separation between 5-party pseudo-telepathy games and two-local theories. We define the notion of strategy in a k-local theory for a game, and extend the method of Chao and Reichardt. We also study variation of the game to minimize the classical winning probability.

DOI: 10.48550/arxiv.1806.08661

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We give an

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We give an

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3 \times 3

}. This is optimal for two-player games, but the most efficient pseudo-telepathy game possible, in terms of total dimension, involves \emph{three} players who share a quantum system of dimension~\mbox{

2 \times 2 \times 2

G_n

for testing maximally entangled states of local dimension

Ω(n)

. We leave the robustness of these self-tests as an open question.

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-dimension. A winning strategy for this game is then described with single use of NL-box.