标题： 随机张量网络中的反射熵 III：三向切割 显示英文标题

标题： Reflected entropy in random tensor networks III: triway cuts

摘要： 对于大键维数下的一般随机张量网络态，我们证明了整数Rényi反射熵（在相变之外）由通过网络的最小三向切割决定。 这推广了这些态的双部分纠缠的最小切割描述。 一个自然的外推远离整数Rényi参数，由三向切割问题提出，意味着全息假设$S_R=2EW$，其中$S_R$是反射熵，$EW$是纠缠楔形截面。 最小三向切割可以表述为整数规划，无法放松以找到对偶的最大流/位线描述。 这揭示了全息态中三重纠缠的存在与由位线推动的双部分纠缠结构之间的差距。 特别是，我们证明了衡量三重纠缠的马尔可夫间隙由计算三向切割的整数规划的整数间隙下限。 显示英文摘要

摘要： For general random tensor network states at large bond dimension, we prove that the integer R\'enyi reflected entropies (away from phase transitions) are determined by minimal triway cuts through the network. This generalizes the minimal cut description of bipartite entanglement for these states. A natural extrapolation away from integer R\'enyi parameters, suggested by the triway cut problem, implies the holographic conjecture $S_R=2EW$, where $S_R$ is the reflected entropy and $EW$ is the entanglement wedge cross-section. Minimal triway cuts can be formulated as integer programs which cannot be relaxed to find a dual maximal flow/bit-thread description. This sheds light on the gap between the existence of tripartite entanglement in holographic states and the bipartite entanglement structure motivated by bit-threads. In particular, we prove that the Markov gap that measures tripartite entanglement is lower bounded by the integrality gap of the integer program that computes the triway cut.