Dynamics of Loschmidt echoes and fidelity decay

TL;DR

This paper reviews the different regimes of fidelity decay in quantum systems, discussing theoretical frameworks, experimental results, and applications, emphasizing the importance of fidelity as a measure of quantum dynamics susceptibility.

Contribution

It provides a comprehensive overview of fidelity decay regimes, integrating semiclassical, random matrix theory, and correlation function approaches, with insights into recent experiments and potential applications.

Findings

Identification of various fidelity decay regimes

Connection between theory and recent experimental results

Suggestions for future quantum optics experiments

Abstract

Fidelity serves as a benchmark for the relieability in quantum information processes, and has recently atracted much interest as a measure of the susceptibility of dynamics to perturbations. A rich variety of regimes for fidelity decay have emerged. The purpose of the present review is to describe these regimes, to give the theory that supports them, and to show some important applications and experiments. While we mention several approaches we use time correlation functions as a backbone for the discussion. Vanicek's uniform approach to semiclassics and random matrix theory provides an important alternative or complementary aspects. Other methods will be mentioned as we go along. Recent experiments in micro-wave cavities and in elastodynamic systems as well as suggestions for experiments in quantum optics shall be discussed.