Open quantum dynamics: Complete positivity and entanglement

International Journal of Modern Physics B

Volumn 19, Issue 19, 2005, Pages 3063-3139

  Benatti, Fabio ^a   Floreanini, Roberto ^a  

^a UNIVERSITY OF TRIESTE   (Italy)

Author keywords

Complete positivity; Open quantum systems; Quantum entanglement

Indexed keywords

EID: 23844457177     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979205032097     Document Type: Review

References (113)

1. R. Alicki and K. Lendi, Quantum Dynamical Semi-Groups and Applications, Lect. Notes Phys. Vol. 286 (Springer-Verlag, Berlin, 1987).
2. V. Gorini, A. Frigerio, M. Verri, A. Kossakowski and E. G. C. Sudarshan, Rep. Math. Phys. 13, 149 (1976).
3. H. Spohn, Rev. Mod. Phys. 52, 569 (1980).
4. E. B. Davies, Quantum Theory of Open Systems (Academic Press, New York, 1976).
5. R. Alicki, Invitation to Quantum Dynamical Semigroups, in Lect. Notes Phys. Vol. 597, P. Garbaczewski and R. Olkiewicz, eds. (Springer-Verlag, Berlin, 2002), p. 239.
6. F. Benatti and R. Floreanini (eds.) Dissipative Quantum Dynamics, in Lect. Notes Phys. Vol. 622 (Springer-Verlag, Berlin, 2003).
7. H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
8. W. H. Louisell, Quantum Statistical Properties of Radiation (John Wiley, New York, 1973).
9. F. Haake, Statistical Treatment of Open Systems by Generalized Master Equations, in Springer Tracts in Mod. Phys. Vol. 95 (Springer-Verlag, Berlin, 1973).
10. C. Cohen-Tannoudji, J. Dupont-Roc and G. Grynberg, Atom-Photon Interactions (John Wiley, New York, 1988).
11. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1994).
12. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997).
13. C. W. Gardiner and P. Zoller, Quantum Noise, 2nd. edn. (Springer-Verlag, Berlin, 2000).
14. R. R. Puri, Mathematical Methods of Quantum Optics (Springer-Verlag, Berlin, 2001).
15. C. P. Slichter, Principle of Magnetic Resonance (Springer-Verlag, Berlin, 1990).
16. U. Weiss, Quantum Dissipative Systems, 2nd. edn. (World Scientific, Singapore, 1999).
17. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences, 2nd edn. (Springer-Verlag, Berlin, 1997).
18. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2002).
19. G. Alber et al., eds. Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, Springer Tracts in Mod. Phys. Vol. 173 (Springer-Verlag, Berlin, 2001).
20. D. Bouwmeester et al., (eds.), The Physics of Quantum Information (Springer-Verlag, Berlin, 2000).
21. F. Benatti and R. Floreanini, Ann. of Phys. 273, 58 (1999).
22. F. Benatti and R. Floreanini, Nucl. Phys. B488, 335 (1997).
23. F. Benatti and R. Floreanini, Mod. Phys. Lett. A12, 1465 (1997).
24. F. Benatti and R. Floreanini, Nucl. Phys. B511, 550 (1998).
25. F. Benatti and R. Floreanini, Banach Center Publications 43, 71 (1998).
26. F. Benatti and R. Floreanini, Phys. Lett. B468, 287 (1999).
27. F. Benatti and R. Floreanini, Phys. Lett. B451, 422 (1999).
28. F. Benatti and R. Floreanini, Phys. Rev. D62, 125009 (2000).
29. F. Benatti and R. Floreanini, Phys. Rev. D64, 085015 (2001).
30. F. Benatti, R. Floreanini and R. Romano, Nucl. Phys. B602, 541 (2001).
