Jarzynski equality for quantum stochastic maps

TL;DR

This paper generalizes the Jarzynski equality to arbitrary quantum operations, introducing a correction term for nonunital maps and analyzing its bounds in finite-dimensional quantum systems.

Contribution

It extends the Jarzynski equality to nonunital quantum maps, providing a correction term and bounds for finite quantum systems.

Findings

Derived a generalized Jarzynski equality for nonunital quantum maps.

Established bounds for the correction term due to nonunitality.

Applied results to finite-dimensional quantum systems with quantum channels.

Abstract

Jarzynski equality and related fluctuation theorems can be formulated for various setups. Such an equality was recently derived for nonunitary quantum evolutions described by unital quantum operations, i.e., for completely positive, trace-preserving maps, which preserve the maximally mixed state. We analyze here a more general case of arbitrary quantum operations on finite systems and derive the corresponding form of the Jarzynski equality. It contains a correction term due to nonunitality of the quantum map. Bounds for the relative size of this correction term are established and they are applied for exemplary systems subjected to quantum channels acting on a finite-dimensional Hilbert space.