Quantum work statistics, Loschmidt echo and information scrambling

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.It is a pleasure to thank John Goold, Juan Jaramillo, and Julian Sonner for insightful discussions. Funding support from UMass Boston (project P20150000029279) and the John Templeton Foundation is acknowledged. I.L.E. acknowledges funding from Spanish MINECO/FEDER FIS2015-69983-P, the Basque Government through IT986-16, and UPV/EHU with grant EHUA15/17. J.M.V. is supported by Ministerio de Economia y Competitividad FIS2015-69512-R and Programa de Excelencia de la Fundacion Seneca 19882/GERM/15. A.C. and A.d.C. acknowledge the hospitality of the Simons Center for Geometry and Physics during completion of this work