Exact decoherence to pointer states in free open quantum systems is universal

Physical Review Letters

Volumn 92, Issue 21, 2004, Pages

  Eisert, Jens ^a,b  

^a UNIVERSITY OF POTSDAM   (Germany)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOVEMENT; CONFORMAL MAPPING; CORRELATION METHODS; DAMPING; DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; ELECTROMECHANICAL DEVICES; ENTROPY; GREEN'S FUNCTION; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; MATRIX ALGEBRA; PROBLEM SOLVING;

COUPLING STRENGTH; GAUSSIAN STATES; QUANTUM PARTICLES; QUANTUM SYSTEMS;

QUANTUM THEORY;

EID: 3142592456     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.92.210401     Document Type: Article

References (43)

1. W. H. Zurek, Rev. Mod Phys. 75, 715 (2003); J.-P. Paz and W. H. Zurek, quant-ph/0010011; D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Heidelberg, 1996); D. Guilini, C. Kiefer, and H.D. Zeh, Phys. Lett. A 199, 291 (1995); J. R. Anglin, J. P. Paz, and W.H. Zurek, Phys. Rev. A 55, 4041 (1997); H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Cambridge University Press, Cambridge, 2002).
2. W. H. Zurek, Rev. Mod Phys. 75, 715 (2003); J.-P. Paz and W. H. Zurek, quant-ph/0010011; D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Heidelberg, 1996); D. Guilini, C. Kiefer, and H.D. Zeh, Phys. Lett. A 199, 291 (1995); J. R. Anglin, J. P. Paz, and W.H. Zurek, Phys. Rev. A 55, 4041 (1997); H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Cambridge University Press, Cambridge, 2002).
3. W. H. Zurek, Rev. Mod Phys. 75, 715 (2003); J.-P. Paz and W. H. Zurek, quant-ph/0010011; D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Heidelberg, 1996); D. Guilini, C. Kiefer, and H.D. Zeh, Phys. Lett. A 199, 291 (1995); J. R. Anglin, J. P. Paz, and W.H. Zurek, Phys. Rev. A 55, 4041 (1997); H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Cambridge University Press, Cambridge, 2002).
4. W. H. Zurek, Rev. Mod Phys. 75, 715 (2003); J.-P. Paz and W. H. Zurek, quant-ph/0010011; D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Heidelberg, 1996); D. Guilini, C. Kiefer, and H.D. Zeh, Phys. Lett. A 199, 291 (1995); J. R. Anglin, J. P. Paz, and W.H. Zurek, Phys. Rev. A 55, 4041 (1997); H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Cambridge University Press, Cambridge, 2002).
5. W. H. Zurek, Rev. Mod Phys. 75, 715 (2003); J.-P. Paz and W. H. Zurek, quant-ph/0010011; D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Heidelberg, 1996); D. Guilini, C. Kiefer, and H.D. Zeh, Phys. Lett. A 199, 291 (1995); J. R. Anglin, J. P. Paz, and W.H. Zurek, Phys. Rev. A 55, 4041 (1997); H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Cambridge University Press, Cambridge, 2002).
6. W. H. Zurek, Rev. Mod Phys. 75, 715 (2003); J.-P. Paz and W. H. Zurek, quant-ph/0010011; D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Heidelberg, 1996); D. Guilini, C. Kiefer, and H.D. Zeh, Phys. Lett. A 199, 291 (1995); J. R. Anglin, J. P. Paz, and W.H. Zurek, Phys. Rev. A 55, 4041 (1997); H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Cambridge University Press, Cambridge, 2002).
7. A. O. Caldeira and A. J. Leggett, Physica (Amsterdam) 121A, 587 (1983).
8. N. Gisin and I. C. Percival, J. Phys. A 26, 2233 (1993); J. J. Halliwell and A. Zoupas, Phys. Rev. D 52, 7294 (1995).
