The distillability problem revisited

Quantum Information and Computation

Volumn 6, Issue 6, 2006, Pages 539-560

  Clarisse, Lieven ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

INFORMATION THEORY; NUMERICAL METHODS; QUANTUM OPTICS;

BOUND ENTANGLEMENT; LOW DIMENSIONAL; MATHEMATICAL TOOLS; PARAMETER STATE; QUANTUM INFORMATION THEORY; QUANTUM SYSTEM; SCHMIDT NUMBERS; TOOLS AND TECHNIQUES;

QUANTUM ENTANGLEMENT;

EID: 33746925640     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. R. F. Werner (1989), Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model, Phys. Rev. A, 40, pp. 4277-4281.
2. M. Horodecki, P. Horodecki, and R. Horodecki (1998), Mixed-state entanglement and distillation: is there a 'bound' entanglement in nature?, Phys. Rev. Let., 80, pp. 5239-5242.
3. D. Yang, M. Horodecki, R. Horodecki, and B. Synak-Radtke (2005), Irreversibility for all bound entangled states, Phys. Rev. Let., 95, pp. 190501.
4. M. Horodecki (2001), Entanglement measures, Quantum Inf. Comp., 1, pp. 3-26.
5. M. B. Plenio and S. Virmani (2005), An introduction to entanglement measures, quant-ph/0504163.
6. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher (1996), Concentrating partial entanglement by local operations, Phys. Rev. A, 53, pp. 2046-2052.
7. M. Horodecki, P. Horodecki, and R. Horodecki (1999), Limits for entanglement measures, Phys. Rev. Let., 84, pp. 2014-2017.
8. G. Vidal and J. I. Cirac (2001), Irreversibility in asymptotic manipulations of entanglement, Phys. Rev. Let., 86, pp. 5803-5806.
9. G. Vidal, W. Dür, and J. I. Cirac (2002), Entanglement cost of antisymmetric states, Phys. Rev. Let., 89, pp. 027901.
10. K. G. H. Vollbrecht, R. F. Werner, and M. M. Wolf (2004), On the irreversibility of entanglement distillation, Phys. Rev. A, 69, pp. 062304.
11. O. Krueger and R. F. Werner (2005), Some open problems in quantum information theory. http://www.imaph.tu-bs.de/qi/problems/
12. M. Horodecki, P. Horodecki, and R. Horodecki (1997) Inseparable two spin-1/2 density matrices can be distilled to a singlet form, Phys. Rev. Let., 78, pp. 574-577.
13. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters (1996), Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Let., 76, pp. 722-725.
14. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters (1996), Mixed-state entanglement and quantum error correction, Phys. Rev. A, 54, pp. 3824-3851.
15. W. Dur, J. I. Cirac, M. Lewenstein, and D. Bruß (2000), Distillability and partial transposition in bipartite systems, Phys. Rev. A, 61, pp. 062313.
16. G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, and A. Zeilinger (2001), Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, Springer (Berlin).
17. M. Horodecki and P. Horodecki (1999), Reduction criterion of separability and limits for a class of distillation protocols, Phys. Rev. A, 59, pp. 4206-4216.
18. D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal (2000), Evidence for bound entangled states with negative partial transpose, Phys. Rev. A, 61, pp. 062312.
19. J. Watrous (2004), On the number of copies required for entanglement distillation, Phys. Rev. Let., 93, pp. 010502.
20. P. W. Shor, J. A. Smolin, and B. M. Terhal (2001), Nonadditivity of bipartite distillable entanglement follows from conjecture on bound entangled Werner states, Phys. Rev. Let., 86, pp. 2681-2684.
21. T. Eggeling, K. G. H. Vollbrecht, R. F. Werner, and M. M. Wolf (2001), Distillability via protocols respecting the positivity of partial transpose, Phys. Rev. Let., 87, pp. 257902.
22. K. G. H. Vollbrecht and M. M. Wolf (2002), Activating NPT distillation with an infinitesimal amount of bound entanglement, Phys. Rev. Let., 88, pp. 247901.
