An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson’s bound for the nonlocal correlations. Considering multiple-slit experiments—not only the traditional configuration with two slits, but also configurations with three and more slits—Sorkin detected that third-order (and higher-order) interference is not possible in quantum mechanics. The EPR experiments show that quantum mechanics involves nonlocal correlations which are demonstrated in a violation of the Bell or CHSH inequality, but (...) are still limited by a bound discovered by Tsirelson. It now turns out that Tsirelson’s bound holds in a broad class of probabilistic theories provided that they rule out third-order interference. A major characteristic of this class is the existence of a reasonable calculus of conditional probability or, phrased more physically, of a reasonable model for the quantum measurement process. (shrink)