Physics – Quantum Physics
Scientific paper
2005-06-17
Phys. Rev. E 73, 046204 (2006).
Physics
Quantum Physics
11 pages, 4 figures
Scientific paper
10.1103/PhysRevE.73.046204
General semiclassical expression for quantum fidelity (Loschmidt echo) of arbitrary pure and mixed states is derived. It expresses fidelity as an interference sum of dephasing trajectories weighed by the Wigner function of the initial state, and does not require that the initial state be localized in position or momentum. This general dephasing representation is special in that, counterintuitively, all of fidelity decay is due to dephasing and none due to the decay of classical overlaps. Surprising accuracy of the approximation is justified by invoking the shadowing theorem: twice--both for physical perturbations and for numerical errors. It is shown how the general expression reduces to the special forms for position and momentum states and for wave packets localized in position or momentum. The superiority of the general over the specialized forms is explained and supported by numerical tests for wave packets, non-local pure states, and for simple and random mixed states. The tests are done in non-universal regimes in mixed phase space where detailed features of fidelity are important. Although semiclassically motivated, present approach is valid for abstract systems with a finite Hilbert basis provided that the discrete Wigner transform is used. This makes the method applicable, via a phase space approach, e. g., to problems of quantum computation.
No associations
LandOfFree
Dephasing representation of quantum fidelity for general pure and mixed states does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dephasing representation of quantum fidelity for general pure and mixed states, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dephasing representation of quantum fidelity for general pure and mixed states will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-448523