The CHSH mod 3 Bell inequality is a natural testbed for higher-dimensional quantum nonlocality, yet its maximal quantum violation and self-testing properties have remained unresolved. We determine its exact maximal quantum value and show that, up to unitary equivalence and the natural symmetries of the inequality, it admits a unique optimal irreducible strategy; equivalently, there are four symmetry-related optimal irreducible strategies. Each of these strategies uses a maximally entangled two-qutrit state. We further prove that any strategy whose value is within ε of the optimum is O(ε)-close, up to local isometries, to a direct sum of optimal irreducible strategies.
Cite
@article{arxiv.2604.03700,
title = {Robust self-testing with CHSH mod 3},
author = {Igor Klep and Nando Leijenhorst and Victor Magron},
journal= {arXiv preprint arXiv:2604.03700},
year = {2026}
}