  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.
