R\'enyi Mutual Information in Quantum Field Theory
Abstract
We study a proper definition of R\'enyi mutual information (RMI) in quantum field theory as defined via the Petz R\'enyi relative entropy. Unlike the standard definition, the RMI we compute is a genuine measure of correlations between subsystems, as evidenced by its non-negativity and monotonicity under local operations. Furthermore, the RMI is UV finite and well-defined in the continuum limit. We develop a replica path integral approach for the RMI in quantum field theories and evaluate it explicitly in 1+1D conformal field theory using twist fields. We prove that it bounds connected correlation functions and check our results against exact numerics in the massless free fermion theory.
Keywords
Cite
@article{arxiv.2211.01392,
title = {R\'enyi Mutual Information in Quantum Field Theory},
author = {Jonah Kudler-Flam},
journal= {arXiv preprint arXiv:2211.01392},
year = {2023}
}
Comments
4 pages; v2: typos corrected, minor improvement to correlation bound