Entanglement breaking channels

Reviews in Mathematical Physics

Volumn 15, Issue 6, 2003, Pages 629-641

  Horodecki, Michael ^a   Shor, Peter W ^a,b   Ruskai, Mary Beth ^c  

^a UNIVERSITY OF GDA SK   (Poland)

^b AT AND T LABS RESEARCH   (United States)

^c TUFTS UNIVERSITY   (United States)

Author keywords

Completely positive maps; CQ channels; Entanglement breaking maps; Extreme points; Quantum channels; Separable states

Indexed keywords

EID: 0141481846     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X03001709     Document Type: Article

References (22)

1. C. H. Bennett, D. P. DiVincenzo, J. Smolin and W. K. Wootter, Mixed-state entanglement and quantum error correction, Phys. Rev. A 54 (1996), 3824-3851, quant-ph/9604024.
2. M.-D. Choi, Completely positive linear maps on complex matrices, Lin. Alg. Appl. 10 (1975), 285-290.
3. J. Cortese, The Holevo-Schumacher-Westmoreland channel capacity for a class of qudit unital channels, quant-ph/0211093.
4. D. P. DiVincenzo, B. M. Terhal and A. V. Thapliyal, Optimal decompositions of barely separable states, J. Mod. Optics 47 (2000), 377-385, quant-ph/9904005
5. D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal and A. V. Thapliyal, Evidence for bound entangled states with negative partial transpose, Phys. Rev. A 61, 062312 (2000), quant-ph/9910026.
6. A. S. Holevo, Coding theorems for quantum channels, Russian Math. Surveys 53 (1999), 1295-1331, quant-ph/9809023.
7. M. Hordecki, P. Hordecki and R. Hordecki, Separability of mixed states: necessary and sufficient conditions, Phys. Lett. A223 (1996), 1-8.
8. M. Horodecki and P. Horodecki, Reduction criterion of separability and limits for a class of protocols of entanglement distillation, Phys. Rev. A 59 (1999), 4206-4216, quant-ph/9708015.
9. M. Horodecki, P. Horodecki and R. Horodecki, Binding entanglement channels, J. Mod. Opt. 47 (2000), 347-354, quant-ph/9904092.
10. P. Hordecki, M. Lewenstein, G. Vidal and I. Cirac, Operational criterion and constructive checks for the separability of low rank density matrices, Phys. Rev. A 032310 (2000), quant-ph/0002089.
11. P. Horodecki, J. Smolin, B. Terhal and A. Thapliyal, Rank two bound entangled states do not exist, J. Theor. Comp. Sci. 292 (2003), 589-596, ArXiv.org preprint quant-ph/9910122.
12. A. Jamiołkowski, Linear transformations which preserve trace and positive semidefiniteness of operators, Rep. Math. Phys. 3 (1972), 275-278.
13. p norms for some product channels, J. Math. Phys. 43 (2002), 1247-1260.
14. C. King, Maximal p-norms of entanglement breaking channels, Quant. Information and Computations 3 (2003), 186-190, quant-ph/0212057.
15. C. King, Capacity of the depolarizing channel, Lecture in workshop on Quantum Information and Cryptography at Mathematical Sciences Research Institute (November, 2002). http://www.msri.org/publications/ln/msri/2002/quantumcrypto/king/1/index.html
16. D. Leung, Choi's proof as a recipe for quantum process tomography, J. Math. Phys. 44 (2003), 528-533, quant-ph/0201119.
17. A. O. Pittenger and M. H. Rubin, Separability and Fourier representations of density matrices, Phys. Rev. A 62, 032313 (2000), quant-ph/0001014.
18. M. B. Ruskai, Qubit entanglement breaking maps, quant-ph/0302032, Rev. Math. Phys. 15 (2003), 643-662.
19. 2, Lin Alg. Appl. 347 (2002), 159-187, quant-ph/0101003.
20. P. W. Shor, Additivity of the classical capacity of entanglement-breaking quantum channels, J. Math. Phys. 43 (2002), 4334-4340, quant-ph/0201149.
21. F. Verstraete and H. S. Verschelde, On one-qubit channels, ArXiv.org preprint quant-ph/0202124, version 1.
22. G. Vidal, W. Dür and J. I. Cirac, Entanglement cost of bipartite mixed states, Phys. Rev. Lett. 89, 027901 (2002), quant-ph/0112131.