Quantum Skew Divergence

Abstract: In this paper we study the quantum generalisation of the skew divergence, which is a dissimilarity measure between distributions introduced by L. Lee in the context of natural language processing. We provide an in-depth study of the quantum skew divergence, including its relation to other state distinguishability measures. Finally, we present a number of important applications: new continuity inequalities for the quantum Jensen-Shannon divergence and the Holevo information, and a new and short proof of Bravyi's Small Incremental Mixing conjecture.