快速混合是否稳定？

中文摘要 AI 辅助

若干具有物理意义的Lindblad算子，例如描述一般开放量子系统模型以及工程化态制备过程的那些，通常是快速混合的，即它们以随系统大小呈多对数时间尺度弛豫到稳态。由于混合时间短，物理上预期局部扰动不会显著增加混合时间。在本工作中，我们质疑这一预期，并询问快速混合是否得以存续。我们提供了反例，表明快速混合在一般情况下并不稳定，即使扰动不改变稳态也是如此。我们还表明，任意弱的局部哈密顿扰动可以破坏快速混合。作为这些结果的补充，我们发展了一系列充分条件，这些条件蕴含稳定的快速混合，包括几类准自由费米子系统、交换的Lindblad算子以及局部自旋系统。我们还确定了修正对数索博列夫不等式（MLSIs）——一种更强的收敛形式——在何种条件下导致稳定的快速混合。作为我们结果的进一步推论，我们表明快速混合并不蕴含正的MLSI常数。

英文摘要

Several physically interesting Lindbladians, such as those describing generic open quantum system models as well as engineered state preparation processes, are often rapidly mixing, that is, they relax to steady states in time scaling polylogarithmically with the system size. Owing to the short mixing times, it is physically expected that local perturbations do not substantially increase the mixing time. In this work we question this expectation and ask whether rapid mixing survives. We provide counterexamples showing that rapid mixing is not stable in general, even when the perturbation does not change the steady state. We also show that arbitrarily weak local Hamiltonian perturbations can destroy rapid mixing. Complementing these results, we develop an array of sufficient conditions which imply stable rapid mixing, including several classes of quasifree fermionic systems, commuting Lindbladians, and local spin systems. We also identify conditions under which modified logarithmic Sobolev inequalities (MLSIs), a stronger form of convergence, lead to stable rapid mixing. As a further implication of our results, we show that rapid mixing does not imply a positive MLSI constant.

发表机构

• Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）
• Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
• Gran Sasso Science Institute（格兰萨索科学研究所）
• TU München（慕尼黑工业大学）
• University of Cambridge（剑桥大学）
• Universität Tübingen（蒂宾根大学）

机构由 AI 辅助整理，请以论文原文为准。