Quantum work statistics, Loschmidt echo and information scrambling

A Chenu,J Molina-Vilaplana,A Del Campo,I L Egusquiza

doi:10.1038/s41598-018-30982-w

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.

Highlights

Quantum thermodynamics provides a framework to unify quantum theory, statistical mechanics, information theory and thermodynamics[1]
We show below that a universal relation exists between the work probability distribution p(W) in an arbitrary unitary protocol and the dynamics of a Loschmidt echo, for any initial state, including mixed states, e.g. at finite temperature
We have shown a universal relation between the quantum work statistics and Loschmidt echo under arbitrary dynamics

Summary

Results

Universal relation between quantum work statistics and Loschmidt echo dynamics. Let us consider an isolated quantum system in a Hilbert space and described by the time-dependent Hermitian Hamiltonian Hs = ∑n Ens|ns〉〈ns|, with instantaneous eigenstates |ns〉 and eigenenergies Ens. The results of both measurements, two-energy measurement scheme prevents respectively En0 and Emτ , give the work from being defined as an observable in the quantum world[2] Even so, it can be understood in terms of a generalized measurement scheme[22,23]. We show below that a universal relation exists between the work probability distribution p(W) in an arbitrary unitary protocol and the dynamics of a Loschmidt echo, for any initial state, including mixed states, e.g. at finite temperature. Using the explicit definition of the transition probability, Eq (3), the characteristic function (5) can be written as ( ) χ(t, τ) = Tr U †(τ)eitHτU (τ) e−itH 0ρmix This form allows us to identify the auxiliary variable t as a second time of evolution, different from s, as was first proposed in ref..

Notice that the mixed state ρmix is stationary with respect to

Hτ when the dynamics

Conclusion

Additional Information