Exhibition of Monogamy Relations between Entropic Non-contextuality Inequalities

We exhibit the monogamy relation between two entropic non-contextuality inequalities in the scenario where compatible projectors are orthogonal. We show the monogamy relation can be exhibited by decomposing the orthogonality graph into perfect induced subgraphs. Then we find two entropic non-contextuality inequalities are monogamous while the KCBS-type non-contextuality inequalities are not if the orthogonality graphs of the observable sets are two odd cycles with two shared vertices.

We exhibit the monogamy relation between two entropic non-contextuality inequalities in the scenario where compatible projectors are orthogonal. We show the monogamy relation can be exhibited by decomposing the orthogo- nality graph into perfect induced subgraphs. Then we find two entropic non-contextuality inequalities are monogamous while the KCBS-type non-contextuality inequalities are not i~ the orthogonality graphs of the observable sets are two odd cycles with two shared vertices.