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Quantum correlations for bipartite continuous-variable systems

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Abstract

Two quantum correlations Q and \(Q_\mathcal P\) for \((m+n)\)-mode continuous-variable systems are introduced in terms of average distance between the reduced states under the local Gaussian positive operator-valued measurements, and analytical formulas of these quantum correlations for bipartite Gaussian states are provided. It is shown that the product states do not contain these quantum correlations, and conversely, all \((m+n)\)-mode Gaussian states with zero quantum correlations are product states. Generally, \(Q\ge Q_{\mathcal P}\), but for the symmetric two-mode squeezed thermal states, these quantum correlations are the same and a computable formula is given. In addition, Q is compared with Gaussian geometric discord for symmetric squeezed thermal states.

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Acknowledgements

The authors thank all referees for their many helpful comments. This work is partially supported by Natural Science Foundation of China (11671006, 11671294) and Outstanding Youth Foundation of Shanxi Province (201701D211001).

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Authors and Affiliations

  1. Department of Mathematics, Shanxi University, Taiyuan, 030006, People’s Republic of China

    Ruifen Ma, Jinchuan Hou, Xiaofei Qi & Yangyang Wang

  2. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan, 030024, People’s Republic of China

    Ruifen Ma

  3. Department of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    Jinchuan Hou

  4. Institute of Big Data Science and Industry, Shanxi University, Taiyuan, 030006, People’s Republic of China

    Xiaofei Qi

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  1. Ruifen Ma
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  2. Jinchuan Hou
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Correspondence to Xiaofei Qi.

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Ma, R., Hou, J., Qi, X. et al. Quantum correlations for bipartite continuous-variable systems. Quantum Inf Process 17, 98 (2018). https://doi.org/10.1007/s11128-018-1866-1

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