Quantum Jarzynski-Sagawa-Ueda relations

TL;DR

This paper extends the quantum Jarzynski relations to systems with measurement and feedback, providing new theoretical insights into quantum thermodynamics and the role of information in energy transformations.

Contribution

It derives quantum versions of Sagawa and Ueda's generalized Jarzynski relations, including an error-free case and one with classical measurement errors.

Findings

Derived quantum Jarzynski relations with feedback control.

Established a quantum second law incorporating feedback efficiency.

Extended classical feedback relations to quantum systems.

Abstract

We consider a (small) quantum mechanical system which is operated by an external agent, who changes the Hamiltonian of the system according to a fixed scenario. In particular we assume that the agent (who may be called a demon) performs measurement followed by feedback, i.e., it makes a measurement of the system and changes the protocol according to the outcome. We extend to this setting the generalized Jarzynski relations, recently derived by Sagawa and Ueda for classical systems with feedback. One of the two relations by Sagawa and Ueda is derived here in error-free quantum processes, while the other is derived only when the measurement process involves classical errors. The first relation leads to a second law which takes into account the efficiency of the feedback.