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

Understand

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.