  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.
