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

Ming-Jing Zhao, Teng Ma, Ting-Gui Zhang, and Shao-Ming Fei

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Submission date: 04. Jan. 2017
Pages: 13
published in: Science in China : physics, mechanics and astronomy, 59 (2016) 12, art-no. 120313 
DOI number (of the published article): 10.1007/s11433-016-0356-2
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Abstract:
We study the von Neumann measurement on an m-dimensional quantum system. The properties of the matrices related to von Neumann measurement are investigated. It is shown that such (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.