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A separation between divergence and Holevo information for ensembles

Published online by Cambridge University Press:  27 October 2010

RAHUL JAIN ,
ASHWIN NAYAK  and
YI SU
RAHUL JAIN
Affiliation:
Centre for Quantum Technologies, and Department of Computer Science, National University of Singapore, Block S15, 3 Science Drive 2, Singapore 11754 Email: rahul@comp.nus.edu.sg
ASHWIN NAYAK
Affiliation:
Department of Combinatorics and Optimization, and Institute for Quantum Computing, University of Waterloo, and Perimeter Institute for Theoretical Physics., 200 University Ave. W., Waterloo, ON N2L 3G1, Canada Email: ashwin.nayak@uwaterloo.ca
YI SU
Affiliation:
Department of Mathematics, University of Michigan, 2074 East Hall, 530 Church Street, Ann Arbor, MI 48109-1043, U.S.A. Email: yisu@umich.edu
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Abstract

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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.

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