Rényi Mutual Information in Quantum Field Theory.

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.

Citation

Jonah Kudler-Flam. Rényi Mutual Information in Quantum Field Theory. Physical review letters. 2023 Jan 13;130(2):021603

PMID: 36706421

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