论文标题
矩阵产品状态和量子条件互信息的衰减
Matrix product states and the decay of quantum conditional mutual information
论文作者
论文摘要
在三方旋转系统上定义的统一矩阵产品状态，用$ abc表示，当子系统的大小$ b，$表示$ | b |，$，$足够大时，$显示为近似量子马尔可夫链。研究了量子条件共同信息（QCMI），并证明是由与$ \ exp（-q（| b | -k）+2k \ ln | b |）$成正比的函数界定的，并带有$ q $和$ q $和$ k $ COMPUTABLE常数。边界函数的属性由一种新方法得出，其渐近衰变率$ q $给出了相应的改进值。我们显示了最佳的$ Q $的改进值。据报道，QCMI衰减的数值研究是针对通过选择有关HAAR测量的定义等距生成的基质产物状态的集合的。
A uniform matrix product state defined on a tripartite system of spins, denoted by $ABC,$ is shown to be an approximate quantum Markov chain when the size of subsystem $B,$ denoted $|B|,$ is large enough. The quantum conditional mutual information (QCMI) is investigated and proved to be bounded by a function proportional to $\exp(-q(|B|-K)+2K\ln|B|)$, with $q$ and $K$ computable constants. The properties of the bounding function are derived by a new approach, with a corresponding improved value given for its asymptotic decay rate $q$. We show the improved value of $q$ to be optimal. Numerical investigations of the decay of QCMI are reported for a collection of matrix product states generated by selecting the defining isometry with respect to Haar measure.
