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The Mermin-Peres Magic Square Game With Three or More Players
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 ≥ 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 ≥ 3 is a consequence of monogamy.
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BibTeX
@misc{lorian2026merminperes,
title = {{The Mermin-Peres Magic Square Game With Three or More Players}},
author = {Itamar Lorian and J. E. Avron},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06534},
eprint = {2610.06534},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06534},
}
RIS
TY - UNPB
TI - The Mermin-Peres Magic Square Game With Three or More Players
AU - Itamar Lorian
AU - J. E. Avron
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.06534
UR - https://arxiv.org/abs/2610.06534
AB - 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 ≥ 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 ≥ 3 is a consequence of monogamy.
ER -