The Greenberger-Horne-Zeilinger (GHZ) argument against noncontextual local hidden variables is recast in quantum logical terms of fundamental propositions, states and probabilities. Unlike Kochen-Specker- and Hardy-like configurations, this operator based argument proceeds within four nonintertwining contexts. The nonclassical performance of the GHZ argument is due to the choice or filtering of observables with respect to a particular state. We study the varieties of GHZ games one could play in these four contexts, depending on the chosen state of the GHZ basis.
Keywords: Born rule; Gadget graphs; Gleason theorem; Greechie diagram; Greenberger–Horne–Zeilinger argument; Kochen–Specker theorem; McKay–Megill–Pavicic diagram (MMP); Orthogonality hypergraph.
© The Author(s) 2021.