A holographic realization of correlation and mutual information

Abstract

The status of the inequality existing between mutual information and (normalized) thermal two-point connected correlation function, namely, $I(A:B)\ge\frac{(\expval{\mathcal{O}_{A}\mathcal{O}_{B}}_{\beta}-\expval{\mathcal{O}_{A}}_{\beta}\expval{\mathcal{O}_{B}}_{\beta})^2}{2\expval{\mathcal{O}_{A}^2}_{\beta}\expval{\mathcal{O}_{B}^2}_{\beta}}$ has been explicitly probed by using the gauge/gravity correspondence. In the holographic analysis, the geodesic approximation for heavy operators ($\Delta\sim mR$) has been used. We observe that the study leads to some non-trivial insights depending upon the method of calculating the thermal object $\expval{\mathcal{O}^2}_{\beta}$. For a particular computed result of $\expval{\mathcal{O}^2}_{\beta}$ we propose that all of the existing quantum mechanical dependencies (correlations) and classical correlations between the subsystems $A$ and $B$ vanishes at two different separation lengths, namely, $sT|c$ and $sT|_I$ where $sT|_I>sT|_c$.