Rényi Mutual Information in Quantum Field Theory
Jonah Kudler-Flam
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.
Topics & Concepts
Mutual informationQuantum field theoryMassless particleConformal field theoryPath integral formulationTwistPhysicsFree fieldMonotonic functionEntropy (arrow of time)Field theory (psychology)QuantumMathematicsQuantum mechanicsMathematical physicsConformal mapMathematical analysisStatisticsGeometryBlack Holes and Theoretical PhysicsQuantum many-body systemsCosmology and Gravitation Theories