Robust self-testing with CHSH mod 3
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917383951613952 |
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| author | Klep, Igor Leijenhorst, Nando Magron, Victor |
| author_facet | Klep, Igor Leijenhorst, Nando Magron, Victor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust self-testing with CHSH mod 3 Klep, Igor Leijenhorst, Nando Magron, Victor Optimization and Control Quantum Physics 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. |
| title | Robust self-testing with CHSH mod 3 |
| topic | Optimization and Control Quantum Physics |
| url | https://arxiv.org/abs/2604.03700 |