Rényi Mutual Information in Quantum Field Theory

Abstract

We study a proper definition of Rényi mutual information (RMI) in quantum field theory as defined via the Petz Rényi 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.

4 pages; v2: typos corrected, minor improvement to correlation bound

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• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
• Proof of Renyi QNEC for free fermions
• Rényi mutual information in quantum field theory, tensor networks, and gravity
• Extensive Long-Range Entanglement at Finite Temperatures from a Nonequilibrium Bias
• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states