Deep thermalization in Gaussian continuous-variable quantum systems

TL;DR

This paper reveals a universal form of equilibration in multimode Gaussian quantum systems, where the induced ensemble of states becomes independent of measurement basis and is characterized by a maximum entropy principle.

Contribution

It extends the concept of deep thermalization to continuous-variable systems, introducing the Gaussian Scrooge distribution and linking quantum information theory with quantum dynamics.

Findings

Universal ensemble of coherent states with normally distributed displacements

Independence from measurement basis in the induced ensemble

Connection to maximum entropy principle and minimal accessible information

Abstract

We uncover emergent universality arising in the equilibration dynamics of multimode continuous-variable systems. Specifically, we study the ensemble of pure states supported on a small subsystem of a few modes, generated by Gaussian measurements on the remaining modes of a globally pure bosonic Gaussian state. We find that beginning from highly entangled, complex global states, such as random Gaussian states and product squeezed states coupled via a deep array of linear optical elements, the induced ensemble attains a universal form, independent of the choice of measurement basis: it is composed of unsqueezed coherent states whose displacements are distributed normally and isotropically, with variance depending on only the particle-number density of the system. We further show that the emergence of such a universal form is consistent with a generalized maximum entropy principle, which endows the limiting ensemble, which we call the "Gaussian Scrooge distribution", with a special quantum information-theoretic property of having minimal accessible information. Our results represent a conceptual generalization of the recently introduced notion of "deep thermalization" in discrete-variable quantum many-body systems -- a novel form of equilibration going beyond thermalization of local observables -- to the realm of continuous-variable quantum systems. Moreover, it demonstrates how quantum information-theoretic perspectives can unveil new physical phenomena and principles in quantum dynamics and statistical mechanics.