发表机构
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出静态证明方法，改进量子吉布斯态在正温度下的局部马尔可夫性质，对有限程、指数及幂律相互作用分别建立指数、拉伸指数及代数衰减的CMI界，优于Chen和Rouzé的动态结果。
AI 中文摘要
我们在每个固定正温度下建立了量子吉布斯态的改进的局部马尔可夫性质。对于具有有界相互作用度的有限程相互作用，条件互信息（CMI）随分离距离指数衰减，其前因子随边界大小呈指数增长。这改进了Chen和Rouzé \u003c引用 Chen2025\u003e 建立的局部马尔可夫界中体积的指数依赖性。对于指数衰减和拉伸指数衰减的相互作用，我们获得了具有边界依赖前因子的拉伸指数CMI衰减。对于幂律相互作用，我们证明了逆对数或代数衰减，并具有多项式区域大小依赖性。我们的证明是静态的，与Chen和Rouzé的动态方法形成对比。我们将吉布斯态与通过移除边界相互作用获得的产品态进行比较，将CMI界简化为相对熵损失，我们使用局域性估计来控制该损失。
英文摘要
We establish improved locally Markovian properties of quantum Gibbs states at every fixed positive temperature. For finite-range interactions of bounded interaction degree, the conditional mutual information (CMI) decays exponentially with separation, with a prefactor exponential in the boundary size of only one of the two regions and independent of the size of the other region and the total system. This improves the exponential volume dependence of the local Markov bounds established by Chen and Rouzé \cite{Chen2025}. For exponentially and stretched-exponentially decaying interactions, we obtain stretched-exponential CMI decay with a boundary-dependent prefactor. For power-law interactions, we prove inverse-logarithmic or algebraic decay with polynomial region-size dependence. Our proof is static, in contrast to the dynamical approach of Chen and Rouzé. We compare the Gibbs state with a product state obtained by removing boundary interactions, reducing the CMI bound to a relative-entropy loss that we control using locality estimates.
Comments35 pages, no figures, improved exposition
