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

TLDR

The paper investigates how to compare disorder between quantum processes. The authors aim to provide a quantum‑mechanical generalization of majorization that supplies necessary and sufficient conditions for arbitrary quantum state transformations under thermodynamic processes, explicitly accounting for coherence. They construct a framework of generalized thermal processes grounded in energy conservation, equilibrium, and coherence, described by single‑shot entropies, which extends thermal operations and applies to quantum statistical models, channels, asymmetry, and thermodynamics. This framework delivers a complete set of conditions for state transformations, recovers thermo‑majorization when coherence is absent, and imposes a Page‑Wootters clock constraint in the asymptotic coherence regime.

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.