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In this paper we analyze the existence of joint probabilities for theBell-type and GHZ entangled states. We then propose the usage of nonmonotonicupper probabilities as a tool to derive consistent joint upper probabilitiesfor the contextual hidden variables. Finally, we show that for the extremeexample of no error, the GHZ state allows for the definition of a joint upperprobability that is consistent with the strong correlations.

Probabilistic Inequalities and Upper Probabilities in Quantum Mechanical Entanglement