A separation between divergence and Holevo information for ensembles

Authors:
Rahul Jain;Ashwin Nayak;Yi Su
Affiliations:
School of Computer Science and Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada;Department of Combinatorics and Optimization and Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada and Perimeter Institute;Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada
Venue:
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Year:
2008

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Abstract

The notion of divergence information of an ensemble of probability distributions was introduced by Jain, Radhakrishnan, and Sen [1,2] in the context of the "substate theorem". Since then, divergence has been recognized as a more natural measure of information in several situations in 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 lower bounds previously shown for Holevo information are weaker than similar ones shown for divergence information.