
6. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, e-print arXiv:quant-ph/0702225.
7. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
8. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)00706-2 223, 1 (1996).
9. O. Rudolph, e-print arXiv:quant-ph/0202121;
10. K. Chen and L.-A. Wu, Quantum Inf. Comput. QICUAW 1533-7146 3, 193 (2003).
11. B. Terhal, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00401-1 271, 319 (2000);
12. G. Tóth and O. Gühne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.060501 94, 060501 (2005);
13. M. A. Jafarizadeh, M. Rezaee, and S. K. A. Seyed Yagoobi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.062106 72, 062106 (2005).
14. H. F. Hofmann and S. Takeuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032103 68, 032103 (2003);
15. H. F. Hofmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.034307 68, 034307 (2003).
16. O. Gühne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 117903 92, 117903 (2004).
17. J. S. Bell, Physics (Long Island City, N.Y.) PYCSAP 0554-128X 1, 195 (1964).
18. J. Clauser, M. Horne, A. Shimony, and R. Holt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.23.880 23, 880 (1969).
19. N. D. Mermin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65. 1838 65, 1838 (1990);
20. M. Ardehali, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.46.5375 46, 5375 (1992);
21. A. V. Belinskii and D. N. Klyshko, Phys. Usp. PHUSEY 1063-7869 10.1016/0375-9601(93)90228-R 36, 653 (1993);
22. N. Gisin and H. Bechmann-Pasquinucci, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98)00516-7 246, 1 (1998).
23. O. Gühne and N. Lütkenhaus, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.170502 96, 170502 (2006).
24. F. A. Bovino, G. Castagnoli, A. Ekert, P. Horodecki, C. M. Alves, and A. V. Sergienko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.240407 95, 240407 (2005);
25. R. Augusiak, P. Horodecki, and M. Demianowicz, e-print arXiv:quant-ph/0604109.
26. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998).
27. A. Uhlmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.032307 62, 032307 (2000).
28. P. Rungta, V. Buek, C. M. Caves, M. Hillery, and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.042315 64, 042315 (2001).
29. F. Mintert, M. Ku, and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.167902 92, 167902 (2004).
30. K. Chen, S. Albeverio, and S.-M. Fei, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.040504 95, 040504 (2005).
31. J. I. de Vicente, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75. 052320 75, 052320 (2007).
32. H. P. Breuer, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/38/010 39, 11847 (2006).
33. S. Yu and N.-L. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.150504 95, 150504 (2005).
34. O. Gühne, M. Mechler, G. Tóth, and P. Adam, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.010301 74, 010301 (R) (2006).
35. C. Kothe and G. Björk, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.012336 75, 012336 (2007);
36. Z.-W. Wang, Y.-F. Huang, X.-F. Ren, Y.-S. Zhang, and G.-C. Guo, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/78/40002 78, 40002 (2007).
37. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, U.K., 1985), Theorem 7.4.9.
38. M. A. Nielsen, Ph.D. thesis, University of New Mexico, 1998, e-print arXiv:quant-ph/0011036;
39. M. A. Nielsen, C. M. Dawson, J. L. Dodd, A. Gilchrist, D. Mortimer, T. J. Osborne, M. J. Bremner, A. W. Harrow, and A. Hines, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052301 67, 052301 (2003).
40. C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.5385 82, 5385 (1999).
41. J. I. de Vicente, Quantum Inf. Comput. QICUAW 1533-7146 7, 624 (2007).
42. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.052310 62, 052310 (2000);
43. M. Lewenstein, B. Kraus, P. Horodecki, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.044304 63, 044304 (2001).
44. See O. Gühne, P. Hyllus, O. Gittsovich, and J. Eisert, e-print arXiv:quant-ph/0611282v2, Proposition 3.