23. J. I. Cirac, W. Dür, B. Kraus, and M. Lewenstein (2001), Entangling operations and their implementation using a small amount of entanglement, Phys. Rev. Let., 86, pp. 544-547.
24. L. Masanes (2005), All entangled states are useful for information processing, quant-ph/0508071.
25. K. G. H. Vollbrecht and R. F. Werner (2001), Entanglement measures under symmetry, Phys. Rev. A, 64, pp. 062307.
26. E. M. Rains (1999), Bound on distillable entanglement, Phys. Rev. A, 60, pp. 179-184.
27. B. M. Terhal and P. Horodecki (2000), A Schmidt number for density matrices, Phys. Rev. A, 61, pp. 040301(R).
28. A. Sanpera, D. Bruß, and M. Lewenstein (2001), Schmidt number witnesses and bound entanglement, Phys. Rev. A, 63, pp. 050301 (R).
29. B. Kraus, M. Lewenstein, and J. I. Cirac (2002), Characterization of distillable and activable states using entanglement witnesses, Phys. Rev. A, 65, pp. 042327.
30. F. Hulpke, D. Bruß, M. Lewenstein, and A. Sanpera (2004), Simplifying Schmidt number witnesses via higher-dimensional embeddings, Quantum Inf. Comput., 4, pp. 207.
31. L. Gurvits (2003), Classical deterministic complexity of Edmonds' problem and quantum entanglement, In Proceedings of the 35th ACM Symposium on Theory of Computing, pp. 10-19 (New York).
32. A. Peres (1993) Quantum theory: concepts and methods, Kluwer Academic Publishers (Dordrecht).
33. A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri (2002), Distinguishing separable and entangledstates, Phys. Rev. Let., 88, pp. 187904.
34. A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri (2004) Complete family of separability criteria, Phys. Rev. A, 69, pp. 022308.
35. J. Eisert, P. Hyllus, O. Gühne, and M. Curty (2005), Complete hierarchies of efficient approximations to problems in entanglement theory, Phys. Rev. A, 70, pp. 062317.
36. S. Ishizaka (2004), Bound entangled states provide overall convertibility of pure entangled states, Phys. Rev. Let., 93, pp. 190501.
37. B. M. Terhal (2001), Detecting quantum entanglement, Theor. Comp. Sc, 287, pp. 313-335.
38. M. Horodecki, P. Horodecki, and R. Horodecki (1996), Separability of mixed states: necessary and sufficient conditions, Phys. Let. A, 223, pp. 1-8.
39. L. Clarisse (2005), Characterization of distillability of entanglement in terms of positive maps, Phys. Rev. A, 71, pp. 032332.
40. F. Hulpke and D. Bruß (2005), A two-way algorithm for the entanglement problem, J. Phys. A: Math. Gen., 38, pp. 5573-5579.
41. K. Życzkowski, P. Horodecki, A. Sanpera, and M. Lewenstein (1998), On the volume of the set of mixed entangled states, Phys. Rev. A, 58, pp. 883-892.
42. K. Życzkowski (1999), Volume of the set of mixed entangled states II, Phys. Rev. A, 60, pp. 3496-3507.
43. K. Życzkowski and M. Kuś (1994), Random unitary matrices. Journal of Physics A: Mathematics and General, 27, pp. 4235-4245.
44. M. Poźniak, K. Życzkowski, and M. Kuś (1998) Composed ensembles of random unitary matrices, J. Phys. A, 31, pp. 1059-1071.
45. G. W. Stewart (1980) The efficient generation of random orthogonal matrices with an application to condition estimators, SIAM J. Num. An., 17, pp. 403-409.
46. A. Edelman and N. R. Rao (2005), Random matrix theory, Act. Num., 14, pp. 1-65.
47. P. Horodecki, J. I. Cirac, and M. Lewenstein (2003), Bound entanglement for continuous variables is a rare phenomenon In S. L. Braunstein and A. K. Pati, editors, Quantum Information with Continuous Variables, pp 211-230 (Springer).
48. J. Eisert, C. Simon, and M. B. Plenio (2002), On the quantification of entanglement in infinite dimensional quantum systems, J. Phys. A 35, pp. 3911-3923.
49. P. Hayden, D. W. Leung, and A. Winter (2005), Aspects of generic entanglement, quant-ph/0407049.