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A Note of Bell Inequalities for Graph States

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Abstract

In this paper, we construct a general Bell inequality for the graph state. Firstly, we show that the Bell inequality is maximally violated by graph state corresponding to some given graph. In addition, we obtain the classical bound and maximal quantum violation of Bell inequality are N + |n(i)|− 1 and \(N+(\sqrt {2}-1)(|n(i)|+1)\), respectively. Furthermore, the classical bound and maximal quantum violation of Bell inequality are dependent on the choice of the vertex for most graphs expect for complete graph.

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Acknowledgements

The author would like to thank anonymous referees for his/her valuable comments and suggestions which helped to improve the presentation of this paper.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, China

    Mengfei Niu, Zhengli Chen & Xiaole Lv

  2. School of Ethnic Education, Shaanxi Normal University, Xi’an, 710062, China

    Wenhua Wang

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  1. Mengfei Niu
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  2. Zhengli Chen
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  3. Xiaole Lv
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  4. Wenhua Wang
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Correspondence to Zhengli Chen.

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This research was partially supported by the National Natural Science Foundation of China(No.11571213, 11871318, 11771009) and the Fundamental Research Funds for the Central Universities (GK202007002).

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Niu, M., Chen, Z., Lv, X. et al. A Note of Bell Inequalities for Graph States. Int J Theor Phys 60, 2511–2519 (2021). https://doi.org/10.1007/s10773-020-04647-2

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  • DOI: https://doi.org/10.1007/s10773-020-04647-2

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