A geometrization of quantum mutual information

TL;DR

This paper introduces a geometric approach to quantum mutual information, defining a new measure of total correlations in quantum systems using Gaussian integrals within the geometric framework of quantum mechanics.

Contribution

It proposes a novel geometric measure of quantum mutual information based on Gaussian integrals, linking quantum correlations to the geometry of the state space.

Findings

New measure of total correlations introduced

Expressed in terms of Gaussian integrals

Applicable to continuous variable quantum systems

Abstract

It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the geometric description of a composite quantum system introducing a new measure of total correlations that can be computed in terms of Gaussian integrals.