Interference in quantum correlations

We show that the expectation values of operators of multiparticle systems consist of two contributions: (1) one that solely involves probabilities and (2) one arising from interference. We demonstrate that a nonvanishing interference contribution is necessary to either surpass classical bounds, such as the Clauser-Horne-Shimony-Holt border, or create contradictions to classical predictions, as in the Greenberger-Horne-Zeilinger scenario.