Entropic inequalities as a necessary and sufficient condition to noncontextuality and locality

Understand

The assumption of local realism in a Bell locality scenario imposes non-trivial conditions on the Shannon entropies of the associated probability distributions, expressed by linear entropic Bell inequalities.

• In principle, these entropic inequalities provide necessary but not sufficient criteria for the existence of a local hidden variable model reproducing the correlations, as, for example, the paradigmatic nonlocal PR-box is entropically not different from a classically correlated box.
• In this paper we show that for the n-cycle scenario, entropic inequalities completely characterize the set of local correlations.
• In particular, every nonsignalling box which violates the CHSH inequality -- including the PR-box -- can be locally modified so that it also violates the entropic version of CHSH inequality.