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.

Figure 1

Values of the classical correlation $\kappa$ obeying the TGS additivity condition as a function of classical probability $p$ at various $q$ values with decoherence values (a) $\mid z\mid =0$ (TGS model) and (b) $\mid z\mid =0.2$. Note that for $\mid z\mid >0$, the additivity condition has solutions only for restricted ranges of $p$ and $q$.

Figure 2

Regions of solutions obeying the TGS additivity condition at $q=0.5$ as a function of classical probability $p$ and decoherence $z$ showing (a) classical correlation $\kappa$ and (b) concurrence $C(A,B)$.

Figure 3

Regions of solutions obeying the TGS additivity condition at $q=0.7$ as a function of classical probability $p$ and decoherence $z$ showing (a) classical correlation $\kappa$ and (b) concurrence $C(A,B)$.