发表机构
Perimeter Institute for Theoretical Physics; Department of Mathematics and Statistics, Dalhousie University; Institute for Quantum Computing, University of Waterloo（佩里曼理论物理研究所; 达尔豪斯大学数学与统计系; 滑铁卢大学量子计算研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明 Haag 对偶等价于条件互信息的渐近消失，并给出二维系统及自旋链中的具体判据，关联拓扑纠缠熵与熵密度。
AI 中文摘要
受量子自旋系统中 Haag 对偶的启发，我们证明：由有限维矩阵代数的递增序列生成的一对交换因子，其 Haag 对偶等价于某个适当条件互信息的渐近消失。对于二维自旋系统，设一个环带将有限区域与外部区域分开。则区域 $A$ 的 Haag 对偶成立，当且仅当内区域与外部的互信息（以 $A$ 在环带内的部分为条件）在外半径变大时趋于零。作为推论，在具有次领头修正的严格面积律假设下，Haag 对偶对单锥成立；而对两个或更多不相交锥的并集成立，当且仅当拓扑纠缠熵消失。对于自旋链上的平移不变纯态，半链 Haag 对偶等价于熵密度为零。
英文摘要
Motivated by Haag duality in quantum spin systems, we show that Haag duality for a pair of commuting factors generated by increasing sequences of finite-dimensional matrix algebras is equivalent to the asymptotic vanishing of a suitable conditional mutual information. For spin systems, let an annulus separate a finite region from the exterior. Haag duality then holds for a region $A$ if and only if the mutual information of the inner region and the exterior, conditioned on the part of $A$ inside the annulus, vanishes as the outer radius becomes large. As a corollary, assuming a strict area law with subleading corrections, Haag duality holds for single cones, and it holds for unions of two or more disjoint cones precisely when the topological entanglement entropy vanishes. For translation-invariant pure states on spin chains, half-chain Haag duality is equivalent to vanishing entropy density.
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