  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 experimentally 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 noncontextual
hidden-variable theories and are in good agreement with the maxima predicted by
quantum theory.
