多体量子系统中2类特殊图的可分性  

Separability of Two Classes of Special Graphs in Multipartite Quantum Systems

作　　者：赵慧[1] 赵静云 ZHAO Hui ,ZHAO Jingyun(College of Applied Sciences,Beijing University of Technology,Beijing 100124, Chin)

机构地区：[1]北京工业大学应用数理学院,北京100124

出　　处：《北京工业大学学报》2018年第8期1152-1156,共5页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(11101017);北京市青年拔尖人才培育计划资助项目(CITTCD201404067)

摘　　要：为了研究2类特殊密度矩阵的可分判据,通过研究2类特殊图的性质,给出了多体量子系统中这2类图的可分判据.首先,推广了并图在多体量子系统中的概念,给出了在多体系统中图顶点的分层方式.利用并图的概念、图顶点的分层、拉普拉斯矩阵的性质,证明了简单图的并图在多体量子系统下是可分的.其次,通过部分对称图的概念和图顶点分层的方式构造了一类新图.结合图的性质和图的分层,分析了新图及其拉普拉斯矩阵的性质,证明了新图在多体量子系统下代表可分态.Quantum entanglement is one of the most fascinating features of quantum theory and has numerous applications in quantum information processing and communication. Many unsolved problems in classical information theory can be solved by bipartite entanglement and multipartite entanglement. In this paper,the separable criterion of classes of density matrices was studied. The separable criterion of two classes of graphs was presented by studying two classes of special graphs in multipartite systems. Firstly, the concept of union graph was generalized. The separability of union graphs of simple graph in multipartite quantum systems was proven by the method of graph 爷 s layer and the property of Laplacian matrices. Secondly,a class of graph was constructed by the concept of partially symmetric and graph 爷 s layer. Combining the properties of graph and graph＇s layer ,this class of graph and the properties of the relevant Laplacian matrices were analyzed. The research shows that the classes of graph represent a separable state in multipartite quantum systems.

关 键 词：并图 拉普拉斯矩阵 可分性 

分 类 号：O413[理学—理论物理]