This is an elaboration of the "extra" advantage of the performance of quantized physical systems over classical ones, both in terms of single outcomes as well as probabilistic predictions. From a formal point of view, it is based on entities related to (dual) vectors in (dual) Hilbert spaces, as compared to the Boolean algebra of subsets of a set and the additive measures they support.
Keywords: Kochen-Specker theorem; bell inequality; correlation polytope; klyachko inequality; pitowsky principle of indeterminacy.