Quantum work statistics, Loschmidt echo and information scrambling

TL;DR

This paper establishes a universal relation connecting quantum work statistics, Loschmidt echo dynamics, and information scrambling, providing new insights into quantum thermodynamics and quantum chaos.

Contribution

It introduces a novel relation linking quantum work distribution with Loschmidt echo and information scrambling, especially for canonical initial states.

Findings

Loschmidt echo of the thermofield double state measures information scrambling.

Quantum work statistics relate to the analytic continuation of the partition function.

The framework applies to driven quantum systems with time-reversal operations.

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.