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PreprintCC BY 4.0arXiv

Linear equations mod n are pseudo-telepathic

  • Lorenzo Ciardo
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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≥ 2, there exists an unsatisfiable system of linear equations over ℤn 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.

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Cite

BibTeXRIS
BibTeX
@misc{ciardo2026linear,
  title = {{Linear equations mod $n$ are pseudo-telepathic}},
  author = {Lorenzo Ciardo},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14632},
  eprint = {2609.14632},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14632},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Linear equations mod n are pseudo-telepathic
AU  - Lorenzo Ciardo
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14632
UR  - https://arxiv.org/abs/2609.14632
AB  - 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≥ 2, there exists an unsatisfiable system of linear equations over 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.
ER  -