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

2017/08/31 by Gilad Gour, David Jennings, Francesco Buscemi +2 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Coherence (philosophical gambling strategy) #Discrete mathematics #Majorization #Mathematics #Open quantum system #Physics #Quantum #Quantum Information and Cryptography #Quantum discord #Quantum dynamics #Quantum mechanics #Quantum operation #Quantum process #Quantum thermodynamics #Statistical Mechanics and Entropy #Statistical physics #Theoretical physics #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1038/s41467-018-06261-7

published as Nature Communicationsvolume 9, Article number: 5352 (2018) · 11 pages main text + 12 pages appendix, 2 figures, v2 contains significant improvement of the presentation. Particularly, the appendix has been completely restructured and proofs expanded with more details, and with a re-derivation of thermo-majorization from quantum majorization

arxiv created 2017/12/07 · openalex publication_date 2018/12/11 · arxiv updated 2018/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

What does it mean for one quantum process to be more disordered than another? Interestingly, this apparently abstract question arises naturally in a wide range of areas such as information theory, thermodynamics, quantum reference frames, and the resource theory of asymmetry. Here we use a quantum-mechanical generalization of majorization to develop a framework for answering this question, in terms of single-shot entropies, or equivalently, in terms of semi-definite programs. We also investigate some of the applications of this framework, and remarkably find that, in the context of quantum thermodynamics it provides the first complete set of necessary and sufficient conditions for arbitrary quantum state transformations under thermodynamic processes, 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.

Citations

• An information-theoretic account of the Wigner-Araki-Yanase theorem
• Untersuchungen über die Grundlagen der Thermodynamik
• A quantum version of randomization criterion
• Limitations on the Evolution of Quantum Coherences: Towards Fully Quantum Second Laws of Thermodynamics
• The Quantum Blackwell Theorem and Minimum Error State Discrimination
• Quantum clocks and their synchronisation - the Alternate Ticks Game
• Fully quantum second-law--like statements from the theory of statistical comparisons
• Entanglement versusStosszahlansatz: Disappearance of the thermodynamic arrow in a high-correlation environment
• Evolution without evolution: Dynamics described by stationary observables
• Equivalent Comparisons of Experiments
• Time from quantum entanglement: an experimental illustration
• ON THE EXISTENCE OF PHYSICAL TRANSFORMATIONS BETWEEN SETS OF QUANTUM STATES
• Reference frames, superselection rules, and quantum information
• The physics and mathematics of the second law of thermodynamics
• Thermodynamic resource theories, non-commutativity and maximum entropy principles
• An example of a quantum statistical model which cannot be mapped to a less informative one by any trace preserving positive map
• From clocks to cloners: Catalytic transformations under covariant operations and recoverability

Cited by

• Virtual temperatures as a key quantifier for passive states in quantum thermodynamic processes
• Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
• Probabilistic transformations of quantum resources
• Quantum resource theories
• Macroscopicity and observational deficit in states, operations, and correlations