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arXiv · 2610.19286

Mutual Information of Measurement in Conformal Field Theories

Israel Klich·Ravisankar Rajagopal·Diana Vaman
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Abstract

The mutual information of measurement of a local operator between two spatial regions characterizes the reduction in the uncertainty of measurement outcomes in one region given the outcome in the other. We study the Rényi-Shannon mutual information of measurement in conformal field theories (CFTs). Explicit calculations for scalar primaries and descendants in large $N$ CFTs are performed in the two extreme limits of the intervals being adjacent or largely separated. The results depend on only the cross ratio and the scaling dimension $Δ$ of the operator being measured, with striking similarities to the mutual information of entanglement. We find a surprising quadratic dependence as $(Δ-1/2)^2$ for adjacent intervals. This dependence superficially seems to violate the information processing inequality, which we discuss and resolve. We also offer a holographic interpretation of the mutual information of measurement.

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Israel Klich, Ravisankar Rajagopal, Diana Vaman. 2026-10-13. Mutual Information of Measurement in Conformal Field Theories. https://arxiv.org/abs/2610.19286

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