A holographic realization of correlation and mutual information

TL;DR

This paper explores the relationship between mutual information and correlation functions in holographic systems using gauge/gravity duality, revealing non-trivial insights into their behavior at different separation lengths.

Contribution

It provides a holographic analysis of the inequality between mutual information and correlation functions, highlighting the dependence on the method of calculating thermal correlators and identifying points where correlations vanish.

Findings

Mutual information bounds correlation functions in holographic models.

Correlation vanishes at specific separation lengths depending on the calculation method.

The study offers new insights into quantum and classical correlations in holographic systems.

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 $sT|_I>sT|_c$.