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Optimizing incompatible triple quantum measurements

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Abstract

We investigate the optimal approximation to triple incompatible quantum measurements within the framework of statistical distance and joint measurability. According to the lower bound of the uncertainty inequality presented in [Physical Review A 99, 312107 (2019)], we give the analytical expressions of the optimal jointly measurable approximation to two kinds of triple incompatible unbiased qubit measurements. We also obtain the corresponding states which give the minimal approximation errors in measuring process. The results give rise to plausible experimental verifications of such statistical distance-based uncertainty relations.

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This manuscript has associated data in a data repository. [Authors’ comment: All the data that support the findings of this work is accessible in the main manuscript.]

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Acknowledgements

This work is supported by the NSF of China under Grant Nos. 11701128, 12075159 and 12171044; Beijing Natural Science Foundation (Grant No. Z190005); Academy for Multidisciplinary Studies, Capital Normal University; Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology (No. SIQSE202001); Academician Innovation Platform of Hainan Province.

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Authors and Affiliations

  1. School of Sciences, Hangzhou Dianzi Unversity, Hangzhou, 310018, China

    Hui-Hui Qin

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

    Shao-Ming Fei

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

    Shao-Ming Fei

Authors
  1. Hui-Hui Qin
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  2. Shao-Ming Fei
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Correspondence to Hui-Hui Qin.

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Hui-Hui Qin and Shao-Ming Fei are equally contribution to the work.

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Qin, HH., Fei, SM. Optimizing incompatible triple quantum measurements. Eur. Phys. J. Plus 137, 635 (2022). https://doi.org/10.1140/epjp/s13360-022-02826-0

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