发表机构
Harvard University; Massachusetts Institute of Technology（哈佛大学; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究利用量子热化与量子纠错的关联，将近似量子纠错框架拓展至热化研究，发现有限温度热化的编码结构达到熵量子单例界，确立了新的最优码族。
AI 中文摘要
量子热化解释了孤立多体系统如何自然演化至热态，使得局域测量无法获取初始条件的信息，这正是量子纠错所利用的机制——量子纠错通过非局域编码设计保护信息。本研究利用这一关联，将（近似）量子纠错的严格框架拓展至量子热化研究：将典型的后期态视为码字，刻画了一般热化动力学的纠错性质；通过数值计算揭示了涌现码的编码率、距离与热熵密度之间的普适关系。在无限温度下，该普适曲线达到量子单例界，与Haar随机码的最优极限一致；在有限温度下，我们引入基于Scrooge系综的码族（Haar系综的自然热类似物），证明其满足熵量子单例界，确立该码族在熵约束下的最优性。我们提取的普适曲线同样满足该界，表明有限温度热化本身是最优的。最后，我们证明守恒量会限制热化的纠错行为：具有不同能量或其他守恒荷的码字仅泄露经典信息，纠错性持续到差异达到热涨落的尺度。本研究结果揭示了热化动力学中存在的普适最优编码结构，同时引入了达到近似量子纠错基本极限的新最优码。
英文摘要
Quantum thermalization explains how an isolated many-body system naturally evolves towards a thermal state, rendering information about the initial conditions inaccessible to local measurements. This is precisely the mechanism utilized in quantum error correction, where information is protected by design through a nonlocal encoding. In this work, we leverage this connection to port the rigorous framework of (approximate) quantum error correction to the study of quantum thermalization. Treating typical late-time states as codewords, we characterize the error-correcting properties of generic thermalizing dynamics. We numerically uncover a universal relationship between the encoding rate, distance, and thermal entropy density of the emergent code. At infinite temperature, this universal curve saturates the quantum Singleton bound, achieving the same optimal limit as Haar-random codes. At finite temperature, we introduce a code family based on the Scrooge ensemble, the natural thermal analogue of the Haar ensemble, and prove it saturates the entropic quantum Singleton bound, establishing this family as optimal within entropic constraints. Our extracted universal curve independently saturates this same bound, revealing that finite-temperature thermalization is itself optimal. Finally, we show how conserved quantities limit the error-correcting behavior of thermalization: codewords with differing energies, or other conserved charges, leak only classical information, and correctability persists until the difference reaches the scale of thermal fluctuations. Our results reveal a universal optimal coding structure in thermalizing dynamics, while introducing new optimal codes that achieve fundamental limits of approximate quantum error correction.
Comments8 + 32 pages, 5 figures
