Entanglement, purity, and information entropies in continuous variable systems

Open Systems and Information Dynamics

Volumn 12, Issue 2, 2005, Pages 189-205

  Adesso, Gerardo ^a   Serafini, Alessio ^a   Illuminati, Fabrizio ^a  

^a UNIVERSITY OF SALERNO   (Italy)

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EID: 23944471194     PISSN: 12301612     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11080-005-5730-2     Document Type: Article

References (46)

1. E. Schrödinger, Discussion of probability relations between separated systems (I), Proceedings of the Cambridge Philosophical Society 31, (1935), p. 555.
2. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
3. L. Henderson and V. Vedral, Phys. Rev. Lett. 84, 2263 (2000).
4. S.L. Braunstein and A. K. Pati, eds., Quantum Information Theory with Continuous Variables, Kluwer, Dordrecht, 2002.
5. S. L. Braunstein and P. van Loock, quant-ph/0410100, and Rev. Mod. Phys., to appear.
6. R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 36, 3868 (1987).
7. J. Williamson, Am. J. Math. 58, 141 (1936);
8. see also V.I. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1978.
9. A. Serafini, F. Illuminati, and S. De Siena, J. Phys. B: At. Mol. Opt. Phys. 37, L21 (2004).
10. M.G.A. Paris, F. Illuminati, A. Serafini, and S. De Siena, Phys. Rev. A 68, 012314 (2003).
11. M. J. Bastiaans, J. Opt. Soc. Am. 1, 711 (1984);
12. M. J. Bastiaans, J. Opt. Soc. Am. 3, 1243 (1986).
13. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
14. A. Rényi, Probability Theory, North Holland, Amsterdam, 1970.
15. A. Peres, Phys. Rev. Lett. 77, 1413 (1996);
16. R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 210, 377 (1996).
17. R. Simon, Phys. Rev. Lett. 84, 2726 (2000).
18. G. Vidai and R. F. Werner, Phys. Rev. A 65, 032314 (2002);
19. K. Zyczkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A 58, 883 (1998);
20. J. Eisert, PhD Thesis, University of Potsdam, Potsdam, 2001.
21. G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. Lett. 93, 220504 (2004).
22. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
23. G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A 70, 022318 (2004).
24. + of the partially transposed CM of a two-mode Gaussian state is always greater than 1 and so it does not enter in the computation of the logarithmic negativity (2), see [18].
25. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W.K. Wootters, Phys. Rev. A 54, 3824 (1996).
26. G. Giedke, M. M. Wolf, O. Krüger, R. F. Werner, and J. I. Cirac, Phys. Rev. Lett. 91, 107901 (2003).
27. S. Ishizaka and T. Hiroshima, Phys. Rev. A 62, 022310 (2000).
28. F. Verstraete, K. Audenaert, and B. De Moor, Phys. Rev. A 64, 012316 (2001);
29. W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302 (2001).
30. T.-C. Wei, K. Nemoto, P. M. Goldbart, P. G. Kwiat, W. J. Munro, and F. Verstraete, Phys. Rev. A 67, 022110 (2003).
31. J. Eisert and M. Plenio, J. Mod. Opt. 46, 145 (1999);
32. F. Verstraete, K. Audenaert, J. Dehaene, and B. de Moor, J. Phys. A 34, 10327 (2001).
33. K. Zyczkowski, P. Horodecki, A. Sanpera and M. Lewenstein, Phys. Rev. A 58, 883 (1998);
34. K. Zyczkowski, Phys. Rev. A 60, 3496 (1999).
35. G. Adesso, F. Illuminati, and S. De Siena, Phys. Rev. A 68, 062318 (2003).
36. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
37. G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. Lett. 92, 087901 (2004).
38. A. K. Ekert, C.M. Alves, D.K.L. Oi, M. Horodecki, P. Horodecki, and L. C. Kwek, Phys. Rev. Lett. 88, 217901 (2002);
39. R. Filip, Phys. Rev. A 65, 062320 (2002).
40. J. Fiurášek and N. J. Cerf, Phys. Rev. Lett. 93, 063601 (2004).
41. J. Wenger, J. Fiurášek, R. Tualle-Brouri, N. J. Cerf, and Ph. Grangier, Phys. Rev. A 70, 053812 (2004).
42. K. Zyczkowski, Open Sys. Information Dyn. 10, 297 (2003).
43. Being all equivalent to two-mode entanglements, all the 1 × K entanglements can be directly compared to each other. For further details see [16].
44. P. van Loock, Fortschr. Phys. 50, 12 1177 (2002).
45. A. Serafini, G. Adesso, and F. Illuminati, quant-ph/0411109 (2004).
46. G. Adesso and F. Illuminati, quant-ph/0410050 (2004).