  Full nonlocality (FN) is the strongest form of nonlocality and plays a
crucial role in quantum information and computation. It has been recently shown
that FN, all versus nothing (AVN) nonlocality, and pseudo telepathy (PT) are
equivalent, and this has led to advance in the long-standing open problem of
what is the simplest form of bipartite FN/AVN/PT. It has been shown that
bipartite FN/AVN/PT is impossible in Bell scenarios with small input and output
cardinalities and that existing tools cannot help answer whether it is possible
in larger scenarios. Here, we prove that FN/AVN/PT is equivalent to a specific
type of Kochen-Specker (KS) set and, by exploring all known KS sets with small
cardinality, we show that, arguably, (i) the simplest bipartite FN/AVN/PT is
the correlation in Phys. Rev. Lett. 87, 010403 (2001), and (ii) the simplest
bipartite FN/AVN/PT in the simplest bipartite quantum system that allows for
FN/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 observation
of qutrit-qutrit FN/AVN/PT and to connect the Bell and KS theorems in one
experiment.
