Solution of the Lindblad equation in the Kraus representation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 6, 2006, Pages

  Nakazato, H ^a   Hida, Y ^a   Yuasa, K ^b   Militello, B ^c   Napoli, A ^c   Messina, A ^c  

^a WASEDA UNIVERSITY   (Japan)

^b NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^c UNIVERSITY OF PALERMO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PROBLEM SOLVING;

FINITE LEVEL SYSTEMS; KRAUS REPRESENTATION; LINDBLAD EQUATION;

QUANTUM THEORY;

EID: 33846356292     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.062113     Document Type: Article

References (60)

1. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1993).
2. D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1994).
3. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics, 2nd edition (Springer, Berlin, 1995).
4. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
5. H. J. Carmichael, Statistical Methods in Quantum Optics 1 (Springer, Berlin, 1999).
6. R. Alicki and M. Fannes, Quantum Dynamical Systems (Oxford University Press, Oxford, 2001).
7. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
8. C. W. Gardiner and P. Zoller, Quantum Noise, 3rd edition (Springer, Berlin, 2004).
9. W. H. Zurek, Phys. Today PHTOAD 0031-9228 10.1103/PhysRevD.24.151610. 1103/PhysRevD.26.1862 44, 36 (1991);
10. W. H. Zurek, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.75.715 75, 715 (2003);
11. E. Joos, H. D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, and I. O. Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd edition (Springer-Verlag, Berlin, 2003).
12. D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1796 76, 1796 (1996);
13. D. J. Wineland, C. Monroe, W. M. Itano, D. Leibfried, B. E. King, and D. M. Meekhof, J. Res. Natl. Inst. Stand. Technol. JRITEF 1044-677X 103, 259 (1998);
14. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.75.281 75, 281 (2003).
15. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
16. The Physics of Quantum Information, edited by, D. Bouwmeester, A. Zeilinger, and, A. Ekert, (Springer-Verlag, Heidelberg, 2000).
17. C. H. Bennett and D. P. DiVincenzo, Nature (London) NATUAS 0028-0836 10.1038/35005001 404, 247 (2000).
18. J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.73.565 73, 565 (2001).
19. Y. Makhlin, G. Schön, and A. Shnirman, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.73.357 73, 357 (2001).
20. A. Galindo and M. A. Martín-Delgado, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.347 74, 347 (2002).
21. L. M. K. Vandersypen and I. L. Chuang, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.1037 76, 1037 (2004).
22. G. Lindblad, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01608499 48, 119 (1976);
23. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.522979 17, 821 (1976).
24. G. Lindblad, Rep. Math. Phys. RMHPBE 0034-4877 10.1016/0034-4877(76) 90029-X 10, 393 (1976);
25. A. Sandulescu and H. Scutaru, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(87)90162-X 173, 277 (1987);
26. A. Isar, W. Scheid, and A. Sandulescu, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.529185 32, 2128 (1991);
27. A. Isar, A. Sandulescu, and W. Scheid, J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/17/3/015 17, 385 (1991);
28. A. Isar, A. Sandulescu, and W. Scheid, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.530013 34, 3887 (1993);
29. A. Isar, Helv. Phys. Acta HPACAK 0018-0238 67, 436 (1994);
30. A. Isar, Helv. Phys. Acta HPACAK 0018-0238 68, 225 (1995);
31. A. Isar, A. Sandulescu, and W. Scheid, Int. J. Mod. Phys. B IJPBEV 0217-9792 10, 2767 (1996);
32. A. Isar, A. Sandulescu, and W. Scheid, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.6371 60, 6371 (1999);
33. S. Gao, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3101 79, 3101 (1997);
34. S. Gao, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.57.4509 57, 4509 (1998);
35. A. K. Rajagopal, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98) 00463-0 246, 237 (1998).
36. K. Kraus, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(71)90108-4 64, 311 (1971);
37. States, Effects, and Operations (Springer-Verlag, Berlin, 1983).
38. M. Ban, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.529540 33, 3213 (1992);
39. M. Ban, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.47.5093 47, 5093 (1993);
40. L. M. Arévalo-Aguilar and H. Moya-Cessa, Quantum Semiclassic. Opt. QUSOEC 1355-5111 10.1088/1355-5111/10/5/004 10, 671 (1998);
41. A. B. Klimov and J. L. Romero, J. Opt. B: Quantum Semiclassical Opt. JOBOFD 1464-4266 10.1088/1464-4266/5/3/363 5, S316 (2003);
42. H.-X. Lu, J. Yang, Y.-D. Zhang, and Z.-B. Chen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.024101 67, 024101 (2003).
43. A. Napoli, S. Nicolosi, and A. Messina, Acta Phys. Hung. 23, 83 (2005).
44. M. D. Srinivas and E. B. Davies, Opt. Acta OPACAT 0030-3909 28, 981 (1981);
45. D. F. Walls and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.31.2403 31, 2403 (1985);
46. A. V. Dodonov, S. S. Mizrahi, and V. V. Dodonov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.023816 72, 023816 (2005).
47. P. Zoller, M. Marte, and D. F. Walls, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.35.198 35, 198 (1987);
48. M. B. Plenio and P. L. Knight, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.101 70, 101 (1998).
49. L. van Hove, Physica (Utrecht) PHYSAG 0031-8914 10.1016/S0031-8914(54) 92646-4 21, 517 (1955);
50. L. van Hove, Physica (Utrecht) PHYSAG 0031-8914 10.1016/S0031-8914(57) 92891-4 23, 441 (1957);
51. E. B. Davies, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01608389 39, 91 (1974);
52. H. Spohn and J. L. Lebowitz, Adv. Chem. Phys. ADCPAA 0065-2385 38, 109 (1979);
53. I. Ojima, J. Stat. Phys. JSTPBS 0022-4715 56, 203 (1989);
54. P. Facchi and S. Pascazio, Physica A PHYADX 0378-4371 10.1016/S0378-4371(99)00209-5 271, 133 (1999);
55. L. Accardi, Y. G. Lu, and I. Volovich, Quantum Theory and Its Stochastic Limit (Springer, Berlin, 2002);
56. S. Tasaki, K. Yuasa, P. Facchi, G. Kimura, H. Nakazato, I. Ohba, and S. Pascazio, e-print quant-ph0602184, Ann. Phys. (N.Y.) (to be published);
57. K. Yuasa, S. Tasaki, P. Facchi, G. Kimura, H. Nakazato, I. Ohba, and S. Pascazio, e-print quant-ph0602185, ibid. (to be published).
58. P. F. Palmer, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.523296 18, 527 (1977);
59. H. Spohn, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.52.569 52, 569 (1980).
60. P. Facchi, S. Tasaki, S. Pascazio, H. Nakazato, A. Tokuse, and D. A. Lidar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.022302 71, 022302 (2005).