31. F. Benatti and R. Floreanini, Phys. Rev. A66, 043617 (2002).
32. F. Benatti, R. Floreanini and R. Romano, J. Phys. A35, 4955 (2002).
33. R. Alicki and M. Fannes, Quantum Dynamical Systems (Oxford University Press, Oxford, 2001).
34. K. Kraus, States, Effects and Operations: Fundamental Notions of Quantum Theory, in Lect. Notes Phys. Vol. 190 (Springer-Verlag, Berlin, 1983).
35. M. Takesaki, Theory of operator algebras, Vol. 1 (Springer-Verlag, New York, 1979).
36. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, 1993).
37. W. Thirring, Quantum Mathematical Physics: Atoms, Molecules and Large Systems (Springer-Verlag, Berlin, 2002).
38. O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, Vol. I and II (Springer-Verlag, Berlin, 1981).
39. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994).
40. A. Royer, Phys. Rev. Lett. 77, 3272 (1996).
41. A. Royer, Phys. Lett. A315, 335 (2003).
42. M. D. Choi, Canad. J. Math. 24, 520 (1972).
43. M. Horodecki, P. Horodecki and R. Horodecki, Mixed State Entanglement and Quantum Communication, in Spring Tracts in Mod. Phys. Vol. 173 (Springer Verlag, Berlin, 2001).
44. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
45. M. Horodecki, P. Horodecki and R. Horodecki, Phys. Lett. A223, 1 (1996).
46. S. L. Woronowicz, Rep. Math. Phys. 10, 165 (1976).
47. R. F. Werner, Phys. Rev. A40, 4277 (1989).
48. S. Hill and W. K. Wootters, Phys. Rev. Lett. 78, 5022 (1997).
49. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
50. W. K. Wootters, Quantum Inf. Comp. 1, 27 (2001).
51. S. Nakajima, Progr. Theor. Phys. 20, 948 (1958).
52. R. Zwanzig, J. Chem. Phys. 33, 1338 (1960).
53. R. Kubo, M. Toda and N. Hashitsume, Statistical Physics II (Springer-Verlag, Berlin, 1985).
54. V. Gorini, A. Kossakowski and E. C. G. Sudarshan, J. Math. Phys. 17, 821 (1976).
55. G. Lindblad, Comm. Math. Phys. 48, 119 (1976).
56. A. Kossakowski, Bull. Acad. Pol. Sc. 12, 1021 (1972).
57. A. Kossakowski, Open Sys. Inf. Dyn. 10, 1 (2003).
58. F. Benatti, R. Floreanini and M. Piani, Phys. Lett. A326, 187 (2004).
59. F. Benatti, R. Floreanini and M. Piani, Open Sys. Inf. Dyn. 11, 325 (2004).
60. J. Budimir and J. L. Skinner, J. Stat. Phys. 49, 1029 (1987).
61. B. B. Laird, J. Budimir and J. L. Skinner, J. Chem. Phys. 94, 4391 (1991).
62. B. B. Laird and J. L. Skinner, J. Chem. Phys. 94, 4405 (1991).
63. S. Gnutzmann and F. Haake, Z. Phys. B10, 263 (1996).
64. A. Suarez, R. Silbey and I. Oppenheim, J. Chem. Phys. 97, 5101 (1992).
65. P. Gaspard and M. Nagaoka, J. Chem. Phys. 111, 5668 (1999).
66. J. Wielkie, J. Chem. Phys. 114, 7736 (2001).
67. G. M. Palma, K.-A. Suominen and A. Ekert, Proc. R. Soc. Lond. A452, 567 (1996).
68. A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, Integrals and Series, Vol. 1 (Gordon and Breach, New York, 1986).
69. A. Erdélyi (ed.), Higher Transcendental Functions, Bateman Manuscript Project, Vol. 1 (McGraw-Hill, New-York, 1953).
70. A. J. van Wonderen and K. Lendi, J. Stat. Phys. 80, 273 (1995).
71. R. Dümcke and H. Spohn, Z. Phys. B34, 419 (1979).
72. E. B. Davies, Comm. Math. Phys. 39, 91 (1974).
