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Quantum Coherence of Qubit States with respect to Mutually Unbiased Bases

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Abstract

We study the coherence of qubit states with respect to any set of mutually unbiased bases (MUBs), in terms of the l1 norm of coherence, the modified trace norm of coherence and the geometry measure of coherence. We present the arbitrary expressions of a complete set of MUBs in C2 and the forms of any qubit states under these complete sets of MUBs. Then we calculate coherence of qubit states with respect to any complete sets of MUBs based on different coherence measures. It is shown that the sum of the coherence or the squared coherence is upper or lower bounded. We derive analytically these bounds and establish tight relations between quantum coherence and mutually unbiased bases.

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Acknowledgments

This work is supported by NSFC under Nos 11761073 and 11675113, and Beijing Municipal Commission of Education (KZ201810028042), Beijing Natural Science Foundation (Z190005), and Academy for Multidisciplinary Studies, Capital Normal University.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Yanbian University, Yanji, 133002, China

    Ming-Yang Shen, Yi-Hao Sheng & Yuan-Hong Tao

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

    Yao-Kun Wang

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

    Yao-Kun Wang

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

    Shao-Ming Fei

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

    Shao-Ming Fei

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  1. Ming-Yang Shen
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  2. Yi-Hao Sheng
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  3. Yuan-Hong Tao
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  4. Yao-Kun Wang
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Correspondence to Yuan-Hong Tao.

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Shen, MY., Sheng, YH., Tao, YH. et al. Quantum Coherence of Qubit States with respect to Mutually Unbiased Bases. Int J Theor Phys 59, 3908–3914 (2020). https://doi.org/10.1007/s10773-020-04642-7

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  • DOI: https://doi.org/10.1007/s10773-020-04642-7

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