Extending quantum detailed balance through optimal transport

TL;DR

This paper introduces a novel framework for analyzing quantum dynamical systems using optimal transport theory, specifically Wasserstein distances, to extend the concept of detailed balance to broader classes of quantum systems.

Contribution

It develops a general approach employing transport plans and Wasserstein distances to study quantum systems with properties like detailed balance, broadening the scope of quantum dynamical analysis.

Findings

Framework for quantum systems using optimal transport

Extension of detailed balance concept to new quantum classes

Potential applications in quantum information theory

Abstract

We develop a general approach to setting up and studying classes of quantum dynamical systems close to and structurally similar to systems having specified properties, in particular detailed balance. This is done in terms of transport plans and Wasserstein distances between systems on possibly different observable algebras.