1304.5935 (Koenraad M. R. Audenaert)

Quantum Skew Divergence: Theory and Applications    [PDF]

Koenraad M. R. Audenaert

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 also introduce the differential skew divergence, which is a closely related concept with the benefit of an additional symmetry. We provide an in-depth study of both the quantum skew divergence and differential skew divergence, including their 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 (which has been proven by Van Acoleyen).

View original: http://arxiv.org/abs/1304.5935