  Entanglement is a uniquely quantum resource giving rise to many quantum
technologies. It is therefore important to detect and characterize entangled
states, but this is known to be a challenging task, especially for multipartite
mixed states. The correlation minor norm (CMN) was recently suggested as a
bipartite entanglement detector employing bounds on the quantum correlation
matrix. In this paper we explore generalizations of the CMN to multipartite
systems based on matricizations of the correlation tensor. It is shown that the
CMN is able to detect and differentiate classes of multipartite entangled
states. We further analyze the correlations within the reduced density matrices
and show their significance for entanglement detection. Finally, we employ
matricizations of the correlation tensor for introducing a measure of global
quantum discord.
