We study the relative entropy of highly excited quantum states. First, we sample states from Wishart ensemble and develop a large-$N$ diagrammatic technique for entropy. The solution is exactly expressed in terms elementary functions. compare analytic results to small-$N$ numerics, finding precise agreement. Furthermore, random matrix theory accurately match behavior chaotic many-body eigenstat...

Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, the...