Proper Measures of Correlations: The Case for Rényi Mutual Informations*

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   • The quantum mutual information between two spatial subregions is known to be a good measure of total correlations between the degrees of freedom contained in those subregions. This is because it is strictly non-negative and monotonically decreasing under local operations acting on either subregion. For this reason, it has played a central role in characterizing equilibrium and non-equilibrium phenomena in many-body physics. Frequently in these contexts, to obtain additional correlation data, one computes Rényi counterparts of the quantum mutual information, defined simply as a linear combination of Rényi entropies. These are however not genuine correlation measures since they're neither non-negative, nor monotonic under local operations and thus carry no real operational meaning. Here we consider properly defined 2-parameter Rényi generalizations of the quantum mutual information. We show that these measures are computable via a novel replica trick and we use this to derive a number of universal results in 2D CFTs. We also compute these measures in Haar random tensor networks, explicitly deriving the associated Page curve. Finally we end with a discussion on the prospect of measuring these new Rényi mutual informations in quantum simulator experiments.