The volume of Gaussian states by information geometry

TL;DR

This paper uses information geometry to calculate the volume of Gaussian states, including classical, quantum, and entangled states, revealing hierarchical inclusion relationships.

Contribution

It introduces a geometric framework to quantify the volume of Gaussian states, encompassing classical, quantum, and entangled states, using the Fisher-Rao metric.

Findings

Quantifies the volume of Gaussian states in phase space.

Shows chains of strict inclusion among classical, quantum, and entangled states.

Provides a geometric perspective on state space structure.

Abstract

We formulate the problem of determining the volume of the set of Gaussian physical states in the framework of information geometry. That is, by considering phase space probability distributions parametrized by the covariances and supplying this resulting statistical manifold with the Fisher-Rao metric. We then evaluate the volume of classical, quantum and quantum entangled states for two-mode systems showing chains of strict inclusion.