Complete characterisation of state conversions by work extraction

TL;DR

This paper develops a comprehensive framework for understanding quantum state conversions via work extraction, linking thermodynamics and quantum resource theories, and providing universal criteria for resource certification.

Contribution

It introduces a thermodynamic work extraction task that characterizes quantum state conversions with majorisation-like conditions applicable across resource theories.

Findings

Provides necessary and sufficient conditions for quantum state conversions.

Reduces to known majorisation conditions in specific resource contexts.

Establishes a universal resource certification method based on thermodynamics.

Abstract

We introduce a thermodynamic work extraction task that describes the energy storage enhancement of quantum systems, which is naturally related to quantum battery's charging process. This task induces majorisation-like conditions that provide a necessary and sufficient characterisation of state conversions in general quantum resource theories. When applied to specific resources, these conditions reduce to the majorisation conditions under unital channels and provide a thermodynamic version of Nielsen's theorem in entanglement theory. We show how this result establishes the first universal resource certification class based on thermodynamics, and how it can be employed to quantify general quantum resources based on work extraction.