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Some Measurement-Based Characterizations of Separability of Bipartite States

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Abstract

Importance of quantum entanglement has been demonstrated in various applications. Usually, separability of a bipartite state is defined by its algebraic structure, i.e. a convex combination of product states. But it seems to be hard to check separability (equivalently, entanglement) of a state from its algebraic structure. In this note, we give some characterizations of separability of bipartite states based on POVM measurements. For bipartite pure states, we prove the separability, Bell locality, unsteerability and classical correlation are the same. As a consequence, every entangled pure bipartite state is always Bell nonlocal, steerable and quantum correlated.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11871318, 11771009,12001480), 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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  1. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    Huaixin Cao, Chengyang Zhang & Zhihua Guo

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  1. Huaixin Cao
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Correspondence to Zhihua Guo.

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Cao, H., Zhang, C. & Guo, Z. Some Measurement-Based Characterizations of Separability of Bipartite States. Int J Theor Phys 60, 2558–2572 (2021). https://doi.org/10.1007/s10773-020-04678-9

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