A holographic realization of correlation and mutual information

Ashis Saha; Anirban Roy Chowdhury; Sunandan Gangopadhyay

doi:10.1016/j.physletb.2025.139933

paper

A holographic realization of correlation and mutual information

arXiv:2501.07091 · doi:10.1016/j.physletb.2025.139933

Abstract

The status of the inequality existing between mutual information and (normalized) thermal two-point connected correlation function, namely, $I(A:B)\ge\frac{(\expval{\mathcal{O}_{A}\mathcal{O}_{B}}_β-\expval{\mathcal{O}_{A}}_β\expval{\mathcal{O}_{B}}_β)^2}{2\expval{\mathcal{O}_{A}^2}_β\expval{\mathcal{O}_{B}^2}_β}$ has been explicitly probed by using the gauge/gravity correspondence. In the holographic analysis, the geodesic approximation for heavy operators ( $Δ \sim m R$ ) has been used. We observe that the study leads to some non-trivial insights depending upon the method of calculating the thermal object $\expval{\mathcal{O}^2}_β$. For a particular computed result of $\expval{\mathcal{O}^2}_β$ 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, $s T ∣ c$ and $s T ∣_{I}$ where $s T ∣_{I} > s T ∣_{c}$ .

v1: 7 pages LaTex and 2 figures; v2: Substantial modifications have been made. 12 pages LaTex and 2 figures

A holographic realization of correlation and mutual information

Abstract

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