Mutual Information of Measurement in Conformal Field Theories

@misc{klich2026mutual,
  title = {{Mutual Information of Measurement in Conformal Field Theories}},
  author = {Israel Klich and Ravisankar Rajagopal and Diana Vaman},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19286},
  eprint = {2610.19286},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19286},
}

TY  - UNPB
TI  - Mutual Information of Measurement in Conformal Field Theories
AU  - Israel Klich
AU  - Ravisankar Rajagopal
AU  - Diana Vaman
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19286
UR  - https://arxiv.org/abs/2610.19286
AB  - 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.
ER  -