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Main Authors: 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
Format: Preprint
Published: 2021
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Online Access:https://arxiv.org/abs/2109.05521
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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