Isometries of the qubit state space with respect to quantum Wasserstein distances

TL;DR

This paper characterizes the isometries of quantum Wasserstein distances on the qubit state space, providing a detailed understanding of symmetries with respect to these quantum metrics.

Contribution

It offers a complete description of isometries for the symmetric quantum Wasserstein divergence and the divergence related to the Pauli matrix _z, advancing the understanding of quantum metric symmetries.

Findings

Characterization of isometries for symmetric quantum Wasserstein divergence

Complete description of isometries for the _z-based Wasserstein distance

Insights into symmetries of quantum state space under Wasserstein metrics

Abstract

In this paper we study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the symmetric quantum Wasserstein divergence $d_{sym}$, the divergence induced by all of the Pauli matrices. We also give a complete characterization of isometries with respect to $D_z$, the quantum Wasserstein distance corresponding to the single Pauli matrix $\sigma_z$.