von Neumann measurement-related matrices and the nullity condition for quantum correlation
Ming-Jing Zhao, Teng Ma, Ting-Gui Zhang, and Shao-Ming Fei
TL;DR
This paper explores the properties of matrices related to von Neumann measurements and establishes necessary conditions for the nullity of quantum correlations, with an application to Bell diagonal states.
Contribution
It introduces specific properties of measurement-related matrices and links them to conditions for quantum correlation nullity in bipartite systems.
Findings
Matrices are idempotent with rank m-1
Necessary conditions for quantum correlation nullity
Application to Bell diagonal states
Abstract
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.
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