Mauricio Arias, Gustavo Cañas, E. S. Gómez, J. F. Barra, G. B. Xavier, G. Lima, Vincenzo D’Ambrosio, Flavio Baccari, Fabio Sciarrino and Adan Cabello
PHYSICAL REVIEW A (2015)
Measurement scenarios containing events with relations of exclusivity represented by pentagons, heptagons, nonagons, etc., or their complements are the only ones in which quantum probabilities cannot be described classically. Interestingly, quantum theory predicts that the maximum values for any of these graphs cannot be achieved in Bell inequality scenarios. With the exception of the pentagon, this prediction remained experimen- tally unexplored. Here we test the quantum maxima for the heptagon and the complement of the heptagon using three- and five-dimensional quantum states, respectively. In both cases, we adopt two different encodings: linear transverse momentum and orbital angular momentum of single photons. Our results exclude maximally non- contextual hidden-variable theories and are in good agreement with the maxima predicted by quantum theory.