基于协方差矩阵的量子网络关联  

Quantum Correlation of Quantum Networks Based on Their Covariance Matrices

作　　者：赵怡 郭志华[1] 曹怀信[1] Yi ZHAO;Zhi Hua GUO;Huai Xin CAO(School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,P.R.China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119

出　　处：《数学学报（中文版）》2024年第4期756-780,共25页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12271325,11871318);陕西省高层次人才特支计划项目(1503070117)。

摘　　要：量子网络的特性是由网络的拓扑结构和节点之间共享的量子态所决定的.本文基于有向无环图,建立了量子网络的数学框架,给出了量子网络基于概率张量的协方差矩阵的构造方法,并得到了协方差矩阵的相关性质.进一步构造了量子网络关于量子测量的协方差矩阵,通过定义协方差矩阵的分块相干度量,得到了量子网络的关联度量,证明了量子网络关联度为0当且仅当网络共享态皆为乘积态.The characteristics of a quantum network are determined by the topology of the network and quantum states shared between nodes.In this paper,we establish a mathematical framework for quantum networks based on directed acyclic graphs.We provide a method for constructing the covariance matrix of a quantum network based on probability tensors,and obtain relevant properties of the covariance matrix.We further constructed a covariance matrix of a quantum network with respect to some quantum measurement.By defining a block coherence measure of the covariance matrix,we obtain a correlation measure of quantum networks.We proved that quantum correlation of quantum networks is 0 if and only if all shared states of the network are product states.

关 键 词：量子网络 量子测量 协方差矩阵 量子关联 

分 类 号：O177.92[理学—数学]