Visualizing coherence, Bell-nonlocality and their interrelation for two-qubit X states in quantum steering ellipsoid formalism

  • Huan Yang
  • Zhi-Yong Ding
  • Wen-Yang Sun
  • Fei Ming
  • Dong Wang
  • Chang-Jin Zhang
  • Liu YeEmail author


Quantum steering ellipsoid has been regarded as a faithful representation of arbitrary two-qubit state and provides a visualized geometry for quantum resources. Herein, considering two-qubit X states, the generally form of quantum steering ellipsoid is derived. It shows the l1 norm of coherence can be visually denoted by the x or y semiaxis length of the ellipsoid. By using ellipsoid with largest volume, we obtain the upper bounds of the l1 norm and relative entropy of coherence for two-qubit X states. We also reveal that the dynamics of l1 norm of coherence can be exhibited by the evolution of quantum steering ellipsoid under noisy channels. In addition, the expression of Bell-nonlocality for two-qubit X states is provided in the frame of quantum steering ellipsoids, and this expression is relevant to semiaxis lengths of ellipsoid. Based on this, we investigate relationship between the l1 norm of coherence and Bell-nonlocality. Notably, Bell-nonlocality of two-qubit X states can be detected according to the l1 norm of coherence. Finally, Bell-nonlocality and l1 norm of coherence for two-qubit Heisenberg spin-1/2 XX model with inhomogeneous field are researched as a verification of our results.


Coherence Bell-nonlocality Quantum steering ellipsoid 



This work was supported by the National Science Foundation of China under Grants Nos. 11575001 and 61601002, the Anhui Provincial Natural Science Foundation (Grant No. 1508085QF139), the Program for Excellent Talents in University of Anhui Province of China (Grant No. gxyq2018059), the Key projects of Anhui Provincial Department of Education (Grant Nos. KJ2017A406 and KJ2017A401) and the Key Project of West Anhui University (Grant No. KJ103762015B23).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Huan Yang
    • 1
    • 2
    • 3
  • Zhi-Yong Ding
    • 1
    • 4
  • Wen-Yang Sun
    • 1
  • Fei Ming
    • 1
  • Dong Wang
    • 1
  • Chang-Jin Zhang
    • 2
  • Liu Ye
    • 1
    Email author
  1. 1.School of Physics and Material ScienceAnhui UniversityHefeiChina
  2. 2.Institutes of Physical Science and Information TechnologyAnhui UniversityHefeiChina
  3. 3.Department of Experiment and Practical Training ManagementWest Anhui UniversityLu’anChina
  4. 4.School of Physics and Electronic EngineeringFuyang Normal UniversityFuyangChina

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