Natural Metric for Quantum Information Theory

TL;DR

This paper introduces a new natural metric for quantum states based on entropy and purification, analyzing its properties and relation to other distances, with an application to 1-qubit mixed states.

Contribution

It proposes a novel quantum state metric using entropy and purification, expanding the tools for quantum information analysis.

Findings

The metric is well-defined and satisfies key properties.

It relates to existing quantum distances.

Application to 1-qubit states demonstrates its practicality.

Abstract

We study in detail a very natural metric for quantum states. This new proposal has two basic ingredients: entropy and purification. The metric for two mixed states is defined as the square root of the entropy of the average of representative purifications of those states. Some basic properties are analyzed and its relation with other distances is investigated. As an illustrative application, the proposed metric is evaluated for 1-qubit mixed states.