Quantum Wasserstein distance of order 1 between channels

TL;DR

This paper develops a comprehensive quantum Wasserstein distance of order 1 applicable to channels in an operator algebraic setting, extending finite-dimensional results and analyzing key metric properties.

Contribution

It introduces a new quantum Wasserstein distance for channels within an operator algebra framework, broadening previous finite-dimensional approaches.

Findings

The metric applies to channels between composite systems.

Additivity and stability properties of the quantum Wasserstein distance are established.

The theory extends finite-dimensional results to a more general setting.

Abstract

We set up a general theory for a quantum Wasserstein distance of order 1 in an operator algebraic framework, extending recent work in finite dimensions. In addition, this theory applies not only to states, but also to channels, giving a metric on the set of channels from one composite system to another. The additivity and stability properties of this metric are studied.