Non-equilibrium equalities with unital quantum channels

TL;DR

This paper explores the conditions under which quantum fluctuation theorems like Jarzynski equality hold for open quantum systems, emphasizing the role of unital quantum channels and extending these results to feedback control scenarios.

Contribution

It establishes that unital quantum channels are essential for the validity of quantum fluctuation theorems and extends these results to include feedback control and mutual information considerations.

Findings

Jarzynski equality holds for unital quantum channels.

Tasaki-Crooks type theorem formulated for bistochastic maps.

Quantum Jarzynski-Sagawa-Ueda relations derived with feedback control.

Abstract

A general tool for description of open quantum systems is given by the formalism of quantum operations. Most important of them are trace-preserving maps also known as quantum channels. We discuss those conditions on quantum channels under which the Jarzynski equality and related fluctuation theorems hold. It is essential that the representing quantum channel be unital. Under the mentioned condition, we first derive the corresponding Jarzynski equality. For bistochastic map and its adjoint, we further formulate a theorem of Tasaki-Crooks type. In the context of unital channels, some notes on heat transfer between two quantum systems are given. We also consider the case of a finite system operated by an external agent with a feedback control. When unital channels are applied at the first stage and, for a mutual-information form, at the further ones, we obtain quantum Jarzynski-Sagawa-Ueda relations. These are extension of the previously given results to unital quantum operations.