Classical statistics inherent in a quantum density matrix

A density-matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical underpinning of these correlations. As a by-product of this analysis, a physical basis of the classical statistical correlations leading to additive entropy in a bipartite system discussed recently by Tsallis emerges as inherent classical spin fluctuations. It is found that in this example, the quantum correlations shrink the region of additivity in phase space.