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The Kochen-Specker theorem demonstrates that it is not possible to reproducethe predictions of quantum theory in terms of a hidden variable model where thehidden variables assign a value to every projector deterministically andnoncontextually. A noncontextual value-assignment to a projector is one thatdoes not depend on which other projectors - the context - are measured togetherwith it. Using a generalization of the notion of noncontextuality that appliesto both measurements and preparations, we propose a scheme for derivinginequalities that test whether a given set of experimental statistics isconsistent with a noncontextual model. Unlike previous inequalities inspired bythe Kochen-Specker theorem, we do not assume that the value-assignments aredeterministic and therefore in the face of a violation of our inequality, thepossibility of salvaging noncontextuality by abandoning determinism is nolonger an option. Our approach is operational in the sense that it does notpresume quantum theory: a violation of our inequality implies the impossibilityof a noncontextual model for any operational theory that can account for theexperimental observations, including any successor to quantum theory.

From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism