Anomalous non-classicality via correlative and entropic Bell inequalities

Abstract: Entropic Bell inequalities witness contextual probability distributions on sets of jointly measurable observables. We find that their violation does not entail a violation of the correlative Bell inequality for certain parameter values. This anomaly between the entropic and correlative measures of contextuality helps to precisely qualify the type of non-classical resource. We determine its numerical bounds inviting their experimental verification. Among the permutations of observables that keep this anomaly in place, we identify the 'exotic' type that gives rise to non-classical resources under all non-equivalent operational party assignments in a device-independent approach.