Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911773264707584 |
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| author | Designolle, Sébastien Vértesi, Tamás Pokutta, Sebastian |
| author_facet | Designolle, Sébastien Vértesi, Tamás Pokutta, Sebastian |
| contents | In multipartite Bell scenarios, we study the nonlocality robustness of the Greenberger-Horne-Zeilinger (GHZ) state. When each party performs planar measurements forming a regular polygon, we exploit the symmetry of the resulting correlation tensor to drastically accelerate the computation of (i) a Bell inequality via Frank-Wolfe algorithms, and (ii) the corresponding local bound. The Bell inequalities obtained are facets of the symmetrised local polytope and they give the best known upper bounds on the nonlocality robustness of the GHZ state for three to ten parties. Moreover, for four measurements per party, we generalise our facets and hence show, for any number of parties, an improvement on Mermin's inequality in terms of noise robustness. We also compute the detection efficiency of our inequalities and show that some give rise to activation of nonlocality in star networks, a property that was only shown with an infinite number of measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20677 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms Designolle, Sébastien Vértesi, Tamás Pokutta, Sebastian Quantum Physics Optimization and Control In multipartite Bell scenarios, we study the nonlocality robustness of the Greenberger-Horne-Zeilinger (GHZ) state. When each party performs planar measurements forming a regular polygon, we exploit the symmetry of the resulting correlation tensor to drastically accelerate the computation of (i) a Bell inequality via Frank-Wolfe algorithms, and (ii) the corresponding local bound. The Bell inequalities obtained are facets of the symmetrised local polytope and they give the best known upper bounds on the nonlocality robustness of the GHZ state for three to ten parties. Moreover, for four measurements per party, we generalise our facets and hence show, for any number of parties, an improvement on Mermin's inequality in terms of noise robustness. We also compute the detection efficiency of our inequalities and show that some give rise to activation of nonlocality in star networks, a property that was only shown with an infinite number of measurements. |
| title | Symmetric multipartite Bell inequalities via Frank-Wolfe algorithms |
| topic | Quantum Physics Optimization and Control |
| url | https://arxiv.org/abs/2310.20677 |