arXiv:1711.01277 · Scientific Reports

Quantum work statistics, Loschmidt echo and information scrambling

Aurélia Chenu, I. L. Egusquiza, J. Molina-Vilaplana, A. del Campo

Published Aug 16, 2018• 55 citations

Abstract

A universal relation is established between the quantum work probability distribution of an isolated driven quantum system and the Loschmidt echo dynamics of a two-mode squeezed state. When the initial density matrix is canonical, the Loschmidt echo of the purified double thermofield state provides a direct measure of information scrambling and can be related to the analytic continuation of the partition function. Information scrambling is then described by the quantum work statistics associated with the time-reversal operation on a single copy, associated with the sudden negation of the system Hamiltonian.

DOI: 10.1038/s41598-018-30982-w

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An educated review of "Quantum work statistics, Loschmidt echo and information scrambling".

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The formulation of quantum work statistics as a dynamical problem through the \nLoschmidt echo is at the heart of this work. An introduction to each of these \nconcepts is presented together with the notion of information scrambling, which \nextends the scope of this work to areas such as quantum chaos or even black hole \nphysics. Using the paper of A. Chenu et al. [1] as the guidelines, we first show \nthat the work statistics associated with an arbitrary driving protocol of an isolated quantum system in a generic initial state is equivalent to the Loschmidt echo \ndynamics of a purified density matrix in an enlarged Hilbert space. When the initial state is thermal, the purification leads to a thermofield double state, which is \nused to describe eternal black holes through the AdS/CFT correspondence, often \nargued to be the fastest information scramblers. The field of quantum chaotic \nsystems is shown to emerge naturally from the previous content, and a full description of it in terms of Random Matrix Theory is also presented. Numerical and \nanalytical results are finally obtained for the quantities introduced after imposing \ntime-reversal symmetry in our problem, hence selecting the Gaussian Orthogonal \nEnsemble as the framework within we shall take our averages.

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