The Mermin-Peres Magic Square Game With Three or More Players
We present a generalization of the Mermin-Peres magic square game to $N$ players, in which the square is replaced by an $N$-dimensional hypercube. We show that the winning probability of the optimal classical strategy remains $8/9$ for all $N$, while for $N \ge 3$, a generalization of the quantum strategy for $N = 2$ achieves a winning probability between $1/3$ and $3/4$. This loss of quantum advantage for $N \ge 3$ is a consequence of monogamy.
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