On the Non-robustness of Essentially Conditional Information Inequalities

TL;DR

This paper demonstrates that certain essential conditional entropy inequalities, including Zhang-Yeung's, are not robust for asymptotically entropic points, questioning their practical applicability and interpretability.

Contribution

It proves the non-robustness of key conditional entropy inequalities, challenging their assumed validity in information theory applications.

Findings

Conditional inequalities do not hold asymptotically

These inequalities are non-robust in a strong sense

Raises questions about their practical use

Abstract

We show that two essentially conditional linear inequalities for Shannon's entropies (including the Zhang-Yeung'97 conditional inequality) do not hold for asymptotically entropic points. This means that these inequalities are non-robust in a very strong sense. This result raises the question of the meaning of these inequalities and the validity of their use in practice-oriented applications.