9. N. Gisin and I. C. Percival, J. Phys. A 26, 2233 (1993); J. J. Halliwell and A. Zoupas, Phys. Rev. D 52, 7294 (1995).
10. D. Braun, F. Haake, and W.T. Strunz, Phys. Rev. Lett. 86, 2913 (2001).
11. J. Eisert and M. B. Plenio, Phys. Rev. Lett. 89, 137902 (2002); H. McAneney, J. Lee, and M. S. Kim, Phys. Rev. A 68, 063814 (2003).
12. J. Eisert and M. B. Plenio, Phys. Rev. Lett. 89, 137902 (2002); H. McAneney, J. Lee, and M. S. Kim, Phys. Rev. A 68, 063814 (2003).
13. W. H. Zurek, S. Habib, and J. P. Paz, Phys. Rev. Lett. 70, 1187 (1993).
14. L. Diosi and C. Kiefer, J. Phys. A 35, 2675 (2002).
15. S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 59, 3204 (1999); A.V. Rau, J. A. Dunningham, and K. Burnett, Science 301, 1081 (2003).
16. S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A 59, 3204 (1999); A.V. Rau, J. A. Dunningham, and K. Burnett, Science 301, 1081 (2003).
17. F. Haake and R. Reibold, Phys. Rev. A 32, 2462 (1985); W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071 (1989); R. Karrlein and H. Grabert, Phys. Rev. E 55, 153 (1997).
18. F. Haake and R. Reibold, Phys. Rev. A 32, 2462 (1985); W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071 (1989); R. Karrlein and H. Grabert, Phys. Rev. E 55, 153 (1997).
19. F. Haake and R. Reibold, Phys. Rev. A 32, 2462 (1985); W. G. Unruh and W. H. Zurek, Phys. Rev. D 40, 1071 (1989); R. Karrlein and H. Grabert, Phys. Rev. E 55, 153 (1997).
20. S. Haroche, Phys. Scr. T76, 159 (1998); Q. A. Turchette et al., Phys. Rev. A 62, 053807 (2000); D. A. Kokorowski, A. D. Cronin, T. D. Roberts, and D. E. Pritchard, Phys. Rev. Lett. 86, 2191 (2001); K. Hornberger, S. Uttenthaler, B. Brezger, L. Hackermüller, M. Arndt, and A. Zeilinger, ibid. 90, 160401 (2003); X. M. H. Huang, C. A. Zorman, M. Mehregany, and M. L. Roukes, Nature (London) 421, 496 (2003).
21. S. Haroche, Phys. Scr. T76, 159 (1998); Q. A. Turchette et al., Phys. Rev. A 62, 053807 (2000); D. A. Kokorowski, A. D. Cronin, T. D. Roberts, and D. E. Pritchard, Phys. Rev. Lett. 86, 2191 (2001); K. Hornberger, S. Uttenthaler, B. Brezger, L. Hackermüller, M. Arndt, and A. Zeilinger, ibid. 90, 160401 (2003); X. M. H. Huang, C. A. Zorman, M. Mehregany, and M. L. Roukes, Nature (London) 421, 496 (2003).
22. S. Haroche, Phys. Scr. T76, 159 (1998); Q. A. Turchette et al., Phys. Rev. A 62, 053807 (2000); D. A. Kokorowski, A. D. Cronin, T. D. Roberts, and D. E. Pritchard, Phys. Rev. Lett. 86, 2191 (2001); K. Hornberger, S. Uttenthaler, B. Brezger, L. Hackermüller, M. Arndt, and A. Zeilinger, ibid. 90, 160401 (2003); X. M. H. Huang, C. A. Zorman, M. Mehregany, and M. L. Roukes, Nature (London) 421, 496 (2003).
23. S. Haroche, Phys. Scr. T76, 159 (1998); Q. A. Turchette et al., Phys. Rev. A 62, 053807 (2000); D. A. Kokorowski, A. D. Cronin, T. D. Roberts, and D. E. Pritchard, Phys. Rev. Lett. 86, 2191 (2001); K. Hornberger, S. Uttenthaler, B. Brezger, L. Hackermüller, M. Arndt, and A. Zeilinger, ibid. 90, 160401 (2003); X. M. H. Huang, C. A. Zorman, M. Mehregany, and M. L. Roukes, Nature (London) 421, 496 (2003).
24. S. Haroche, Phys. Scr. T76, 159 (1998); Q. A. Turchette et al., Phys. Rev. A 62, 053807 (2000); D. A. Kokorowski, A. D. Cronin, T. D. Roberts, and D. E. Pritchard, Phys. Rev. Lett. 86, 2191 (2001); K. Hornberger, S. Uttenthaler, B. Brezger, L. Hackermüller, M. Arndt, and A. Zeilinger, ibid. 90, 160401 (2003); X. M. H. Huang, C. A. Zorman, M. Mehregany, and M. L. Roukes, Nature (London) 421, 496 (2003).
