Exact calculation of robustness of entanglement via convex semi-definite programming

International Journal of Quantum Information

Volumn 3, Issue 3, 2005, Pages 511-533

  Jafarizadeh, M A ^a,b   Mirzaee, M ^a,b   Rezaee, M ^a,b  

^a UNIVERSITY OF TABRIZ   (Iran)

^b INSTITUTE FOR STUDIES IN THEORETICAL PHYSICS AND MATHEMATICS IPM   (Iran)

Author keywords

Bell decomposable states; Robustness of entanglement; Semi definite programming; Werner and isotropic states

Indexed keywords

BELLS;

ANALYTIC EXPRESSIONS; BELL DECOMPOSABLE STATE; DENSITY MATRIX; EXACT CALCULATIONS; ISOTROPIC STATE; SEMI-DEFINITE PROGRAMMING; SEPARABLE STATE; TWO-QUBIT STATE;

QUANTUM ENTANGLEMENT;

EID: 33746301661     PISSN: 02197499     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219749905001043     Document Type: Article

References (40)

1. S. J. Akhtarshenas and M. A. Jafarizadeh, Euro. J. Phys. D25, 293 (2003).
2. S. J. Akhtarshenas and M. A. Jafarizadeh, Robustness of entanglement for two qubit density matrix, quant-ph/0211156.
3. J. F. Du, M. J. Shi, X. Y. Zhou and R. D. Han, Phys. Lett. A267, 244 (2000).
4. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
5. C. H. Bennett and S. J. Wiesner, Phys. Rev. Lett. 69, 2881 (1992)
6. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin and W. K. Wootters, Phys. Rev. A54, 3824 (1996).
7. V. Vedral, M. B. Pienio, M. A. Rippin and P. L. Knight, Phys. Rev. Lett. 78, 2275 (1995).
8. V. Vedral and M. B. Plenio, Phys. Rev. A57, 1619 (1998).
9. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
10. G. Vidal and R. Tarrach, Phys. Rev. A59, 141 (1999).
11. G. Vidal and R. F. Werner, Phys. Rev. A65, 032314 (2002).
12. O. Rudolph, quant-ph/0202121.
13. A. K. Rajagopal and R. W. Rendell, Phys. Rev. A65, 032328 (2002).
14. C. Simon and J. Kempe, Phys. Rev. A65, 052327 (2002).
15. M. X. Goemans and D. P. Williamson, J. Assoc. Comput. Mach. 42(6), 1115 (1995).
16. Z. Q. Luo, Math. Program. B97, 177 (2003).
17. T. N. Davidson, Z.-Q. Luo and K. M. Wong, IEEE Trans. Signal Proces. 48(5), 1433 (2000).
18. W. K. Ma, T. N. Davidson, K. M. Wong, Z.-Q. Luo and P. C. Ching, IEEE Trans. Signal Proces. 50, 912 (2002).
19. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics, Vol. 15 (Society for Industrial and Applied Mathematics, 1994).
20. A. C. Doherty, P. A. Parrilo and F. M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002).
21. P. A. Parrilo, A. C. Doherty and F. M. Spedalieri, Entanglement witnesses and semi-definite programming, Proc. 41st IEEE Conf. Decision and Control (2002).
22. A. Kitaev, Quantum coin flipping, Quantum Information Processing, 2003; slides and video at http://www.msri.org (December, 2002).
23. E. M. Rains, IEEE Trans. Inform. Theory 47(7), 2921 (2001).
24. H. Barnum, M. Saks and M. Szegedy, in Proc. 18th IEEE Annual Conf. Computational Complexity 179 (2003).
25. C. W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, 1976).
26. Y. C. Eldar, A. Megretski and G. C. Verghese, IEEE Trans. Inform. Theory 49(4), 1007 (2003).
27. L. Ip, Shor's Algorithm is optimal, University of California, Berkeley, USA MU Seminar (2003), http://www.qcaustralia.org.
28. L. Vandenberghe and S. Boyd, SIAM Rev. 38, 49 (1996).
29. L. Vandenberghe and S. Boyd, Convex Optimization (Cambridge University Press, New York, 2004).
30. S. J. Akhtarshenas and M. A. Jafarizadeh, Quantum Inform. Comput. 3, 229 (2003).
31. R. Horodecki and M. Horodecki, Phys. Rev. A54, 1838 (1996).
32. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
33. P. Horodecki, M. Horodecki and R. Horodecki, Phys. Rev. Lett. 82, 1056 (1999).
34. S. J. Akhtarshenas and M. A. Jafarizadeh, J. Phys. A: Math. Gen. 37, 2965 (2004)
35. M. Horodecki, P. Horodecki and R. Horodecki, Phys. Lett. A223, 1 (1996).
36. S. J. Akhtarshenas, Investigation of quantum correlation in pure and mixed multi-partite systems, PhD thesis, Tabriz University (2003).
37. R. F. Werner, Phys. Rev. A40, 4277 (1989).
38. A. Ericsson, Phys. Lett. A295, 256 (2002).
39. M. Horodecki and P. Horodecki, Phys. Rev. A59, 4206 (1999).
40. A. O. Pittenger and M. H. Rubin, Opt. Commun. 179, 447 (2000).