标题： 时空马尔可夫长度：通过混合态相位实现容错的诊断工具 显示英文标题

标题： Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases

摘要： 我们建立了局部稳定器码在经历测量误差和物理误差时的容错性与高一维退相干资源态的混合态相之间的对应关系。 受物质混合态相最新发展的启发，这促使我们提出了一个容错性的诊断工具，我们称之为时空马尔可夫长度。 这是一个由时空重复的 syndromes 测量结果的经典条件互信息衰减决定的长度尺度。 该诊断方法独立于解码器，其发散标志着容错性的内在失效。 作为副产品，我们发现退相干可能有助于揭示由非相干和相干扰动共同驱动的高阶形式对称保护拓扑相之间的转变。 显示英文摘要

摘要： We establish a correspondence between the fault-tolerance of local stabilizer codes experiencing measurement and physical errors and the mixed-state phases of decohered resource states in one higher dimension. Drawing from recent developments in mixed-state phases of matter, this motivates a diagnostic of fault-tolerance, which we refer to as the spacetime Markov length. This is a length scale determined by the decay of the (classical) conditional mutual information of repeated syndrome measurement outcomes in spacetime. The diagnostic is independent of the decoder, and its divergence signals the intrinsic breakdown of fault tolerance. As a byproduct, we find that decoherence may be useful for exposing transitions from higher-form symmetry-protected topological phases driven by both incoherent and coherent perturbations.