Generalized Iterative Formula for Bell Inequalities

• URL: http://arxiv.org/abs/2109.05521v3
• Date: Fri, 19 May 2023 01:41:30 GMT
• Title: Generalized Iterative Formula for Bell Inequalities
• Authors: Xing-Yan Fan, Zhen-Peng Xu, Jia-Le Miao, Hong-Ye Liu, Yi-Jia Liu, Wei-Min Shang, Jie Zhou, Hui-Xian Meng, Otfried G\"uhne and Jing-Ling Chen
• Abstract summary: This work is 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.
• Score: 12.55611325152539
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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{\u{\i}}-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 $46$ \'{S}liwa's inequalities to the four-partite tight ones, by applying our iteration method to each inequality and its equivalence class.

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