Non-linear information inequalities
Summary: We construct non-linear information inequalities from Matúš's infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they are the first non-trivial examples of non-linear information inequalities.
scientific article; zbMATH DE number 5664147