von Neumann measurement-related matrices and the nullity condition for quantum correlation  

作　　者：MingJing Zhao Teng Ma TingGui Zhang Shao-Ming Fei 

机构地区：[1]School of Science,Beijing Information Science and Technology University,Beijing 100192,China [2]State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics,Tsinghua University,Beijing 100084,China [3]School of Mathematics and Statistics,Hainan Normal University,Haikou 571158,China [4]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China [5]Max-Planck-Institute for Mathematics in the Sciences,Leipzig 04103,Germany

出　　处：《Science China(Physics,Mechanics & Astronomy)》2016年第12期27-32,共6页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11401032,11501153,11275131,and 11675113);the Natural Science Foundation of Hainan Province(Grant No.20161006)

摘　　要：We study von Neumann measurement-related matrices, and the nullity condition of quantum correlation. We investigate the properties of these matrices that are related to a von Neumann measurement. It is shown that these(m^2-1)×(m^2-1) matrices are idempotent, and have rank m-1. These properties give rise to necessary conditions for the nullity of quantum correlations in bipartite systems. Finally, as an example we discuss quantum correlation in Bell diagonal states.We study von Neumann measurement-related matrices, and the nullity condition of quantum correlation. We investigate the prop- erties of these matrices that are related to avon Neumann measurement. It is shown that these （m2 - 1） × （m2 - 1） matrices are idempotent, and have rank m - 1. These properties give rise to necessary conditions for the nullity of quantum correlations in bipartite systems. Finally, as an example we discuss quantum correlation in Bell diagonal states.

关 键 词：von Neumann measurement matrix RANK quantum correlation 

分 类 号：O151.21[理学—数学] O413[理学—基础数学]