A Separation between Divergence and Holevo Information for Ensembles

TL;DR

This paper demonstrates that divergence information can be substantially smaller than Holevo information in certain ensembles, revealing a fundamental separation with implications for quantum communication bounds.

Contribution

The authors construct ensembles where divergence information is significantly less than Holevo information, highlighting a fundamental difference between these measures.

Findings

Divergence can be much smaller than Holevo information in specific ensembles.

Lower bounds for Holevo information are weaker than those for divergence information.

Establishes a separation between divergence and Holevo information measures.

Abstract

The notion of divergence information of an ensemble of probability distributions was introduced by Jain, Radhakrishnan, and Sen 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.