Purification-based metric to measure the distance between quantum states and processes

TL;DR

This paper introduces a purification-based entropic metric for quantifying distances between quantum states and processes, highlighting its mathematical properties and potential applications in quantum information.

Contribution

It proposes a novel purification-based metric for quantum states and processes, analyzing its properties and suitability for theoretical and experimental use.

Findings

The metric satisfies many desirable mathematical properties.

It effectively measures distances between quantum states and processes.

Potential for use in quantum information applications.

Abstract

In this work we study the properties of an purification-based entropic metric for measuring the distance between both quantum states and quantum processes. This metric is defined as the square root of the entropy of the average of two purifications of mixed quantum states which maximize the overlap between the purified states. We analyze this metric and show that it satisfies many appealing properties, which suggest this metric is an interesting proposal for theoretical and experimental applications of quantum information.