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Entanglement Theory Quantum Correlations Quantum Foundations

Robust self-testing with CHSH mod 3

arXiv

Authors: Igor Klep, Nando Leijenhorst, Victor Magron

Year

2026

Paper ID

45215

Status

Preprint

Abstract Read

~2 min

Abstract Words

101

Citations

N/A

Abstract

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 varepsilon of the optimum is O\(sqrt{varepsilon}\)-close, up to local isometries, to a direct sum of optimal irreducible strategies.

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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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2604.03700 [2] arXiv https://arxiv.org/abs/2604.03700 [3] Publisher https://arxiv.org/abs/2604.03700

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