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Full nonlocality (FN) is the strongest form of nonlocality and plays acrucial role in quantum information and computation. It has been recently shownthat FN, all versus nothing (AVN) nonlocality, and pseudo telepathy (PT) areequivalent, and this has led to advance in the long-standing open problem ofwhat is the simplest form of bipartite FN/AVN/PT. It has been shown thatbipartite FN/AVN/PT is impossible in Bell scenarios with small input and outputcardinalities and that existing tools cannot help answer whether it is possiblein larger scenarios. Here, we prove that FN/AVN/PT is equivalent to a specifictype of Kochen-Specker (KS) set and, by exploring all known KS sets with smallcardinality, we show that, arguably, (i) the simplest bipartite FN/AVN/PT isthe correlation in Phys. Rev. Lett. 87, 010403 (2001), and (ii) the simplestbipartite FN/AVN/PT in the simplest bipartite quantum system that allows forFN/AVN/PT, which is a pair of qutrits, happens when Alice (Bob) has 9 (7)measurements of 3 outcomes. This scenario is small enough to allow observationof qutrit-qutrit FN/AVN/PT and to connect the Bell and KS theorems in oneexperiment.

Minimum full nonlocality, all versus nothing nonlocality, and quantum pseudo telepathy