Quantum operations, state transformations and probabilities

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 65, Issue 5, 2002, Pages 9-

  Chefles, Anthony ^a  

^a UNIVERSITY OF HERTFORDSHIRE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84865521914     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.65.052314     Document Type: Article

References (28)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
2. L. Hardy and D. D. Song, Phys. Rev. A 63, 032304 (2001).
3. G. Alber, A. Delgado, and I. Jex, LANL e-print quant-ph/0006040.
4. J. Fiurášek, Phys. Rev. A 64, 062301 (2001).
5. A. Chefles, Phys. Lett. A 270, 14 (2000).
6. A. Uhlmann, Wiss. Z. Karl-Marx-Univ. Leipzig. 20, 633 (1971).
7. A. Uhlmann, Wiss. Z. Karl-Marx-Univ. Leipzig. 21, 427 (1972).
8. A. Uhlmann, Wiss. Z. Karl-Marx-Univ. Leipzig. 22, 139 (1973).
9. R. Bhatia, Matrix Analysis (Springer-Verlag, Berlin, 1991).
10. M. A. Nielsen, Phys. Rev. Lett. 83, 436 (1999).
11. M. A. Nielsen, Phys. Rev. A 63, 022114 (2001).
12. C. A. Fuchs and K. Jacobs, Phys. Rev. A 63, 062305 (2001).
13. M. A. Nielsen, Phys. Rev. A 62, 052308 (2000).
14. R. B. Bapat and V. C. Sunder, Linear Algebra Appl. 72, 107 (1985).
15. K. Kraus, States, Effects and Operations: Fundamental No-tions of Quantum Theory (Springer-Verlag, Berlin, 1983).
16. A. Chefles, Phys. Lett. A 239, 339 (1998).
17. L.-M. Duan and G.-C. Guo, Phys. Rev. Lett. 80, 4999 (1998).
18. G. Visick, Linear Algebra Appl. 304, 45 (2000).
19. A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).
20. M. B. Ruskai, S. Szarek, and E. Werner, LANL e-print quant-ph/0101003.
21. L. J. Landau and R. F. Streater, Linear Algebra Appl. 193, 107 (1993).
22. P. Hausladen, R. Jozsa, B. Schumacher, M. Westmoreland, and W. K. Wootters, Phys. Rev. A 54, 1869 (1996).
23. B. Schumacher, Phys. Rev. A 54, 2614 (1996).
24. R. Jozsa and J. Schlienz, Phys. Rev. A 62, 012301 (2000).
25. The majorization relation (3.19) is actually a special case of the following more general result discussed by Visick 18: let (Formula presented) and (Formula presented) be (Formula presented) Hermitian matrices. If (Formula presented) then (Formula presented). This reduces to the majorization relation (3.19) in the special case where all of the diagonal elements of (Formula presented) are equal to 1, in which case (Formula presented).
26. R. Horn and C. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985).
27. C. A. Fuchs and A. Peres, Phys. Rev. A 53, 2038 (1996).
28. G. Vidal, J. Mod. Opt. 47, 355 (2000).