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Geometric structure of quantum resources for Bell-diagonal states

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Abstract

Two-qubit Bell-diagonal states can be depicted as a tetrahedron in three dimensions. We investigate the geometric structure of quantum resources, including coherence and quantum discord, in the tetrahedron. The ordering of different resources measures is a common problem in resource theories, and which measure should be chosen to investigate the structure of resources is still an open question. We consider the geometric structure of quantum resources which is not affected by the choice of measure. Our work provides a complete structure of coherence and quantum discord for Bell-diagonal states. The pictorial approach also indicates how to explore the structure of resources even when we do not have consistent measure of a concrete quantum resource.

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Acknowledgements

We thank Hai-Long Shi and Guo-Guo Xin for their valuable discussions. This work was supported by the NSFC (Grant Nos. 11775177, 11647057, 11705146), the Special Research Funds of Shaanxi Province Department of Education (No. 16JK1759), Northwest University Scientific Research Funds (No. 15NW26) and the Double First-Class University Construction Project of Northwest University.

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Authors and Affiliations

  1. Institute of Modern Physics, Northwest University, Xi’an, 710069, China

    Jin-Xing Hou, Yun-Long Su, Si-Yuan Liu & Wen-Li Yang

  2. School of Physics, Northwest University, Xi’an, 710069, China

    Yun-Long Su & Xiao-Hui Wang

  3. Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi’an, 710069, China

    Jin-Xing Hou, Si-Yuan Liu, Xiao-Hui Wang & Wen-Li Yang

  4. Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Si-Yuan Liu

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  1. Jin-Xing Hou
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  2. Yun-Long Su
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  4. Xiao-Hui Wang
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  5. Wen-Li Yang
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Correspondence to Si-Yuan Liu.

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Hou, JX., Su, YL., Liu, SY. et al. Geometric structure of quantum resources for Bell-diagonal states. Quantum Inf Process 17, 184 (2018). https://doi.org/10.1007/s11128-018-1950-6

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  • DOI: https://doi.org/10.1007/s11128-018-1950-6

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