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Generalized Steering Robustness of Bipartite Quantum States

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Abstract

EPR steering is a kind of quantum correlation that is intermediate between entanglement and Bell nonlocality. In this paper, by recalling the definitions of unsteerability and steerability, some properties of them are given, e.g, it is proved that a local quantum channel transforms every unsteerable state into an unsteerable state. Second, a way of quantifying quantum steering, which we called the generalized steering robustness (GSR), is introduced and some interesting properties are established, including: (1) GSR of a state vanishes if and only if the state is unsteerable; (2) a local quantum channel does not increase GSR of any state; (3) GSR is invariant under each local unitary operation; (4) as a function on the state space, GSR is convex and lower-semi continuous. Lastly, by using the majorization between the reduced states of two pure states, GSR of the two pure states are compared, and it is proved that every maximally entangled state has the maximal GSR.

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Acknowledgments

This subject was supported by the National Natural Science Foundation of China (11771009, 11571211, 11571213), the Fundamental Research Funds for the Central Universities (GK201703010) and the Hainan province Natural Science Research Grant of China (20151012).

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Authors and Affiliations

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

    Chunming Zheng, Zhihua Guo & Huaixin Cao

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  1. Chunming Zheng
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  2. Zhihua Guo
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  3. Huaixin Cao
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Correspondence to Zhihua Guo.

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Zheng, C., Guo, Z. & Cao, H. Generalized Steering Robustness of Bipartite Quantum States. Int J Theor Phys 57, 1787–1801 (2018). https://doi.org/10.1007/s10773-018-3704-8

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  • DOI: https://doi.org/10.1007/s10773-018-3704-8

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