Pseudo-telepathy games and genuine ns k-way nonlocality using graph states

We define a family of pseudo-telepathy games using graph states that extends the Mermin games. This family also contains a game used to define a quantum probability distribution that cannot be simulated by any number of nonlocal boxes. We extend this result, proving that the probability distribution obtained by the Paley graph state on 13 vertices (each vertex corresponds to a player) cannot be simulated by any number of 4-partite nonlocal boxes and that the Paley graph states on k222k-2 vertices provide a probability distribution that cannot be simulated by k-partite nonlocal boxes, for any k.

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