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The Kochen-Specker theorem demonstrates that it is not possible to reproduce the predictions of quantum theory in terms of a hidden variable model where the hidden variables assign a value to every projector deterministically and noncontextually.
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R. W. Spekkens, The Status of Determinism in Proofs of the Impossibility of a Noncontextual Model of Quantum Theory, Found. Phys
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H. M. Wiseman, The Two Bell’s theorems of John Bell, J. Phys. A: Math. Theor. 47 424001 (2014)
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M. F. Pusey, The robust noncontextuality inequalities in the simplest scenario (2015)
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A. Acin, T. Fritz, A. Leverrier, and A. B. Sainz, A Combinatorial Approach to Nonlocality and Contextuality, Comm. Math. Phys. 334(2), 533-628 (2015)
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R. W. Spekkens, Negativity and Contextuality are Equivalent Notions of Nonclassicality, Phys. Rev. Lett
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The ontological models framework has the advantage of not prejudicing the question of whether any of the variables remain unkown (i.e. hidden) to one who knows the preparation procedure. For an overview, see N. Harrigan and R. W. Spekkens, Einstein, Incompleteness, and the Epistemic View of Quantum States, Found. Phys
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A. Cabello, S. Severini, and A. Winter, Graph-Theoretic Approach to Quantum Correlations, Phys. Rev. Lett
2014
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Indeed, in Ref
Cited in the paper.
Indeed, in Ref
Cited in the paper.