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arXiv · 2610.06534

The Mermin-Peres Magic Square Game With Three or More Players

Itamar Lorian·J. E. Avron
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Abstract

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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Itamar Lorian, J. E. Avron. 2026-10-05. The Mermin-Peres Magic Square Game With Three or More Players. https://arxiv.org/abs/2610.06534

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