Average mutual information for random fermionic Gaussian quantum states

TL;DR

This paper extends the analysis of entanglement entropy to mixed Gaussian states in open quantum systems, using random matrix theory to compute mutual information and von Neumann entropy for finite and large systems.

Contribution

It introduces a method to compute typical mutual information for mixed Gaussian states with fixed spectra, expanding entanglement analysis to open quantum systems.

Findings

Derived formulas for average mutual information and von Neumann entropy.

Applied random matrix theory to compute correlation functions of singular values.

Provided results for both finite and thermodynamic system sizes.

Abstract

Studying the typical entanglement entropy of a bipartite system when averaging over different ensembles of pure quantum states has been instrumental in different areas of physics, ranging from many-body quantum chaos to black hole evaporation. We extend such analysis to open quantum systems and mixed states, where we compute the typical mutual information in a bipartite system averaged over the ensemble of mixed Gaussian states with a fixed spectrum. Tools from random matrix theory and determinantal point processes allow us to compute arbitrary k-point correlation functions of the singular values of the corresponding complex structure in a subsystem for a given spectrum in the full system. In particular, we evaluate the average von Neumann entropy in a subsystem based on the level density and the average mutual information. Those results are given for finite system size as well as in the thermodynamic limit.