Linear equations mod $n$ are pseudo-telepathic

Abstract:We prove that the quantum monad in dimension $2n$ admits no natural transformation to the polymorphism clone of linear equations modulo $n$. Consequently, for every $n\geq 2$, there exists an unsatisfiable system of linear equations over $\mathbb{Z}_n$ whose constraint system game admits a perfect finite-dimensional quantum strategy. As a corollary, we completely characterise pseudo-telepathic constraint languages in finite dimension. The proof combines a result of Harding, Jager, and Smith on group-valued measures on subspaces of Hilbert spaces with the polymorphism-minion characterisation of quantum pseudo-telepathy.

Quantum Physics (quant-ph); Computational Complexity (cs.CC); Logic in Computer Science (cs.LO); Combinatorics (math.CO); Operator Algebras (math.OA)

arXiv:2609.14632 [quant-ph]

(or arXiv:2609.14632v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.14632 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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