Quantum dynamics as an analog of conditional probability

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 4, 2006, Pages

  Leifer, M S ^a  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; CORRELATION THEORY; MEASUREMENT THEORY; PROBABILITY; PROBABILITY DENSITY FUNCTION; STATISTICAL METHODS;

BIPARTITE DENSITY OPERATORS; ISOMORPHISM; QUANTUM DYNAMICS; STATISTICAL CORRELATIONS;

QUANTUM THEORY;

EID: 33749987791     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.042310     Document Type: Article

References (42)

1. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
2. A. N. Kolmogorov, Foundations of the Theory of Probability, 2nd English edition (Chelsea Publishing Company, New York, 1956).
3. J. L. Doob, Am. Math. Monthly AMMYAE 49, 648 (1942).
4. A. Jamiołkowski, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(72)90011-0 3, 275 (1972).
5. M. D. Choi, Linear Algebr. Appl. LAAPAW 0024-3795 10.1016/0024-3795(75) 90075-0 10, 285 (1975).
6. F. Verstraete and H. Verschelde, e-print quant-ph/0202124.
7. P. Arrighi and C. Patricot, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/j.aop.2003.11.005 311, 26 (2004).
8. W. K. Wootters and W. H. Zurek, Nature (London) NATUAS 0028-0836 10.1038/299802a0 299, 802 (1982).
9. D. Dieks, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(82)90084-6 92A, 271 (1982).
10. H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.2818 76, 2818 (1996).
11. B. M. Terhal, IBM J. Res. Dev. IBMJAE 0018-8646 48, 71 (2004).
12. M. Ohya, IEEE Trans. Inf. Theory IETTAW 0018-9448 29, 770 (1983).
13. M. Ohya, Lett. Nuovo Cimento Soc. Ital. Fis. LNUCAE 0375-930X 38, 402 (1983).
14. R. B. Griffiths, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.042337 71, 042337 (2005).
15. G. M. D’Ariano and P. Lo Presti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.047902 91, 047902 (2003).
16. C. A. Fuchs, e-print quant-ph/0205039.
17. C. A. Fuchs, J. Mod. Opt. JMOPEW 0950-0340 10.1080/0950034031000094624 50, 987 (2003).
18. M. Asorey, A. Kossakowski, G. Marmo, and E. C. G. Sudarshan, Open Syst. Inf. Dyn. OSIDFU 1230-1612 12, 319 (2005).
19. N. J. Cerf and C. Adami, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.5194 79, 5194 (1997).
20. N. J. Cerf and C. Adami, Physica D PDNPDT 0167-2789 10.1016/S0167- 2789(98)00045-1 120, 62 (1998).
21. N. J. Cerf and C. Adami, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.60.893 60, 893 (1999).
22. K. Życzkowski and I. Bengtsson, Open Syst. Inf. Dyn. OSIDFU 1230-1612 10.1023/B:OPSY.0000024753.05661.c2 11, 3 (2004).
23. M. A. Nielsen and I. L. Chuang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.321 79, 321 (1997).
24. G. Lüders, Ann. Phys. ANPYA2 0003-3804 8, 322 (1951);
25. translated by K. A. Kirkpatrick, Ann. Phys. ANPYA2 0003-3804 15, 663 (2006).
26. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.052306 61, 052306 (2000).
27. K. A. Dennison and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.010301 65, 010301 (R) (2001).
28. M. Koashi, V. Bǔek, and N. Imoto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.050302 62, 050302 (R) (2000).
29. M. Koashi and A. Winter, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022309 69, 022309 (2004).
30. T. J. Osborne and F. Verstraete, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.220503 96, 220503 (2006).
31. V. I. Paulsen, Completely Bounded Maps and Dilations (Longman, London, 1986).
32. V. I. Paulsen, Completely Bounded Maps and Operator Algebras, Vol. 78 of Cambridge Studies in Advanced Mathematics (Cambridge University Press, Cambridge, England, 2003).
33. G. Lindblad, Lett. Math. Phys. LMPHDY 0377-9017 10.1023/A:1007581027660 47, 189 (1999).
34. C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computer Systems and Signal Processing (IEEE, New York, 1984), pp. 175â€"179.
35. C. H. Bennett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68. 3121 68, 3121 (1992).
36. G. M. D’Ariano, C. Macchiavello, and P. Perinotti, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.060503 95, 060503 (2005).
37. F. Buscemi, G. M. D’Ariano, C. Macchiavello, and P. Perinotti, e-print quant-ph/0510155.
38. G. M. D’Ariano, P. Perinotti, and M. F. Sacchi, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/8/6/099 8, 99 (2006).
39. G. M. D’Ariano, P. Perinotti, and M. F. Sacchi, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2006-10105-x 75, 195 (2006).
40. F. Buscemi, G. M. D’Ariano, C. Macchiavello, and P. Perinotti, e-print quant-ph/0602125, Phys. Rev. A (to be published).
41. R. E. Neapolitan, Probabilistic Reasoning in Expert Systems (Wiley, New York, 1990).
42. L. Hardy, e-print gr-qc/0509120.