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International Journal of Theoretical Physics

, Volume 57, Issue 5, pp 1498–1515 | Cite as

Λ-Nonlocality of Multipartite States and the Related Nonlocality Inequalities

  • Ying Yang
  • Huai-xin Cao
  • Liang Chen
  • Yongfeng Huang
Article

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.

Keywords

Λ-Locality Λ-nonlocality Nonlocality inequality Multipartite state 

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Ying Yang
    • 1
    • 2
  • Huai-xin Cao
    • 1
  • Liang Chen
    • 1
    • 3
  • Yongfeng Huang
    • 1
    • 3
  1. 1.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina
  2. 2.Department of Applied MathematicsYuncheng CollegeYunchengChina
  3. 3.Department of MathematicsChangji CollegeChangjiChina

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