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A new no-go theorem for hidden variables theories

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Consider the quantum predictions for EPR-type measurements on two systems with Hilbert space of dimension at least 3 in any maximally entangled state. I show that the only possible hidden variables model of these probabilities that satisfies both Shimony\'s and Jarrett\'s condition of parameter independence (or `locality\') and Jones and Clifton\'s condition of conditional parameter independence (or `constrained locality\') is trivial, i.e. given by the quantum probabilities themselves. I shall attempt to discuss also the meaning of the conditions and of this result.