Tight Bell inequalities from polytope slices
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866911348540047360 |
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| author | Jesus, José Cruzeiro, Emmanuel Zambrini |
| author_facet | Jesus, José Cruzeiro, Emmanuel Zambrini |
| contents | We derive new tight bipartite Bell inequalities for various scenarios. A bipartite Bell scenario $(X,Y,A,B)$ is defined by the numbers of settings and outcomes per party, $X$, $A$ and $Y$, $B$ for Alice and Bob, respectively. We derive the complete set of facets of the local polytopes of $(6,3,2,2)$, $(3,3,3,2)$, $(3,2,3,3)$, and $(2,2,3,5)$. We provide extensive lists of facets for $(2,2,4,4)$, $(3,3,4,2)$ and $(4,3,3,2)$. For each inequality we compute the maximum quantum violation, the resistance to noise, and the minimal symmetric detection efficiency required to close the detection loophole, for qubits, qutrits and ququarts. Based on these results, we identify scenarios which perform better in terms of visibility, resistance to noise, or both, when compared to CHSH. Such scenarios could find important applications in quantum communication. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_03212 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Tight Bell inequalities from polytope slices Jesus, José Cruzeiro, Emmanuel Zambrini Quantum Physics We derive new tight bipartite Bell inequalities for various scenarios. A bipartite Bell scenario $(X,Y,A,B)$ is defined by the numbers of settings and outcomes per party, $X$, $A$ and $Y$, $B$ for Alice and Bob, respectively. We derive the complete set of facets of the local polytopes of $(6,3,2,2)$, $(3,3,3,2)$, $(3,2,3,3)$, and $(2,2,3,5)$. We provide extensive lists of facets for $(2,2,4,4)$, $(3,3,4,2)$ and $(4,3,3,2)$. For each inequality we compute the maximum quantum violation, the resistance to noise, and the minimal symmetric detection efficiency required to close the detection loophole, for qubits, qutrits and ququarts. Based on these results, we identify scenarios which perform better in terms of visibility, resistance to noise, or both, when compared to CHSH. Such scenarios could find important applications in quantum communication. |
| title | Tight Bell inequalities from polytope slices |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2212.03212 |