发表机构
University of California at San Diego; Kavli Institute for Theoretical Physics, University of California, Santa Barbara（圣地亚哥加利福尼亚大学; 加州大学圣巴巴拉分校卡弗里理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究重整化群（RG）与条件互信息（CMI）的关系，证明局域可逆RG下非相邻区域的CMI紫外有限，分析两个具有长程CMI的分层模型的RG行为与噪声稳定性。
AI 中文摘要
混合量子态偏离局域吉布斯描述的情况通常对局域可观测量不可见，但可通过条件互信息（CMI）检测。本文研究重整化群（RG）与CMI的关系，特别是RG对CMI的约束。首先证明：当态具有固定局域希尔伯特空间维数的局域可逆RG时，非相邻区域A和C在缓冲区域B条件下的CMI是紫外有限的。接着研究两个具有长程CMI但可进行简单RG描述的分层模型：第一个模型在0<T<∞的每个温度下具有发散的马尔可夫长度，但在RG下流至无穷温度乘积态；第二个模型满足局域马尔可夫条件但违反全局马尔可夫条件，且对弱噪声稳定，在临界噪声强度下，两点CMI随系统大小仅呈多项式衰减，而两点互信息消失。
英文摘要
A departure of a mixed quantum state from a local Gibbs description is generally invisible to local observables but can be detected by the conditional mutual information (CMI). Here we study the relationship between the renormalization group (RG) and CMI, and in particular, how RG constrains CMI. We first show that the CMI between nonadjacent regions $A$ and $C$, conditioned on the buffer region $B$, is UV-finite whenever the state admits a locally reversible RG with a fixed on-site Hilbert space dimension. We then study two hierarchical models that have long-range CMI and yet admit a simple RG description. The first model has a divergent Markov length at every temperature $0<T<\infty$ but nevertheless flows to an infinite-temperature product state under RG. The second model satisfies the local Markov condition while violating the global one and is stable against weak noise. At the critical noise strength, the two-point CMI decays only polynomially as a function of the system size, while the two-point mutual information vanishes.
Comments13 pages + appendices; main results are summarized in the introduction
