On the minimum number of unitaries needed to describe a random-unitary channel

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 360, Issue 2, 2006, Pages 256-258

  Buscemi, Francesco ^a  

^a JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

UNITARY OPERATORS; UPPER BOUND;

EID: 33750503156     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2006.08.038     Document Type: Article

References (22)

1. Kraus K. States, Effects, and Operations: Fundamental Notions in Quantum Theory. Lecture Notes in Physics vol. 190 (1983), Springer-Verlag, Berlin
2. For two-dimensional systems, a channel is random-unitary if and only if it is unital. For higher-dimensional systems, if a channel is random-unitary it is also unital, but the converse does not hold. See:. Landau L.J., and Streater R.F. Linear Algebra Appl. 193 (1993) 107
3. Davies E.B. Quantum Theory of Open Systems (1976), Academic Press, London
4. Gregoratti M., and Werner R.F. J. Mod. Opt. 50 (2003) 915
5. Hayden P., and King C. Quantum Inform. Comput. 5 (2005) 156
6. Smolin J.A., Verstraete F., and Winter A. Phys. Rev. A 72 (2005) 052317
7. Winter A. quant-ph/0507045
8. Buscemi F., Chiribella G., and D'Ariano G.M. Phys. Rev. Lett. 95 (2005) 090501
9. Bengtsson I., and Zyczkowski K. Geometry of Quantum States: An Introduction to Quantum Entanglement (2006), Cambridge Univ. Press, Cambridge See, in particular, Chapter 10, Section 7
10. Stinespring W.F. Proc. Am. Math. Soc. 6 (1955) 211
11. Ozawa M. J. Math. Phys. 25 (1984) 79
12. Holevo A.S. Probab. Theory Appl. 51 (2006) 133. quant-ph/0509101
13. Fujiwara A., and Nagaoka H. IEEE Trans. Inform. Theory 44 (1998) 1071
14. Parthasarathy K.R. Infin. Dimens. Anal. 2 (1999) 557
15. R. Mecozzi, Degree Thesis, Pavia, 2002, in Italian
16. D'Ariano G.M., Lo Presti P., and Perinotti P. J. Phys. A: Math. Gen. 38 (2005) 5979
17. Hayashi M. Quantum Information: An Introduction (2006), Springer-Verlag, Berlin See Appendix A.4
18. Buscemi F., D'Ariano G.M., and Sacchi M.F. Phys. Rev. A 68 (2003) 042113
19. Jamiołkowski A. Rep. Math. Phys. 3 (1972) 275
20. Choi M.-D. Linear Algebra Appl. 10 (1975) 285
21. Davies E.B. IEEE Trans. Inform. Theory 24 (1978) 596
22. Shor P.W. In: Tombesi P., and Hirota O. (Eds). Quantum Communication, Computing, and Measurement 3 (2001), Kluwer Academic/Plenum. quant-ph/0009077