Quantum majorization and a complete set of entropic conditions for quantum thermodynamics

TL;DR

This paper introduces a quantum generalization of majorization that characterizes disorder in quantum processes, providing a complete set of entropic conditions for quantum state transformations in thermodynamics, including coherence effects.

Contribution

It develops a comprehensive framework for quantum majorization, extending thermal operations to include quantum coherence and providing necessary and sufficient conditions for state transformations.

Findings

Complete set of conditions for quantum state transformations under thermodynamics.

Framework accounts for quantum coherence and extends thermal operations.

Recovers thermo-majorization in the zero coherence limit.

Abstract

What does it mean for one quantum process to be more disordered than another? Here we provide a precise answer to this question in terms of a quantum-mechanical generalization of majorization. The framework admits a complete description in terms of single-shot entropies, and provides a range of significant applications. These include applications to the comparison of quantum statistical models and quantum channels, to the resource theory of asymmetry, and to quantum thermodynamics. In particular, within quantum thermodynamics, we apply our results to provide the first complete set of of necessary and sufficient conditions for arbitrary quantum state transformation under thermodynamic processes, and which rigorously accounts for quantum-mechanical properties, such as coherence. Our framework of generalized thermal processes extends thermal operations, and is based on natural physical principles, namely, energy conservation, the existence of equilibrium states, and the requirement that quantum coherence be accounted for thermodynamically. In the zero coherence case we recover thermo-majorization while in the asymptotic coherence regime we obtain a constraint that takes the form of a Page-Wootters clock condition.