Quantum correlations for bipartite continuous-variable systems

  • Ruifen Ma
  • Jinchuan Hou
  • Xiaofei Qi
  • Yangyang Wang


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.


Quantum correlation Continuous-variable systems Gaussian states Gaussian measurement 



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

Authors and Affiliations

  • Ruifen Ma
    • 1
    • 2
  • Jinchuan Hou
    • 1
    • 3
  • Xiaofei Qi
    • 1
    • 4
  • Yangyang Wang
    • 1
  1. 1.Department of MathematicsShanxi UniversityTaiyuanPeople’s Republic of China
  2. 2.School of Applied ScienceTaiyuan University of Science and TechnologyTaiyuanPeople’s Republic of China
  3. 3.Department of MathematicsTaiyuan University of TechnologyTaiyuanPeople’s Republic of China
  4. 4.Institute of Big Data Science and IndustryShanxi UniversityTaiyuanPeople’s Republic of China

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