- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Rapid Communication
  • Access by Xinjiang University

Effects of symmetries on quantum fidelity decay

Yaakov S. Weinstein* and C. Stephen Hellberg†

  • Center for Computational Materials Science, Naval Research Laboratory, Washington, DC 20375, USA

  • *Author to whom correspondence should be addressed. Electronic address: weinstei@dave.nrl.navy.mil
  • †Electronic address: hellberg@dave.nrl.navy.mil
PDF

Phys. Rev. E 71, 035203(R) – Published 21 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.035203

Abstract

We explore the effect of a system’s symmetries on fidelity decay behavior. Chaoslike exponential fidelity decay behavior occurs in nonchaotic systems when the system possesses symmetries and the applied perturbation is not tied to a classical parameter. Similar systems without symmetries exhibit faster-than-exponential decay under the same type of perturbation. This counterintuitive result, that extra symmetries cause the system to behave in a chaotic fashion, may have important ramifications for quantum-error correction.

View figure in article

Article Text

References (34)

  1. A. Peres, Phys. Rev. A 30, 1610 (1984).
  2. A. Peres, in Quantum Chaos, edited by H. A. Cerdeira, R. Ramaswamy, M. C. Gutzwiller, and G. Casati (World Scientific, Singapore, 1991), p. 73; A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic, Dordrecht, 1995).
  3. Ph. Jacquod, P. G. Silvestrov, and C. W. J. Beenakker, Phys. Rev. E 64, 055203(R), (2001).
  4. T. Prosen and M. Znidaric, Z. Phys. A 35, 1455 (2002).
  5. Ph. Jacquod, I. Adagideli, and C. W. J. Beenakker, Phys. Rev. Lett. 89, 154103 (2002).
  6. J. Emerson, Y. S. Weinstein, S. Lloyd, and D. G. Cory, Phys. Rev. Lett. 89, 284102 (2002).
  7. R. A. Jalabert and H. M. Pastawski, Phys. Rev. Lett. 86, 2490 (2001).
  8. F. M. Cucchietti et al., Phys. Rev. E 65, 046209 (2002).
  9. T. Prosen and M. Znidaric, New J. Phys. 5, 109 (2003).
  10. R. Sankaranarayanan and A. Lakshminarayan, Phys. Rev. E 68, 036216 (2003).
  11. T. Prosen, Phys. Rev. E 65, 036208 (2002).
  12. P. Jacquod, I. Adagideli, and C. W. J. Beenakker, Europhys. Lett. 61, 729 (2003).
  13. G. Benenti, G. Casati, and G. Veble, Phys. Rev. E 68, 036212 (2003).
  14. Y. S. Weinstein and C. S. Hellberg, Phys. Rev. E 71, 016209 (2005).
  15. W. G. Wang, G. Casati, and B. Li, Phys. Rev. E 69, 025201(R) (2004).
  16. Y. S. Weinstein, S. Lloyd, and C. Tsallis, Phys. Rev. Lett. 89, 214101 (2002).
  17. N. R. Cerruti and S. Tomsovic, Phys. Rev. Lett. 88, 054103 (2002); N. N. Cerruti and S. Tomsovic, J. Phys. A 36, 3451 (2003); W. Wang and B. Li, Phys. Rev. E 66, 056208 (2002).
  18. D. A. Wisniacki and D. Cohen, Phys. Rev. E 66, 046209 (2002).
  19. E. P. Wigner, Ann. Math. 62, 548 (1955); 65, 203 (1957); Y. V. Fyodorov, O. A. Chubykalo, F. M. Izrailev, and G. Casati, Phys. Rev. Lett. 76, 1603 (1996); Ph. Jacquod and D. L. Shepelyansky, ibid. 75, 3501 (1995).
  20. D. Rossini, G. Benenti, and G. Casati, Phys. Rev. E 70, 056216 (2004).
  21. T. Prosen and M. Znidaric, J. Phys. A 34, L681 (2001).
  22. K. M. Frahm, R. Fleckinger, and D. L. Shepelyansky, Eur. Phys. J. D 29, 139 (2004); O. Kern, G. Alber, and D. L. Shepelyansky, 32, 153 (2005).
  23. D. Poulin, R. Blume-Kohout, R. Laflamme, and H. Ollivier, Phys. Rev. Lett. 92, 177906 (2004).
  24. Y. S. Weinstein, S. Lloyd, J. Emerson, and D. G. Cory, Phys. Rev. Lett. 89, 157902 (2002).
  25. F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).
  26. F. Haake, M. Kus, and R. Scharf, Z. Phys. B: Condens. Matter 65, 381 (1987).
  27. L. Viola et al., Science 293, 2059 (2001).
  28. K. Zyczkowski and M. Kus, Phys. Rev. E 53, 319 (1996).
  29. Y. S. Weinstein and C. S. Hellberg, e-print quant-ph/0405053.

  30. The even J QKT transformation matrix has odd Hilbert space dimension 2J+1. To make N even we remove the eigenvector that is all zeros except a one at the N∕2+1 element. The N∕2+1 element in all other eigenvectors is zero and is removed to give them a length of N.

  31. P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, Science 290, 498 (2000); D. Kielpinski et al., 291, 1013 (2001).
  32. D. P. DiVincenzo et al., Nature (London) 408, 339 (2000).
  33. Y. S. Weinstein and C. S. Hellberg, e-print quant-ph/0408037.
  34. L. Thomas, A. Caneschi, and B. Barbara, Phys. Rev. Lett. 83, 2398 (1999).

Outline

Information

Phys. Rev. E 71, 035203(R)– Published 21 March, 2005
  • Received 22 September 2004

© 2005 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation