Proposed experiment to exclude higher-than-quantum violations of the Bell inequality

Abstract

We show that a recent observation by Yan leads to a method to experimentally test whether a higher-than-quantum violation of the Clauser-Horne-Shimony-Holt Bell inequality is possible (assuming that the sum of probabilities of pairwise exclusive propositions cannot exceed 1). The test requires reaching the maximum quantum violation of a noncontextuality inequality involving sequences of three compatible measurements on a five-dimensional quantum system.