On the non-robustness of essentially conditional information inequalities
On the non-robustness of essentially conditional information inequalities
Tarik Kaced,Andrei E. Romashchenko
TLDR
It is shown that two essentially conditional linear inequalities for Shannon's entropies (including the Zhang-Yeung'97 conditional inequality) do not hold for asymptotically entropic points, and these inequalities are non-robust in a very strong sense.
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.