标题： 量子信道中的瓶颈和物质的有限温度相 显示英文标题

标题： Bottlenecks in quantum channels and finite temperature phases of matter

摘要： 我们证明了“瓶颈定理”的类比，该定理在经典马尔可夫链中是众所周知的，适用于马尔可夫量子信道。 特别是，我们表明如果希尔伯特空间的两个区域（子空间）被一个在信道稳态中权重非常低的区域分隔，则在这一屏障一侧初始化的状态将需要很长时间才能放松，从而根据适当定义的“量子瓶颈比”对混合时间给出了下限。 重要的是，这个瓶颈比不仅涉及相关子空间的概率，还涉及它们之间的非对角矩阵元的大小。 对于低温量子多体系统，我们利用瓶颈定理来限制任何准局部吉布斯采样器的性能。 这导致了一种新的视角，即从吉布斯态分解为由瓶颈分隔的多个成分的角度来看热稳定的量子相。 作为一个具体的应用，我们严格证明了具有广义能量屏障的弱扰动交换投影模型（包括某些经典和量子扩展码）具有指数级大的混合时间。 显示英文摘要

摘要： We prove an analogue of the "bottleneck theorem", well-known for classical Markov chains, for Markovian quantum channels. In particular, we show that if two regions (subspaces) of Hilbert space are separated by a region that has very low weight in the channel's steady state, then states initialized on one side of this barrier will take a long time to relax, putting a lower bound on the mixing time in terms of an appropriately defined "quantum bottleneck ratio". Importantly, this bottleneck ratio involves not only the probabilities of the relevant subspaces, but also the size of off-diagonal matrix elements between them. For low-temperature quantum many-body systems, we use the bottleneck theorem to bound the performance of any quasi-local Gibbs sampler. This leads to a new perspective on thermally stable quantum phases in terms of a decomposition of the Gibbs state into multiple components separated by bottlenecks. As a concrete application, we show rigorously that weakly perturbed commuting projector models with extensive energy barriers (including certain classical and quantum expander codes) have exponentially large mixing times.