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| Main Authors: | , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.05521 |
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| _version_ | 1866913198280540160 |
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| author | Fan, Xing-Yan Xu, Zhen-Peng Miao, Jia-Le Liu, Hong-Ye Liu, Yi-Jia Shang, Wei-Min Zhou, Jie Meng, Hui-Xian Gühne, Otfried Chen, Jing-Ling |
| author_facet | Fan, Xing-Yan Xu, Zhen-Peng Miao, Jia-Le Liu, Hong-Ye Liu, Yi-Jia Shang, Wei-Min Zhou, Jie Meng, Hui-Xian Gühne, Otfried Chen, Jing-Ling |
| contents | Bell inequalities are a vital tool to detect the nonlocal correlations, but the construction of them for multipartite systems is still a complicated problem. In this work, inspired via a decomposition of $(n+1)$-partite Bell inequalities into $n$-partite ones, we present a generalized iterative formula to construct nontrivial $(n+1)$-partite ones from the $n$-partite ones. Our iterative formulas recover the well-known Mermin-Ardehali-Belinski{\uı}-Klyshko (MABK) and other families in the literature as special cases. Moreover, a family of ``dual-use'' Bell inequalities is proposed, in the sense that for the generalized Greenberger-Horne-Zeilinger states these inequalities lead to the same quantum violation as the MABK family and, at the same time, the inequalities are able to detect the non-locality in the entire entangled region. Furthermore, we present generalizations of the the I3322 inequality to any $n$-partite case which are still tight, and of the $46$ Śliwa's inequalities to the four-partite tight ones, by applying our iteration method to each inequality and its equivalence class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05521 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Generalized Iterative Formula for Bell Inequalities Fan, Xing-Yan Xu, Zhen-Peng Miao, Jia-Le Liu, Hong-Ye Liu, Yi-Jia Shang, Wei-Min Zhou, Jie Meng, Hui-Xian Gühne, Otfried Chen, Jing-Ling Quantum Physics Bell inequalities are a vital tool to detect the nonlocal correlations, but the construction of them for multipartite systems is still a complicated problem. In this work, inspired via a decomposition of $(n+1)$-partite Bell inequalities into $n$-partite ones, we present a generalized iterative formula to construct nontrivial $(n+1)$-partite ones from the $n$-partite ones. Our iterative formulas recover the well-known Mermin-Ardehali-Belinski{\uı}-Klyshko (MABK) and other families in the literature as special cases. Moreover, a family of ``dual-use'' Bell inequalities is proposed, in the sense that for the generalized Greenberger-Horne-Zeilinger states these inequalities lead to the same quantum violation as the MABK family and, at the same time, the inequalities are able to detect the non-locality in the entire entangled region. Furthermore, we present generalizations of the the I3322 inequality to any $n$-partite case which are still tight, and of the $46$ Śliwa's inequalities to the four-partite tight ones, by applying our iteration method to each inequality and its equivalence class. |
| title | Generalized Iterative Formula for Bell Inequalities |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2109.05521 |