25. B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992).
26. V. Hakim and V. Ambegaokar, Phys. Rev. A 32, 423 (1995).
27. W. Weidlich and F. Haake, Z. Phys. 185, 30 (1965); P. Ullersma, Physica (Utrecht) 32, 27 (1966); H. Grabert, U. Weiss, and P. Hänggi, Phys. Rev. Lett. 52, 2193 (1984); P. S. Riseborough, P. Häggi, and U. Weiss, Phys. Rev. A 31, 471 (1985); P. Talkner, Ann. Phys. (N.Y.) 167, 390 (1986).
28. W. Weidlich and F. Haake, Z. Phys. 185, 30 (1965); P. Ullersma, Physica (Utrecht) 32, 27 (1966); H. Grabert, U. Weiss, and P. Hänggi, Phys. Rev. Lett. 52, 2193 (1984); P. S. Riseborough, P. Häggi, and U. Weiss, Phys. Rev. A 31, 471 (1985); P. Talkner, Ann. Phys. (N.Y.) 167, 390 (1986).
29. W. Weidlich and F. Haake, Z. Phys. 185, 30 (1965); P. Ullersma, Physica (Utrecht) 32, 27 (1966); H. Grabert, U. Weiss, and P. Hänggi, Phys. Rev. Lett. 52, 2193 (1984); P. S. Riseborough, P. Häggi, and U. Weiss, Phys. Rev. A 31, 471 (1985); P. Talkner, Ann. Phys. (N.Y.) 167, 390 (1986).
30. W. Weidlich and F. Haake, Z. Phys. 185, 30 (1965); P. Ullersma, Physica (Utrecht) 32, 27 (1966); H. Grabert, U. Weiss, and P. Hänggi, Phys. Rev. Lett. 52, 2193 (1984); P. S. Riseborough, P. Häggi, and U. Weiss, Phys. Rev. A 31, 471 (1985); P. Talkner, Ann. Phys. (N.Y.) 167, 390 (1986).
31. W. Weidlich and F. Haake, Z. Phys. 185, 30 (1965); P. Ullersma, Physica (Utrecht) 32, 27 (1966); H. Grabert, U. Weiss, and P. Hänggi, Phys. Rev. Lett. 52, 2193 (1984); P. S. Riseborough, P. Häggi, and U. Weiss, Phys. Rev. A 31, 471 (1985); P. Talkner, Ann. Phys. (N.Y.) 167, 390 (1986).
32. H. Grabert, P. Schramm, and G. L. Ingold, Phys. Rep. 168, 155 (1988); H. Grabert, P. Schramm, and G. L. Ingold, Phys. Rev. Lett. 58, 1285 (1987).
33. H. Grabert, P. Schramm, and G. L. Ingold, Phys. Rep. 168, 155 (1988); H. Grabert, P. Schramm, and G. L. Ingold, Phys. Rev. Lett. 58, 1285 (1987).
34. Note that it is an interesting problem in its own right to investigate the influence of correlated initial conditions such that time evolution of the state of the distinguished system no longer corresponds to a completely positive map. This is relevant, e.g., when considering a charged quantum particle coupled to the radiation field, where the assumption of product initial conditions is typically not invariant under gauge transformations [16].
35. H.-P. Breuer and F. Petruccione, Phys. Rev. A 63, 032102 (2001).
36. G. W. Ford and R. F. O'Connell, Phys. Rev, D 64, 105020 (2001).
37. 2.
38. The mass of the particle will set to unity and units will be employed where ℏ = 1 and k = 1.
39. M. Hillery, R. F. O'Connell, M. O. Scully, and E. P. Wigner, Phys. Rep. 106, 121 (1984).
40. This is meant in the sense that for any ε > 0 there exists a ζ > 0 such that |B∞ - T| ø ε.
41. Needless to say, there is a certain degree of ambiguity in the choice of the pointer states here. The key argument is that the final state after a finite time can be exactly represented as a convex combination of these reasonable pointer states.
42. W. Schleich, Quantum Optics in Phase Space (Wiley-VCH, Berlin, 2001).
43. G. M. D'Ariano and M. F. Sacchi, Nuovo Cimento Soc. Ital. Fis. 112B, 881 (1997).