随机图状态、极大流和Fuss-Catalan分布
Random graph states, maximal flow and Fuss-Catalan distributions
摘要：
对于任何由$k$顶点和$m$边组成的图，我们构造了一个描述由$2m$子系统组成的系统的随机纯量子态系综。图的每条边代表一个二分的最大纠缠态。每个顶点表示根据Haar测度生成的随机酉矩阵，其描述子系统之间的耦合。把所有的子系统分成两部分，我们可以研究关于这个划分的纠缠。本文给出了一种推导随机纯态平均纠缠熵的一般方法。我们的技术依赖于Weingarten演算和流动问题。我们分析了这种随机密度矩阵的频谱的统计特性，并显示在何种情况下，他们所描述的自由泊松（马琴科-帕斯图）分布。我们推导出一个离散的家庭的广义，Fuss-Catalan分布和明确构建的图形，导致合奏的随机状态特征在于这些新的分布的特征值。
英文摘要：
For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state. Each vertex represents a random unitary matrix generated according to the Haar measure, which describes the coupling between subsystems. Dividing all subsystems into two parts, one may study entanglement with respect to this partition. A general technique to derive an expression for the average entanglement entropy of random pure states associated to a given graph is presented. Our technique relies on Weingarten calculus and flow problems. We analyze statistical properties of spectra of such random density matrices and show for which cases they are described by the free Poissonian (Marchenko-Pastur) distribution. We derive a discrete family of generalized, Fuss-Catalan distributions and explicitly construct graphs which lead to ensembles of random states characterized by these novel distributions of eigenvalues.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
