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The discussion on noncontextual hidden variable models as an underlying description for the quantum-mechanical predictions started in ernest with 1967 paper by Kochen and Specker. There, it was shown that no noncontextual hidden-variable model can give these predictions. The proof used in that paper is complicated, but recently, a paper by Yu and Oh [PRL, 2012] proposes a simpler statistical proof that can also be the basis of an experimental test. Here we report on a sharper version of that statistical proof, and also explain why the algebraic upper bound to the expressions used are not reachable, even with a reasonable contextual hidden variable model. Specifically, we show that the quantum mechanical predictions reach the maximal possible value for a contextual model that keeps the expectation value of the measurement outcomes constant. [ABSTRACT FROM AUTHOR]

The question of whether noncontextual hidden variable models can give the quantum-mechanical predictions has been under discussion for a long time. The question originates in the sixties, perhaps best known from the 1967 paper by Kochen and Specker where it was shown that no noncontextual hidden-variable model can give these predictions. Recently, the question has gained interest from experimentalists trying to test this in the laboratory. The experimental setups in question have used a sequential setup rather than the alternative, joint (simultaneous) measurement. There has been discussion in the community whether this is appropriate. This brief paper argues that sequential measurement is not only the correct choice, but the best possible. [ABSTRACT FROM AUTHOR]