Negativity of asymmetric two-mode Gaussian states: An explicit analytic formula and physical interpretation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 5, 2007, Pages

  Poon, Phoenix S Y ^a   Law, C K ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRONIC STATES; PARAMETER ESTIMATION; UNCERTAINTY ANALYSIS;

GAUSSIAN STATES; SEPARABILITY CRITERION;

ELECTRON ENERGY LEVELS;

EID: 36048955711     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.054305     Document Type: Article

References (31)

1. For a review, see M. B. Plenio and S. Virmani, Quantum Inf. Comput. QICUAW 1533-7146 7, 1 (2007).
2. G. Vidal and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032314 65, 032314 (2002).
3. M. B. Plenio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 090503 95, 090503 (2005).
4. K. Audenaert, M. B. Plenio, and J. Eisert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.027901 90, 027901 (2003).
5. T. Hiroshima, Gerardo Adesso, and Fabrizio Illuminati, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.050503 98, 050503 (2007)
6. Yong-Cheng Ou and Heng Fan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.062308 75, 062308 (2007).
7. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.3824 54, 3824 (1996).
8. M. M. Wolf, G. Giedke, O. Krüger, R. F. Werner, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052320 69, 052320 (2004).
9. Gerardo Adesso and Fabrizio Illuminati, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.032334 72, 032334 (2005).
10. For a review of covariance matrix treatment of entanglement in Gaussian states, see G. Adesso and F. Illuminati, J. Phys. A JPHAC5 0305-4470 10.1088/1751-8113/40/28/S01 40, 7821 (2007)
11. G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.022318 70, 022318 (2004)
12. A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian States in Quantum Information, Napoli Series on Physics and Astrophysics (Bibliopolis, Napoli, 2005).
13. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
14. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)00706-2 223, 1 (1996).
15. P. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(97)00416- 7 232, 333 (1997).
16. R. Simon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2726 84, 2726 (2000).
17. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2722 84, 2722 (2000).
18. V. Giovannetti, S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.022320 67, 022320 (2003).
19. S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.120401 88, 120401 (2002).
20. J. Mizuno, K. Wakui, A. Furusawa, and M. Sasaki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.012304 71, 012304 (2005).
21. G. S. Agarwal and A. Biswas, N. J. Phys. 7, 211 (2005). 1367-2630
22. E. Shchukin and W. Vogel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.230502 95, 230502 (2005).
23. M. Hillery and M. S. Zubairy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.050503 96, 050503 (2006).
24. H. F. Hofmann and S. Takeuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032103 68, 032103 (2003).
25. J. C. Howell, R. S. Bennink, S. J. Bentley, and R. W. Boyd, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.210403 92, 210403 (2004).
26. P. S. Y. Poon and C. K. Law, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.012333 76, 012333 (2007).
27. The third case where both α1 < β1 and α2 < β2 is not physical, since ρ would no longer be a positive definite matrix. This can be easily checked by noting ρ (0,0;0,0) ρ (1,0;1,0) < [ρ (1,0;0,0)] 2 if α1 < β1 and α2 < β2.
28. O. Gühne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, and A. Sanpera, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66. 062305 66, 062305 (2002).
29. W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.043601 90, 043601 (2003)
30. N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.063601 96, 063601 (2006)
31. W. P. Bowen, R. Schnabel, P. K. Lam, and T. C. Ralph, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.012304 69, 012304 (2004).