Abstract
We show that the fidelity decay between an initial eigenstate evolved under a unitary chaotic operator and the same eigenstate evolved under a perturbed operator saturates well before the 1/N limit expected for a generic initial state, where N is the dimension of the Hilbert space. We provide a theoretical argument and numerical evidence that, for perturbations of intermediate strength, the saturation level depends quadratically on the perturbation strength.
PACS: 05.45.Mt; 03.67.Lx
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
M. V. Berry and M. Tabor, Proc. Roy. Soc. Lond. A356, 375 (1977).
O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).
F. Haake, Quantum Signatures of Chaos (Springer, New York, 1991).
A. Peres, Phys. Rev. A 30, 1610 (1984); Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, 1995).
R. Schack and C. M. Caves, Phys. Rev. Lett. 71, 525–528, 1993.
W. H. Zurek and J. P. Paz, Physica D 83, 300–308, 1995.
T. Prosen and M. Znidaric, J. Phys. A 35, 1455, 2002.
Ph. Jacquod, P. G. Silvestrov, and C. W. J. Beenakker, Phys. Rev. E 64, 055203 (2001).
J. Emerson, Y. S. Weinstein, S. Lloyd, and D. G. Cory, Phys. Rev. Lett. 89, 284102 (2002).
Ph. Jacquod, I. Adagideli, and C. W. J. Beenakker, Phys. Rev. Lett. 89, 154103 (2002).
N. Cerruti and S. Tomsovic, Phys. Rev. Lett. 88, 054103 (2002).
R. A. Jalabert and H. M. Pastawski, Phys. Rev. Lett. 86, 2490 (2001); F. Cucchietti, C. H. Lewenkopf, E. R. Mucciolo, H. Pastawski, and R. O. Vallejos nlin. CD/0112015.
G. Beneti and G. Casati, quant-ph/0112060.
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, Phys. Rev. Lett. 75, 3501 (1995).
F. Haake and K. Zyczkowski, Phys. Rev. A 42, 1013 (1990).
D. A. Wisniacki, nlin.CD/0208044.
L. Viola, E. Fortunato, M. A. Pravia, E. Knill, R. Laflamme, and D. G. Cory, Science 293, 2059 (2001).
F. Haake, M. Kus, and R. Scharf, Z. Phys. B 65, 381 (1987).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Weinstein, Y.S., Emerson, J., Lloyd, S. et al. Fidelity Decay Saturation Level for Initial Eigenstates. Quantum Information Processing 1, 439–448 (2002). https://doi.org/10.1023/A:1024018431394
Issue Date:
DOI: https://doi.org/10.1023/A:1024018431394