Preprint 15/2022

No eleventh conditional Ingleton inequality

Tobias Boege

Contact the author: Please use for correspondence this email.
Submission date: 11. Apr. 2022
Link to arXiv: See the arXiv entry of this preprint.

A rational probability distribution on four binary random variables X,Y,Z,U is constructed which satisfies the conditional independence relations [X Y ], [X ZU], [Y UZ] and [Z UXY ] but whose entropy vector violates the Ingleton inequality. This settles a recent question of Studený (IEEE Trans. Inf. Theory vol. 67, no. 11) and shows that there are, up to symmetry, precisely ten inclusion-minimal sets of conditional independence assumptions on four discrete random variables which make the Ingleton inequality hold.

18.05.2022, 02:22