73. E. B. Davies, Math. Ann. 219, 147 (1976).
74. L. Accardi, J. Gough and Y. G. Lu, Rep. Math. Phys. 36, 155 (1995).
75. L. Accardi, Y. G. Lu and I. V. Volovich, Quantum Theory and its Stochastic Limit (Springer-Verlag, Berlin, 2003).
76. L. Lanz and B. Vacchini, Int. J. Mod. Phys. A17, 435 (2002).
77. R. Dümcke, Comm. Math. Phys. 97, 331 (1985).
78. V. Gorini and A. Kossakowski, J. Math. Phys. 17, 1298 (1975).
79. A. Frigerio and V. Gorini, J. Math. Phys. 17, 2123 (1976).
80. P. F. Palmer, J. Math. Phys. 18, 527 (1977).
81. F. Benatti, R. Floreanini and R. Romano, Phys. Rev. D68, 094007 (2003).
82. F. Benatti and R. Floreanini, Phys. Rev. D71, 013003 (2005).
83. F. Benatti, R. Floreanini and M. Piani, Phys. Rev. A67, 042110 (2003).
84. V. F. Sears, Neutron Optics (Oxford University Press, Oxford, 1989).
85. H. Rauch, S. A. Werner, Neutron Interferometry (Oxford University Press, Oxford, 2000).
86. F. Benatti, R. Floreanini and R. Romano, J. Phys. A35, L551 (2002).
87. F. Benatti, R. Floreanini, M. Piani and R. Romano, Complete positivity and dissipative factorized dynamics: some comments, Proceedings of the IV Workshop on Time Asymmetric Quantum Mechanics (Lisboa, Portugal, 2003), quant-ph/0310151.
88. L. Diosi, Progressive Decoherence and Total Environmental Disentanglement, in Lect. Notes Phys. Vol. 622 (Springer-Verlag, Berlin, 2003).
89. D. Braun, Phys. Rev. Lett. 89, 277901 (2002).
90. M. S. Kim et al., Phys. Rev. A65, 040101(R) (2002).
91. S. Schneider and G. J. Milburn, Phys. Rev. A65, 042107 (2002).
92. Z. Ficek and R. Tanas, Phys. Rep. 372, 369 (2002).
93. F. Benatti, R. Floreanini and M. Piani, Phys. Rev. Lett. 91, 070402 (2003).
94. A. LeClair, Phys. Rev. D56, 782 (1997).
95. A. LeClair, F. Lessage, S. Lukyanov and H. Saleur, Phys. Lett. A235, 203 (1997).
96. A. LeClair, Ann. of Phys. 271, 268 (1999).
97. R. Haag, Local Quantum Physics: Fields, Particles, Algebras (Springer, Berlin, 1996).
98. J. Bros and D. Buchholz, Nucl. Phys. B627, 289 (2002).
99. S. Takagi, Prog. Theor. Phys. Suppl. 88, 1 (1986).
100. K.-P. Marzlin and J. Audretsch, Phys. Rev. D57, 1045 (1998).
101. P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (Academic Press, San Diego, 1994).
102. K. Lendi, J. Phys. A20, 15 (1987).
103. F. Benatti and R. Floreanini, Controlling entanglement generation in external quantum fields, preprint.
104. P. Zanardi, C. Zalka and L. Faoro, Phys. Rev. A62, 030301 (2000).
105. P. Zanardi, Phys. Rev. A63, 040304 (2001).
106. J. I. Cirac, W. Dür, B. Kraus and M. Lewenstein, Phys. Rev. Lett. 86, 544 (2001).
107. W. Dür, G. Vidal, J. I. Cirac, N. Linden and S. Popescu, Phys. Rev. Lett. 87, 137901 (2001).
108. B. Kraus and J. I. Cirac, Phys. Rev. A63, 062309 (2001).
109. K. Zyckowski, P. Horodecki, M. Horodecki and R. Horodecki, Phys. Rev. A65, 012101 (2001).
110. G. S. Agarwal, A. C. Brown, L. M. Narducci and G. Vetri, Phys. Rev. A15, 1613 (1977).
111. A. Frigerio, Comm. Math. Phys. 63, 269 (1977).
112. F. Benatti and R. Floreanini, Phys. Rev. A70, 012112 (2004).
113. F. Benatti and R. Floreanini, Asymptotic entanglement of two independent systems in a common bath, preprint.