发表机构
Center for Theoretical Physics — a Leinweber Institute, Massachusetts Institute of Technology; California Institute of Technology; Department of Physics, The University of Texas at Austin; National University of Singapore; Centre for Quantum Technologies, National University of Singapore（麻省理工学院莱因韦伯理论物理中心; 加州理工学院; 德克萨斯大学奥斯汀分校物理系; 新加坡国立大学; 新加坡国立大学量子技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本综述探讨深度热化与希尔伯特空间遍历性，基于量子信息理论和最大熵原理的统一框架，解释量子态最大随机分布如何从幺正动力学涌现，并讨论相关开放问题与应用。
AI 中文摘要
量子模拟的最新进展使得人们能够发现量子多体动力学中新型的普适性。在本综述中，我们讨论深度热化和希尔伯特空间遍历性——这两个最近发现的现象，其特征是量子态分布以精确意义上的“最大随机”方式涌现。它们为不可逆统计力学如何从可逆的幺正量子动力学中产生提供了新的视角，超越了传统的量子热化和平衡理论。我们回顾了一个统一框架，该框架植根于量子信息理论和最大熵原理，解释了在不同物理约束下出现的各种遍历性形式。我们讨论了开放问题和活跃的研究方向，包括超越纯量子态系综的推广、与更深层次的遍历性破缺相关的深度热化中的相变、与量子热化和遍历性更广泛主题的联系，以及在量子信息科学中的应用，例如用于基准测试或层析成像。
英文摘要
Recent advances in quantum simulation have enabled the discovery of novel forms of universality in quantum many-body dynamics. In this Review, we discuss deep thermalization and Hilbert space ergodicity--two recently discovered phenomena characterized by the emergence of distributions of quantum states that are "maximally random" in a precise sense. They offer a new perspective on how irreversible statistical mechanics arises from reversible unitary quantum dynamics, going beyond conventional theories of quantum thermalization and equilibration. We review a unifying framework, rooted in quantum information theory and principles of maximum entropy, that explains the different forms of ergodicity which arise under various physical constraints. We discuss open questions and active research directions, including generalizations beyond ensembles of pure quantum states, phase transitions in deep thermalization tied to deeper forms of ergodicity-breaking, connections to broader topics in quantum thermalization and ergodicity, and applications in quantum information science, such as for benchmarking or tomography.
Comments11 pages, 5 figures. Comments welcome!
