Adan Cabello, Lars Eirik Danielsen, Antonio J. Lopez-Tarrida, Jose R. Portillo
We prove that a necessary condition for an experiment to reveal genuinely quantum correlations is that the exclusive disjunction structure of the events tested in the experiment contains, as induced structures, (i) odd cycles of length 5 or more, and/or (ii) their complements. Family (i) is a well-known family of quantum structures. Family (ii) is identified here as a family of quantum structures. We characterize its maximum classical and quantum values and show that it provides valuable information on the dimension of the system. Finally, we show that the present knowledge in graph theory is compatible with/strongly suggests that the quantum correlations of family (i)/(ii) are singled out by the principle that the sum of probabilities of pairwise exclusive events cannot be higher than 1.
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http://arxiv.org/abs/1211.5825
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