QLunch: Michael Jabbour

Speaker: Michael Jabbour from DTU

Title: From Classical to Quantum: Uniform Continuity bounds on entropies in Infinite Dimensions

Abstract: We prove a variety of improved uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate on the Shannon entropy of random variables with a countably infinite alphabet. The proof relies on a new mean-constrained Fano-type inequality. We then employ this classical result to derive a tight energy-constrained continuity bound for the von Neumann entropy. To deal with more general entropies in infinite dimensions, e.g. Rényi and Tsallis entropies, we develop a novel approximation scheme based on operator Hölder continuity estimates.