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Partial Steerability and Nonlocality of Multipartite Quantum States

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Abstract

In this paper, we discuss partial steerability and nonlocality of multipartite quantum states. For a state ρ of an n-partite system A1A2⋯An, we introduce the concepts of the steerability of ρ from i to j and the (i, j)-Bell nonlocality of ρ. By establishing necessary conditions for a state ρ to be unsteerable from i to j (resp. (i, j)-Bell local), we derive sufficient conditions for a state ρ to be steerable from i to j (resp. (i, j)-Bell nonlocal). We prove that if there are some 1 ≤ i < j ≤ n such that ρ is steerable from i to j (resp. (i, j)-Bell nonlocal), then it is steerable from A to B (resp. (A, B)-Bell nonlocal) provided that A = A1A2⋯Ak and B = Ak+ 1Ak+ 2⋯An with 1 ≤ i ≤ k and k < j ≤ n, leading to new methods for detecting steerability and (A, B)-Bell nonlocal of multipartite states.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 11871318, 11771009), the Fundamental Research Funds for the Central Universities (GK202007002, GK201903001) and the Special Plan for Young Top-notch Talent of Shaanxi Province (1503070117).

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Authors and Affiliations

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

    Mohamed Ismael Ali & Huaixin Cao

  2. Mathematics Department, Faculty of Science, Al-Azhar University, Assuit Branch, Assuit, 71524, Egypt

    Mohamed Ismael Ali

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  1. Mohamed Ismael Ali
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  2. Huaixin Cao
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Correspondence to Huaixin Cao.

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Ali, M.I., Cao, H. Partial Steerability and Nonlocality of Multipartite Quantum States. Int J Theor Phys 60, 2543–2557 (2021). https://doi.org/10.1007/s10773-020-04665-0

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