Mutual Information of Measurement in Conformal Field Theories

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 $\Delta$ of the operator being measured, with striking similarities to the mutual information of entanglement. We find a surprising quadratic dependence as $(\Delta-1/2)^2$ 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.

High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2610.19286 [hep-th]

(or arXiv:2610.19286v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2610.19286 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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