We show that the exclusivity (E) principle singles out the set of quantumcorrelations associated to any exclusivity graph assuming the set of quantumcorrelations for the complementary graph. Moreover, we prove that, forself-complementary graphs, the E principle, by itself (i.e., without furtherassumptions), excludes any set of correlations strictly larger than the quantumset. Finally, we prove that, for vertex-transitive graphs, the E principlesingles out the maximum value for the quantum correlations assuming only thequantum maximum for the complementary graph. This opens the door for testingthe impossibility of higher-than-quantum correlations in experiments.
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