I will argue that the Peres-Mermin square does not necessarily rule out a value-definite noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements: each operator is uniquely realized by a single physical measurement; commuting operators are realized by simultaneous measurements. To underpin this claim, I will construct three hidden variable models for three different physical realizations of the Peres-Mermin square: one violating, another violating, and a third one violating both and.
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DOI 10.1007/s13194-020-00339-0
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La Nouvelle Cuisine.J. S. Bell - 2004 - In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. pp. 232--248.
Hidden Variables and the Two Theorems of John Bell.N. David Mermin - 1993 - Reviews of Modern Physics 65:803--815.

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