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The notion of divergence information of an ensemble of probabilitydistributions was introduced by Jain, Radhakrishnan, and Sen in the context ofthe ``substate theorem''. Since then, divergence has been recognized as a morenatural measure of information in several situations in quantum and classicalcommunication. We construct ensembles of probability distributions for whichdivergence information may be significantly smaller than the more standardHolevo information. As a result, we establish that lower bounds previouslyshown for Holevo information are weaker than similar ones shown for divergenceinformation.

A Separation between Divergence and Holevo Information for Ensembles