Jarzynski-like Equality of Nonequilibrium Information Production Based on Quantum Cross Entropy

TL;DR

This paper introduces a Jarzynski-like equality for nonequilibrium information production using quantum cross entropy, providing a new framework for analyzing quantum information processes beyond traditional measurement schemes.

Contribution

It proposes a novel one-time measurement scheme and an information production distribution based on quantum cross entropy, extending the understanding of quantum fluctuation theorems.

Findings

Derivation of a Jarzynski-like equality for quantum information production.

Establishment of a new framework using quantum cross entropy.

Potential applications in quantum communication, machine learning, and thermodynamics.

Abstract

The two-time measurement scheme is well studied in the context of quantum fluctuation theorem. However, it becomes infeasible when the random variable determined by a single measurement trajectory is associated with the von-Neumann entropy of the quantum states. We employ the one-time measurement scheme to derive a Jarzynski-like equality of nonequilibrium information production by proposing an information production distribution based on the quantum cross entropy. The derived equality further enables one to explore the roles of the quantum cross entropy in quantum communications, quantum machine learning and quantum thermodynamics.