Mixed-quantum-state detection with inconclusive results

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 4, 2003, Pages 423091-4230914

  Eldar, Yonina C ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; DATA PROCESSING; MATHEMATICAL OPERATORS; POLYNOMIALS; PROBABILITY; SET THEORY;

OPTIMAL QUANTUM DETECTORS;

QUANTUM THEORY;

EID: 4043109603     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. A. Peres, Found. Phys. 20, 1441 (1990).
2. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Boston, MA, 1995).
3. A.S. Holevo, J. Multivariate Anal. 3, 337 (1973).
4. H.P. Yuen, R.S. Kennedy, and M. Lax, IEEE Trans. Inf. Theory IT-21, 125 (1975).
5. Y.C. Eldar, A. Megretski, and G.G. Verghese, IEEE Trans. Inform. Theory (to be published).
6. C.W. Helstrom, Quantum Detection and Estimation Theory (Academic Press, New York, 1976).
7. M. Charbit, C. Bendjaballah, and C.W. Heistrom, IEEE Trans. Inform. Theory 35, 1131 (1989).
8. M. Osaki, M. Ban, and O. Hirota, Phys. Rev. A 54, 1691 (1996).
9. M. Ban, K. Kurokawa, R. Momose, and O. Hirota, Int. J. Theor. Phys. 36, 1269 (1997).
10. Y.C. Eldar and G.D. Fomey, Jr., IEEE Trans. Inform. Theory 47, 858 (2001).
11. Y.C. Eldar, A. Megretski, and G.G. Verghese, e-print quant-ph/0211111.
12. C.W. Heistrom, IEEE Trans. Inform. Theory 28, 359 (1982).
13. I.D. Ivanovic, Phys. Lett. A 123, 257 (1987).
14. D. Dieks, Phys. Lett. A 126, 303 (1988).
15. A. Peres, Phys. Lett. A 128, 19 (1988).
16. G. Jaeger and A. Shimony, Phys. Lett. A 197, 83 (1995).
17. A. Peres and D.R. Terno, J. Phys. A 31, 7105 (1998).
18. A. Chefles, Phys. Lett. A 239, 339 (1998).
19. A. Chefles and S.M. Barnett, Phys. Lett. A 250, 223 (1998).
20. Y.C. Eldar, IEEE Trans. Inform. Theory 49, 446 (2003).
21. A. Chefles and S.M. Barnett, J. Mod. Opt. 45, 1295 (1998).
22. C.W. Zhang, C.F. Li, and G.C. Guo, Phys. Lett. A 261, 25 (1999).
23. J. Fiurášek and M. Ježek, Phys. Rev. A 67, 012321 (2003).
24. L. Vandenberghe and S. Boyd, SIAM Rev. 38, 40 (1996).
25. F. Alizadeh, Ph.D. thesis, University of Minnesota, Minneapolis, MN, 1991.
26. F. Alizadeh, in Advances in Optimization and Parallel Computing, edited by P. Pardalos (North-Holland, Amsterdam, 1992).
27. Y. Nesterov and A. Nemirovski, Interior-Point Polynomial Algorithms in Convex Programming (SIAM, Philadelphia, 1994).
28. Y.C. Eldar and H. Bölcskei, IEEE Trans. Inform. Theory (to be published), e-print math.FA/0108096.
29. G.H. Golub and C.F.V. Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, Baltimore, MD, 1996).
30. M. Ježek, J. Řeháček, and J. Fiurášek, Phys. Rev. A 65, 060301 (2002).
31. A.C. Doherty, P.A. Parrilo, and F.M. Spedalieri, Phys. Rev. Lett. 88, 187904 (2002).
32. E.M. Rains, IEEE Trans. Inform. Theory 47, 2921 (2001).
33. K. Audenaert and B.D. Moor, Phys. Rev. A 65, 030302 (2002).
34. A.S. Holevo, IEEE Trans. Inform. Theory 44, 269 (1998).
35. P. Hausladen and W.K. Wootters, J. Mod. Opt. 41, 2385 (1994).
36. P. Hausladen, R. Josza, B. Schumacher, M. Westmoreland, and W.K. Wootters, Phys. Rev. A 54, 1869 (1996).
37. M. Sasaki, K. Kato, M. Izutsu, and O. Hirota, Phys. Rev. A 58, 146 (1998).
38. M. Sasaki, T. Sasaki-Usuda, M. Izutsu, and O. Hirota, Phys. Rev. A 58, 159 (1998).
39. K. Kalo, M. Osaki, M. Sasaki, and O. Hirota, IEEE Trans. Commun. 47, 248 (1999).
40. G.D. Forney, Jr., IEEE Trans. Inform. Theory 37, 1241 (1991).
41. M.A. Armstrong, Groups and Symmetry (Springer-Verlag, New York, 1988).
42. D.G. Luenberger, Optimization by Vector Space Methods (Wiley, New York, 1968).
43. i,1 ≤ i ≤ m}.
44. Interior point methods are iterative algorithms that terminate once a prespecified accuracy has been reached. A worst-case analysis of interior point methods shows that the effort required to solve a semidefmite program to a given accuracy grows no faster than a polynomial of the problem size. In practice, the algorithms behave much better than predicted by the worst case analysis, and in fact in many cases the number of iterations is almost constant in the size of the problem.
45. A set C is convex if for any x,y ∈ C, αx + (1 - α)y ∈ C for all α ∈ [0,1].