Dynamic Distance Measures on Spaces of Isospectral Mixed Quantum States

TL;DR

This paper introduces a new dynamic distance measure for mixed quantum states, which is practical for quantum information tasks and compares favorably with existing measures like the Bures distance.

Contribution

The paper proposes a novel dynamic distance measure for mixed quantum states, demonstrating its validity and applicability in quantum information processing.

Findings

The dynamic distance measure is a proper metric for mixed quantum states.

It is defined using a measurable quantity, enhancing practical applicability.

Comparison shows advantages over the Bures distance.

Abstract

Distance measures are indispensable tools in quantum information processing and quantum computing. This since they can be used to quantify to what extent information is preserved, or altered, by quantum processes. In this paper we propose a new distance measure for mixed quantum states, that we call the dynamic distance measure, and show that it is a proper distance measure. The dynamic distance measure is defined in terms of a measurable quantity, which make it very suitable for applications. In a final section we compare the dynamical distance measure with the well-known Bures distance.