Separability, entanglement, and full families of commuting normal matrices

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 76, Issue 2, 2007, Pages

  Samsonowicz, Jan ^a   Kuś, Marek ^b   Lewenstein, MacIej ^c  

^a WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b CENTER FOR THEORETICAL PHYSICS   (Poland)

^c INSTITUCIÓ CATALANA DE RECERCA I ESTUDIS AVANÇATS ICREA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CHARACTERIZATION; NUMERICAL METHODS; PROBLEM SOLVING;

MATRIX ELEMENTS; QUANTUM MIXED STATE; SEPARABILITY;

QUANTUM THEORY;

EID: 34548070240     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.76.022314     Document Type: Article

References (36)

1. See, for instance, Lectures on Quantum Information, edited by, D. Bruß, and, G. Leuchs, (Wiley-VCH, Berlin, 2007).
2. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, e-print arXiv:quant-ph/0702225, Rev. Mod. Phys. (to be published).
3. I. Bengtsson and K. Życzkowski, Geometry of Quantum States (Cambridge University Press, Cambridge, U.K., 2006).
4. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
5. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)00706-2 223, 1 (1996).
6. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
7. K. Eckert, J. Schliemann, D. Bruss, and M. Lewenstein, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1006/aphy.2002.6268 299, 88 (2002).
8. Lu-Ming Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2722 84, 2722 (2000).
9. R. Simon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2726 84, 2726 (2000).
10. G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.167904 87, 167904 (2001).
11. G. Giedke, B. Kraus, M. Lewenstein, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.052303 64, 052303 (2001).
12. For a general description of the method, see A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.187904 88, 187904 (2002)
13. for a specific formulation of the semidefinite approach for 2×N systems, see H. J. Woerdeman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67. 010303 67, 010303 (R) (2003).
14. L. Gurvits, J. Comput. Syst. Sci. 69, 448 (2004). 0022-0000
15. See, for instance, B. M. Terhal, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/S0024-3795(00)00251-2 323, 61 (2001)
16. M. Lewenstein, B. Kraus, P. Horodecki, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.044304 63, 044304 (2001)
17. H.-P. Breuer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97. 080501 97, 080501 (2006).
18. See, for instance, B. M. Terhal, Theor. Comput. Sci. TCSCDI 0304-3975 10.1016/S0304-3975(02)00139-1 287, 313 (2002)
19. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.052310 62, 052310 (2000).
20. See, for instance, P. Horodecki and A. Ekert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.127902 89, 127902 (2002)
21. 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)
22. M. Bourennane, M. Eibl, Ch. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, Ph. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.087902 92, 087902 (2004).
23. J. K. Korbicz and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.022318 74, 022318 (2006).
24. E. Schrödinger, Naturwiss. NATWAY 0028-1042 10.1007/BF01491891 23, 807 (1935).
25. L. P. Hughston, R. Jozsa, and W. K. Wootters, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93)90880-9 183, 14 (1993).
26. M. Spivak, A Comprehensive Introduction to Differential Geometry (Publish or Perish, Wilmington, 1979), Vol. 5.
27. J. Korbicz, Ph.D. thesis, Universität Hannover, 2006.
28. F. Mintert, M. Kuś, and A. Buchleitner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.167902 92, 167902 (2004).
29. R. A. Horn and Ch. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, U.K., 1990).
30. B. Kraus, J. I. Cirac, S. Karnas, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.062302 61, 062302 (2000).
31. T. Wellens and M. Kuś, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64.052302 64, 052302 (2001)
32. S. Karnas and M. Lewenstein, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/35/318 34, 6919 (2001).
33. A. Sanpera, R. Tarrach, and G. Vidal, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.826 58, 826 (1998).
34. P. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(97)00416- 7 232, 333 (1997).
35. M. Lewenstein and A. Sanpera, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2261 80, 2261 (1998).
36. G. Vidal, Ph.D. thesis, Universidad Barcelona, 1999.