Black Box Work Extraction and Composite Hypothesis Testing

TL;DR

This paper introduces a framework for black box work extraction in quantum thermodynamics, linking it to composite hypothesis testing and providing exact characterizations using quantum Stein's lemma, highlighting the role of initial state information.

Contribution

It develops a general black box work extraction framework and connects it to composite hypothesis testing, offering exact results via quantum Stein's lemma and a new interpretation of related quantities.

Findings

Optimal work extraction characterized by composite hypothesis testing performance

Reduction to quantum Stein's lemma for asymptotic analysis

Introduction of a new quantum Stein's lemma involving correlations

Abstract

Work extraction is one of the most central processes in quantum thermodynamics. However, the prior analysis of optimal extractable work has been restricted to a limited operational scenario where complete information about the initial state is given. Here, we introduce a general framework of black box work extraction, which addresses the inaccessibility of information on the initial state. We show that the optimal extractable work in the black box setting is completely characterized by the performance of a composite hypothesis testing task, a fundamental problem in information theory. We employ this general relation to reduce the asymptotic black box work extraction to the quantum Stein's lemma in composite hypothesis testing, allowing us to provide their exact characterization in terms of the Helmholtz free energy. We also show a new quantum Stein's lemma motivated in this physical setting, where a composite hypothesis contains a certain correlation. Our work exhibits the importance of information about the initial state and gives a new interpretation of the quantities in the composite quantum hypothesis testing, encouraging the interplay between the physical settings and the information theory.