Geometric measure of mixing of quantum state

TL;DR

This paper introduces a geometric measure of quantum state mixing based on Hilbert-Schmidt distance, providing explicit formulas and examples for spin-1/2 states, linking it to eigenvalue space geometry.

Contribution

It presents a new geometric measure of quantum state mixing with explicit formulas and demonstrates its application to spin-1/2 states.

Findings

Explicit expression for the geometric measure derived.

The measure corresponds to squared Euclidean distance in eigenvalue space.

Application to spin-1/2 states illustrates the measure's utility.

Abstract

We define the geometric measure of mixing of quantum state as a minimal Hilbert-Schmidt distance between the mixed state and a set of pure states. An explicit expression for the geometric measure is obtained. It is interesting that this expression corresponds to the squared Euclidian distance between the mixed state and the pure one in space of eigenvalues of the density matrix. As an example, geometric measure of mixing for spin-1/2 states is calculated.