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Λ-Nonlocality of Multipartite States and the Related Nonlocality Inequalities

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Abstract

Correlations between subsystems of a composite quantum system include Bell nonlocality, steerability, entanglement and quantum discord. Bell nonlocality of a bipartite state is one of important quantum correlations demonstrated by some local quantum measurements. In this paper, we discuss nonlocality of a multipartite quantum system. The Λ-locality and Λ-nonlocality of multipartite states are firstly introduced, some related properties are discussed. Some related nonlocality inequalities are established for {1,2;3}-local, {1;2,3}-local, and Λ-local states, respectively. The violation of one of these inequalities gives a sufficient condition for Λ-nonlocal states. As application, genuinely nonlocality of a tripartite state is checked. Finally, a class of 2-separable nonlocal states are given, which shows that a 2-separable tripartite state is not necessarily local.

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Acknowledgements

This subject was supported by the National Natural Science Foundation of China (Nos. 11371012, 11401359,11571213,11601300)

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    Ying Yang, Huai-xin Cao, Liang Chen & Yongfeng Huang

  2. Department of Applied Mathematics, Yuncheng College, Yuncheng, 044000, China

    Ying Yang

  3. Department of Mathematics, Changji College, Changji, 831100, China

    Liang Chen & Yongfeng Huang

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  1. Ying Yang
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  2. Huai-xin Cao
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  3. Liang Chen
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  4. Yongfeng Huang
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Correspondence to Huai-xin Cao.

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Yang, Y., Cao, Hx., Chen, L. et al. Λ-Nonlocality of Multipartite States and the Related Nonlocality Inequalities. Int J Theor Phys 57, 1498–1515 (2018). https://doi.org/10.1007/s10773-018-3677-7

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  • DOI: https://doi.org/10.1007/s10773-018-3677-7

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