Non-full-rank bound entangled states satisfying the range criterion

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 71, Issue 1, 2005, Pages

  Bandyopadhyay, Somshubhro ^a,b   Ghosh, Sibasish ^a,c   Roychowdhury, Vwani ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF TORONTO   (Canada)

^c UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIPARTITE SYSTEMS; ENTANGLED STATES; HERMITIAN OPERATORS; POSITIVE PARTIAL TRANSPOSITION (PPT);

DATA PROCESSING; INFORMATION THEORY; MATHEMATICAL OPERATORS; PROBLEM SOLVING;

QUANTUM THEORY;

EID: 18544382810     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.012316     Document Type: Article

References (21)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, U.K., 2000).
2. For an excellent introduction, see A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, Dordrecht, 1993).
3. P. Horodecki, Phys. Lett. A 232, 333 (1997).
4. D. Bruss and A. Peres, Phys. Rev. A 61, 030301(R) (2000).
5. C. H. Bennett, D. P. DiVincenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Phys. Rev. Lett. 82, 5385 (1999).
6. P. Horodecki, M. Horodecki, and R. Horodecki, Phys. Rev. Lett. 82, 1056 (1999).
7. W. Dür, J. I. Cirac, M. Lewenstein, and D. Bruß, Phys. Rev. A 61, 062313 (2000);
8. D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal, Phys. Rev. A ibid. 61, 062312 (2000);
9. S. Bandyopadhyay and V. P. Roychowdhury, Phys. Rev. A ibid. 68, 022319 (2003).
10. See, for example, D. Bruß, J. I. Cirac, P. Horodecki, F. Hulpke, B. Kraus, M. Lewenstein, and A. Sanpera, J. Mod. Opt. 49, 1399 (2002), for a general review.
11. L. Gurvits, in Proceedings of the 35th ACM Symposium on Theory of Computing (ACM Press, New York, 2003), pp. 10-19.
12. A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri, Phys. Rev. A 69, 022308 (2004).
13. L. Vandenberghe and S. Boyd, URL http://www.stanford.edu/boyd/cvxbook. html
14. D. Perez-Garcia, Phys. Lett. A 330, 149 (2004).
15. O. Rudolph, J. Phys. A 33, 3951 (2000).
16. K. G. H. Vollbrecht and M. M. Wolf, Phys. Rev. Lett. 88, 247901 (2002).
17. B. M. Terhal, Linear Algebr. Appl. 323, 61 (2000).
18. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Phys. Rev. A 62, 052310 (2000).
19. D. P. DiVmcenzo, T. Mor, P. W. Shor, J. A. Smolin, and B. M. Terhal, Commun. Math. Phys. 238, 379 (2003).
20. N. Alon and L. Lovász, J. Comb. Theory, Ser. A 95, 169 (2001).
21. J. A. Smolin (private communication).