Anomalous non-classicality via correlative and entropic Bell inequalities

TL;DR

This paper explores a unique anomaly where entropic Bell inequalities are violated without violating correlative Bell inequalities, revealing nuanced non-classical resources and their bounds for experimental testing.

Contribution

It identifies and characterizes an anomaly between entropic and correlative Bell inequalities, defining a new type of non-classical resource with potential for device-independent applications.

Findings

Violation of entropic Bell inequalities without correlative Bell violation

Numerical bounds for the anomaly established

Identification of an 'exotic' permutation of observables

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.