The Volume of Two-Qubit States by Information Geometry

TL;DR

This paper uses information geometry to analyze the volume of two-qubit quantum states, focusing on separable and entangled states with fixed purity, and compares classical and quantum Fisher metrics.

Contribution

It introduces a geometric method to quantify the volume of two-qubit states and compares classical and quantum Fisher metrics in this context.

Findings

Classical Fisher metric yields similar qualitative results as quantum Fisher metrics.

The volume of two-qubit states with maximally disordered subsystems is characterized.

Behavior of volumes of separable and entangled states with fixed purity is analyzed.

Abstract

Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled states with fixed purity. We show that the usage of the classical Fisher metric on phase space probability representation of quantum states gives the same qualitative results with respect to different versions of the quantum Fisher metric.