R\'enyi Mutual Information in Quantum Field Theory

TL;DR

This paper introduces a well-defined, UV-finite Rényi mutual information in quantum field theory, developed via a replica path integral approach, and evaluates it explicitly in 1+1D conformal field theories, confirming its properties and bounds.

Contribution

It defines a genuine, UV-finite Rényi mutual information in quantum field theory using the Petz relative entropy and develops a replica path integral method for its computation.

Findings

RMI is non-negative and monotonic under local operations.

Explicit RMI calculations in 1+1D CFT using twist fields.

Numerical checks in free fermion theory confirm theoretical results.

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.