Inequalities witnessing coherence, nonlocality, and contextuality

Quantum coherence, nonlocality, and contextuality are key resources for quantum advantage in metrology, communication, and computation. We introduce a graph-based approach to derive classicality inequalities that bound local, noncontextual, and coherence-free models, offering a unified description of these seemingly disparate quantum resources. Our approach generalizes recently proposed basis-independent coherence witnesses, and it recovers all noncontextuality inequalities of the exclusivity graph approach. Moreover, violations of certain classicality inequalities witness preparation contextuality. We describe an algorithm to find all such classicality inequalities, and we use it to analyze some of the simplest scenarios.