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Geometry of Quantum Coherence for Two Qubit X States

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Abstract

The geometry of the structure of entanglement and discord for Bell-diagonal states is depicted by Lang and Caves (Phys. Rev. Lett. 105, 150501, 2010). In this paper, we investigate the geometry with respect to several distance-based quantifiers of coherence for Bell-diagonal states. We find that as both l1 norm and relative entropy of coherence vary continuously from zero to one, their related geometric surfaces move from the region of separable states to the region of entangled states, a fact illustrating intuitively that quantum states with nonzero coherence can be used for entanglement creation. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equals to its relative entropy of coherence, and depict the surfaces related to the equality. We give surfaces of relative entropy of coherence for X states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherences under local nondissipative channels decrease.

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Acknowledgments

We thank Q. Quan and T. Ma for useful discussions. This work was supported by the National Natural Science Foundation of China under grant No.11675113 and NSF of Beijing under No.KZ201810028042.

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Authors and Affiliations

  1. College of Mathematics, Tonghua Normal University, Tonghua, Jilin, 134001, China

    Yao-Kun Wang

  2. Research Center for Mathematics, College of Mathematics, Tonghua Normal University, Tonghua, Jilin, 134001, China

    Yao-Kun Wang

  3. State and Local Joint Engineering Research Center for Advanced Networking and Intelligent Information Services, School of Computer Science, Xi’an Polytechnic University, Xi’an, Shaanxi, 710048, China

    Lian-He Shao

  4. The Branch Campus of Tonghua Normal University, Tonghua, Jilin, 134001, China

    Li-Zhu Ge

  5. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei & Zhi-Xi Wang

  6. Max-Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany

    Shao-Ming Fei

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  1. Yao-Kun Wang
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  2. Lian-He Shao
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Correspondence to Yao-Kun Wang.

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Wang, YK., Shao, LH., Ge, LZ. et al. Geometry of Quantum Coherence for Two Qubit X States. Int J Theor Phys 58, 2372–2383 (2019). https://doi.org/10.1007/s10773-019-04129-0

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  • DOI: https://doi.org/10.1007/s10773-019-04129-0

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