Average entanglement entropy of a small subsystem in a constrained pure Gaussian state ensemble

TL;DR

This paper analyzes the average entanglement entropy in small subsystems of pure Gaussian states, revealing it equals the entropy of uncorrelated states with the same marginals, with implications for thermalization and Hawking radiation.

Contribution

It introduces a model for pure Gaussian states with specific marginals and correlations, showing the entanglement entropy matches that of uncorrelated states, linking to thermalization and Hawking radiation.

Findings

Average entanglement entropy equals that of uncorrelated Gaussian states.

Ensembles model thermal properties locally while remaining globally pure.

Implications for understanding Hawking radiation and the Page curve.

Abstract

We consider ensembles of pure Gaussian states parametrized by single-mode marginals and (optionally) specific mode-mode correlations. Such ensembles provide a model for the final states when isolated quantum systems thermalize, as they can reproduce thermal properties locally, while being globally pure. By an analysis using real replicas and the coherent state representation of Gaussian states we show that the average entanglement entropy of a small subsystem is the same as the von Neumann entropy of a mixed Gaussian state with the same marginals, but no correlations. Finally, we discuss how these ensembles provide a model for Hawking radiation assuming unitary evolution, and discuss some of their properties in relations to the Page curve of Hawking radiation.