Nonclassical correlation in a multipartite quantum system: Two measures and evaluation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 5, 2008, Pages

  Saitoh, Akira ^a,b   Rahimi, Robabeh ^b   Nakahara, Mikio ^b  

^a OSAKA UNIVERSITY   (Japan)

^b KINKI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; QUANTUM THEORY; UNCERTAINTY ANALYSIS;

DENSITY MATRIX; MULTIPARTITE QUANTUM SYSTEM; NONCLASSICAL CORRELATION;

CORRELATION THEORY;

EID: 43049098984     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.052101     Document Type: Article

References (21)

1. R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
2. A. Peres, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.1413 77, 1413 (1996).
3. A. Peres, in Proceedings of the International Symposium on Fundamental Problems in Quantum Physics, edited by, M. Ferrero, and, A. Van der Merwe, Vol. 81 of Fundamental Theories of Physics (Kluwer, Dordrecht, 1997), pp. 301-310
4. e-print arXiv:quant-ph/9609016.
5. M. B. Plenio and S. Virmani, Quantum Inf. Comput. QICUAW 1533-7146 7, 1 (2007).
6. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(96)00706-2 223, 1 (1996).
7. C. H. Bennett, D. P. DiVincenzo, C. A. Fuchs, T. Mor, E. Rains, P. W. Shor, J. A. Smolin, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.1070 59, 1070 (1999).
8. H. Ollivier and W. H. Zurek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.017901 88, 017901 (2001).
9. J. Oppenheim, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.180402 89, 180402 (2002).
10. M. Horodecki, P. Horodecki, R. Horodecki, J. Oppenheim, A. Sen(De), U. Sen, and B. Synak-Radtke, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71. 062307 71, 062307 (2005).
11. S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.1054 83, 1054 (1999).
12. B. Groisman, D. Kenigsberg, and T. Mor, e-print arXiv:quant-ph/0703103.
13. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2014 84, 2014 (2000).
14. P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed. (Academic Press, San Diego, 1985).
15. M. L. Mehta, Random Matrices, 3rd ed. (Elsevier, Amsterdam, 2004).
16. K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.883 58, 883 (1998).
17. G. Vidal and R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032314 65, 032314 (2002).
18. P. Horodecki, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(97)00416- 7 232, 333 (1997).
19. M. Piani, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.090502 100, 090502 (2008).
20. B. M. Terhal, M. Horodecki, D. W. Leung, and D. P. DiVincenzo, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1498001 43, 4286 (2002).
21. The zero-way setting of CLOCC is as follows: there are two parties allowed to communicate under CLOCC only after local complete dephasing possibly subsequent to local unitary operations. In general, the quantum deficit is equal to minΛ CLOCC [SvN (ρ Alice ′) + SvN (ρ Bob ′)] - SvN (ρ [A,B]) with ρ′ =Λ (ρ [A,B]). In case of zero-way CLOCC, the minimum is obtained for the case where Alice or Bob has ρ′ totally and the other person has a null system. Then the zero-way case quantum deficit is equal to minΛ zero-wayCLOCC SvN (ρ′) - SvN (ρ [A,B]). This is equal to D for the bipartite case.