A unified framework of unitarily residual measures for quantifying dissipation

TL;DR

This paper introduces unitarily residual measures to quantify dissipation in open quantum systems, isolating non-unitary dynamics and providing a unitary-invariant divergence framework that enhances understanding of quantum thermodynamics.

Contribution

The paper develops a novel framework for dissipation quantification by defining unitarily residual measures that are invariant under unitary transformations, linking quantum and classical divergence measures.

Findings

Unitarily residual measures are invariant under unitary evolution.

These measures satisfy properties like monotonicity and convexity.

In some cases, they reduce to classical divergences between eigenvalue distributions.

Abstract

Open quantum systems are governed by both unitary and non-unitary dynamics, with dissipation arising from the latter. Traditional quantum divergence measures, such as quantum relative entropy, fail to account for the non-unitary oriented dissipation as the divergence is positive even between unitarily connected states. We introduce a framework for quantifying the dissipation by isolating the non-unitary components of quantum dynamics. We define equivalence relations among hermitian operators through unitary transformations and characterize the resulting quotient set. By establishing an isomorphism between this quotient set and a set of real vectors with ordered components, we induce divergence measures that are invariant under unitary evolution, which we refer to as the unitarily residual measures. These unitarily residual measures inherit properties such as monotonicity and convexity and, in certain cases, correspond to classical information divergences between sorted eigenvalue distributions. Our results provide a powerful tool for quantifying dissipation in open quantum systems, advancing the understanding of quantum thermodynamics.