Rényi mutual information in quantum field theory, tensor networks, and gravity
Jonah Kudler-Flam (School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, 08540, USA, Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey, 08540, USA); Laimei Nie (Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801, USA, Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, 47906, USA); Akash Vijay (Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801, USA)
We explore a large class of correlation measures called the α − z Rényi mutual informations (RMIs). Unlike the commonly used notion of RMI involving linear combinations of Rényi entropies, the α − z RMIs are positive semi-definite and monotonically decreasing under local quantum operations, making them sensible measures of total (quantum and classical) correlations. This follows from their descendance from Rényi relative entropies. In addition to upper bounding connected correlation functions between subsystems, we prove the much stronger statement that for certain values of α and z, the α − z RMIs also lower bound certain connected correlation functions. We develop an easily implementable replica trick which enables us to compute the α − z RMIs in a variety of many-body systems including conformal field theories, free fermions, random tensor networks, and holography.
