Dynamics of Loschmidt echoes and fidelity decay

By T. Gorin, Tomaz Prosen, T. Seligman, Marko Znidaric. 2006

523 citations recorded by the source corpus.

Fidelity serves as a benchmark for the reliability in quantum information processes, and has recently attracted 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 important alternatives 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6d019d38458adb5a339d7414f9b1dc2a06e587bd

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Citations in the corpus

Decoherence, entanglement and irreversibility in quantum dynamical systems with few degrees of freedom (2008, background): “(Gorin et al., 2006; Prosen et al., 2003)) and also by studying a kicked rotator as an alternative model to the kicked top.”
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer (2016, background): “3(a,c) is also known as the Loschmidt echo, which is important in other contexts such as the theory of quantum chaos [28] and dynamical critical phenomena far from equilibrium [29].”
Leaking chaotic systems (2012, background): “See (Gorin et al., 2006; Jacquod and Petitjean, 2009) for reviews, and (Garćıa-Mata and Wisniacki, 2011) for limitations of the Lyapunov regime.”
Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles (2016, background): “This quantity, also known as return probability and quantum fidelity, formally coincides with the Loschmidt echo (see reviews [188, 211]) when the two Hamiltonians involved in the echo are taken as H0 andH0 + V.”
Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “This time-periodic behavior of the Loschmidt echo should be contrasted with the expectation for quantum chaotic systems, where a rapid decay is expected for typical initial states (64, 65).”
Colloquium: Non-Markovian dynamics in open quantum systems (2015, background): “(79) the decoherence function is directly linked to the concept of the Loschmidt echo L(t) (Cucchietti et al., 2003) which characterizes how the environment responds to perturbations by the system (Cucchietti et al., 2004; Gorin et al., 2006; Goussev et al., 2008; Peres, 1984).”