Hyperfinite-operational Approach to the Problem of Time Reversibility of Quantum Mechanics

类型III渐近假设检验的强逆速率

Strong converse rate for asymptotic hypothesis testing in type III

本文将 sandwiched 相对 Rényi 熵在假设检验强逆中的操作解释从超有限情形推广到一般冯·诺依曼代数，利用约化方法、有限谱近似和量子类型方法完成证明，揭示该熵的操作意义是量子信息的基本性质，并可能连接随机矩阵理论与基础物理量子信息理论。

Von Neumann's information engine without the spectral theorem

Von Neumann obtained the formula for the entropy of a quantum state by assuming the validity of the second law of thermodynamics in a thought experiment involving semipermeable membranes and an ideal gas of quantum-labeled particles. Despite being operational in the most part, von Neumann's argument crucially departs from an operational narrative in its use of the spectral theorem. In this work we show that the role of the spectral theorem in von Neumann's argument can be taken over by the operational assumptions of repeatability and reversibility, and using these we are able to explore the co…

Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems

The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same th…

Operational Resource Theory of Quantum Channels

Quantum resource theories have been widely studied to systematically characterize the non-classicality of quantum systems. Most resource theories focus on quantum states and study their interconversions. Although quantum channels are generally used as the tool for state manipulation, such a manipulation capability can be naturally regarded as a generalized quantum resource, leading to an open research direction in the resource theories of quantum channels. Various resource-theoretic properties of channels have been investigated, however, without treating channels themselves as operational reso…

Approximate reversibility in the context of entropy gain, information gain, and complete positivity

There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty principle of quantum mechanics. Recent results provide physically meaningful enhancements of these limiting statements, determining how well one can attempt to reverse an irreversible process. In this paper, we apply and extend these results to give strong enhancements to several entropy inequalities, having to do with entropy gain, information gain, entropic di…

量子过程的热力学：自由能与可逆非热性的操作框架

Thermodynamics of quantum processes: An operational framework for free energy and reversible athermality

通过公理化定义通道自由能，构建量子过程的非热性资源理论，证明其渐近可逆性，并揭示与信息处理任务的联系。