Exploring the Local Landscape in the Triangle Network
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915325691297792 |
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| author | Bäumer, Elisa Gitton, Victor Kriváchy, Tamás Gisin, Nicolas Renner, Renato |
| author_facet | Bäumer, Elisa Gitton, Victor Kriváchy, Tamás Gisin, Nicolas Renner, Renato |
| contents | Characterizing the set of distributions that can be realized in the triangle network is a notoriously difficult problem. In this work, we investigate inner approximations of the set of local (classical) distributions of the triangle network. A quantum distribution that appears to be nonlocal is the Elegant Joint Measurement (EJM) [Entropy. 2019; 21(3):325], which motivates us to study distributions having the same symmetries as the EJM. We compare analytical and neural-network-based inner approximations and find a remarkable agreement between the two methods. Using neural network tools, we also conjecture network Bell inequalities that give a trade-off between the levels of correlation and symmetry that a local distribution may feature. Our results considerably strengthen the conjecture that the EJM is nonlocal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exploring the Local Landscape in the Triangle Network Bäumer, Elisa Gitton, Victor Kriváchy, Tamás Gisin, Nicolas Renner, Renato Quantum Physics Characterizing the set of distributions that can be realized in the triangle network is a notoriously difficult problem. In this work, we investigate inner approximations of the set of local (classical) distributions of the triangle network. A quantum distribution that appears to be nonlocal is the Elegant Joint Measurement (EJM) [Entropy. 2019; 21(3):325], which motivates us to study distributions having the same symmetries as the EJM. We compare analytical and neural-network-based inner approximations and find a remarkable agreement between the two methods. Using neural network tools, we also conjecture network Bell inequalities that give a trade-off between the levels of correlation and symmetry that a local distribution may feature. Our results considerably strengthen the conjecture that the EJM is nonlocal. |
| title | Exploring the Local Landscape in the Triangle Network |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.08939 |