Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem

Gustavo Cañas, Sebastian Etcheverry Cabrera, E. S. Gómez, C. Saavedra, G. B. Xavier, G. Lima and A. Cabello


For eight-dimensional quantum systems there is a Kochen-Specker (KS) set of 40 quantum yes-no tests that is related to the Greenberger-Horne-Zeilinger (GHZ) proof of Bell’s theorem. Here we experimentally implement this KS set using an eight-dimensional Hilbert space spanned by the transverse momentum of single photons. We show that the experimental results of these tests violate a state-independent noncontextuality inequality. In addition, we show that, if the system is prepared in states that are formally equivalent to a three-qubit GHZ and W states, then the results of a subset of 16 tests violate a noncontextuality inequality that is formally equivalent to the three-party Mermin’s Bell inequality, but for single eight-dimensional quantum systems. These experimental results highlight the connection between quantum contextuality and nonlocality for eight-dimensional quantum systems.

DOI: http://dx.doi.org/10.1103/PhysRevA.90.012119