A separation between divergence and Holevo information for ensembles

Abstract

The notion of divergence information of an ensemble of probability distributions was introduced by Jain, Radhakrishnan and Sen in Jain et al. (2002; 2009) in the context of the substate theorem. Since then, divergence has been recognised as a more natural measure of information in several situations in both quantum and classical communication. We construct ensembles of probability distributions for which divergence information may be significantly smaller than the more standard Holevo information. As a result, we establish that bounds previously shown for Holevo information are weaker than similar ones shown for divergence information. © 2010 Cambridge University Press.