Observable estimation of entanglement for arbitrary finite-dimensional mixed states

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 4, 2008, Pages

  Zhang, Cheng Jie ^a   Gong, Yan Xiao ^a   Zhang, Yong Sheng ^a   Guo, Guang Can ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

DEGREE OF MIXING; EXPERIMENTAL MEASUREMENTS; LINEAR ENTROPIES; LOWER BOUNDS; MIXED STATES; UPPER AND LOWER BOUNDS; UPPER BOUNDS;

CONTROL THEORY;

EID: 54049141373     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.042308     Document Type: Article

References (71)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
2. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.47.777 47, 777 (1935).
3. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) NATUAS 0028-0836 10.1038/416608a 416, 608 (2002).
4. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
5. O. Rudolph, e-print arXiv:quant-ph/0202121;
6. K. Chen and L.-A. Wu, Quantum Inf. Comput. QICUAW 1533-7146 3, 193 (2003);
7. H. Fan, e-print arXiv:quant-ph/0210168.
8. P. Aniello and C. Lupo, J. Phys. A: Math. Theor. ZZZZZZ 1751-8113 41, 355303 (2008);
9. C. Lupo, P. Aniello, and A. Scardicchio, J. Phys. A: Math. Theor. ZZZZZZ 1751-8113 41, 415301 (2008).
10. J. I. de Vicente, Quantum Inf. Comput. QICUAW 1533-7146 7, 624 (2007);
11. M. Li, S.-M. Fei, and Z.-X. Wang, Quantum Inf. Comput. QICUAW 1533-7146 41, 202002 (2008);
12. O. Gühne, P. Hyllus, O. Gittsovich, and J. Eisert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.130504 99, 130504 (2007).
13. J. I. de Vicente, J. Phys. A: Math. Theor. ZZZZZZ 1751-8113 41, 065309 (2008).
14. M. Seevinck and J. Uffink, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.042105 76, 042105 (2007);
15. J. Uffink and M. Seevinck, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2007.09.033 372, 1205 (2008).
16. D. Bruß, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1494474 43, 4237 (2002);
17. F. Mintert, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2005.04.006 415, 207 (2005);
18. M. B. Plenio and S. Virmani, Quantum Inf. Comput. QICUAW 1533-7146 7, 1 (2007);
19. R. Horodecki, e-print arXiv:quant-ph/0702225, Rev. Mod. Phys. RMPHAT 0034-6861 (to be published).
20. W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80. 2245 80, 2245 (1998);
21. A. Uhlmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.032307 62, 032307 (2000).
22. P. Rungta, V. Bužek, C. M. Caves, M. Hillery, and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.042315 64, 042315 (2001).
23. H. Fan, K. Matsumoto, and H. Imai, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/14/316 36, 4151 (2003);
24. H. Fan, V. Korepin, and V. Roychowdhury, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.227203 93, 227203 (2004).
25. Y.-C. Ou and H. Fan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75. 062308 75, 062308 (2007);
26. Y.-C. Ou, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.034305 75, 034305 (2007);
27. H. Fan, Y.-C. Ou, and V. Roychowdhury, e-print arXiv:0707.1578;
28. Y.-C. Ou, H. Fan, and S.-M. Fei, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.012311 78, 012311 (2008).
29. K. Chen, S. Albeverio, and S.-M. Fei, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.210501 95, 210501 (2005);
30. S.-M. Fei, Z.-X. Wang, and H. Zhao, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2004.07.030 329, 414 (2004).
31. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996);
32. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)00706-2 223, 1 (1996);
33. K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.883 58, 883 (1998);
34. G. Vidal and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032314 65, 032314 (2002).
35. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.052306 61, 052306 (2000);
36. A. Wong and N. Christensen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.044301 63, 044301 (2001);
37. T. J. Osborne and F. Verstraete, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.220503 96, 220503 (2006).
38. F. Mintert, M. Kuš, and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.167902 92, 167902 (2004);
39. K. Chen, S. Albeverio, and S.-M. Fei, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.040504 95, 040504 (2005);
40. H. P. Breuer, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/38/010 39, 11847 (2006);
41. J. I. de Vicente, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75. 052320 75, 052320 (2007).
42. F. Mintert, M. Kuš, and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.260502 95, 260502 (2005).
43. F. Mintert and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.140505 98, 140505 (2007).
44. L. Aolita, A. Buchleitner, and F. Mintert, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.022308 78, 022308 (2008).
45. L. Aolita and F. Mintert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.050501 97, 050501 (2006).
46. F. Mintert, Appl. Phys. B: Lasers Opt. APBOEM 0946-2171 10.1007/s00340-007-2864-7 89, 493 (2007).
47. J. Eisert, F. Brandão, and K. Audenaert, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/3/046 9, 46 (2007).
48. O. Gühne, M. Reimpell, and R. F. Werner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.110502 98, 110502 (2007);
49. O. Gühne, M. Reimpell, and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.052317 77, 052317 (2008).
50. C.-S. Yu and H.-S. Song, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.022324 76, 022324 (2007);
51. C.-S. Yu, C. Li, and H.-S. Song, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.012305 77, 012305 (2008).
52. X.-J. Ren, Z.-W. Zhou, X.-X. Zhou, and G.-C. Guo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.054302 77, 054302 (2008).
53. S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, F. Mintert, and A. Buchleitner, Nature (London) NATUAS 0028-0836 10.1038/nature04627 440, 1022 (2006).
54. S. P. Walborn, P. H. Souto Ribeiro, L. Davidovich, F. Mintert, and A. Buchleitner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032338 75, 032338 (2007).
55. F.-W. Sun, J.-M. Cai, J.-S. Xu, G. Chen, B.-H. Liu, C.-F. Li, Z.-W. Zhou, and G.-C. Guo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.052303 76, 052303 (2007).
56. B. Terhal, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00401-1 271, 319 (2000);
57. G. Tóth and O. Gühne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.060501 94, 060501 (2005);
58. 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);
59. O. Gühne and N. Lütkenhaus, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.170502 96, 170502 (2006);
60. F. Mintert, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.052302 75, 052302 (2007);
61. R. Augusiak, M. Demianowicz, and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.030301 77, 030301 (R) (2008).
62. The first inequality has been proved by T. J. Osborne, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.022309 72, 022309 (2005).
63. M. L. Aolita, I. García-Mata, and M. Saraceno, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.062301 70, 062301 (2004).
64. A. R. R. Carvalho, F. Mintert, and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.230501 93, 230501 (2004).
65. E. Santos and M. Ferrero, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.024101 62, 024101 (2000).
66. J.-M. Cai, Z.-W. Zhou, S. Zhang, and G.-C. Guo, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.052324 75, 052324 (2007).
67. J. Preskill, http://www.theory.caltech.edu/people/preskill/ph229/, Chap., Exercise 5.2(g). Although this exercise is for the von Neumann entropy, the same hint can be used for the linear entropy.
68. J.-M. Cai and W. Song, e-print arXiv:0804.2246.
69. C.-K. Hong, Z.-Y. Ou, and L. Mandel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.2044 59, 2044 (1987).
70. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Nature (London) NATUAS 0028-0836 10.1038/37539 390, 575 (1997).
71. A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.74.4083 74, 4083 (1995).