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Uncertainty relations for quantum coherence using wave packet approach in neutrino oscillations

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Abstract

Uncertainty relation is one of the most iconic implications of quantum physics distinguishing classical physics. It demonstrates the inherent uncertainty of nature from the information theory perspectives. In this work, we investigate the uncertainty relations for quantum coherence using wave packet approach in neutrino oscillations. From e and \(\mu \) neutrino sources, the coherence-based uncertainty and two different lower bounds are analyzed in detail under the mutually unbiased bases. It is found that the uncertainty exhibits the characterization of oscillations for short distances, and the lower bound can be strengthened by the Holevo quantity and the mutual information in neutrino oscillations. Particularly, the gap of the improved coherence-based uncertainty relation become smaller with the growth of entanglement for the neutrino-flavor state. Furthermore, compared to the entropy-based uncertainty relations, it shows that coherence-based uncertainty is inversely correlated with the entropy-based uncertainty, which can provide a feasible physical explanation for the uncertainty relations for quantum coherence. The results could pave the theoretical foundation for further application of neutrino oscillations on quantum information science.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12205073, 12075001, 61601002, and 11247009), University Natural Sciences Research Project of Anhui Province (Project Numbers: KJ2021A0989 and 2022AH051807), Key Research and Development Project of Anhui Province (Grant No. 2022b13020004), the fund from CAS Key Laboratory of Quantum Information (Grant No. KQI201701), Talent Research Fund of Hefei University (Grant Nos. 21-22RC04 and 21-22RC03), and the Key Discipline of Hefei University (Grant No. 2018xk03).

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Authors and Affiliations

  1. School of Advanced Manufacturing Engineering, Hefei University, Hefei, 230601, People’s Republic of China

    Fei Ming, Bao-Long Fang, Xueyou Hu & Yang Yu

  2. School of Physics and Optoelectronic Engineering, Anhui University, Hefei, 230601, People’s Republic of China

    Dong Wang

  3. Anhui Provincial Engineering Technology Research Center of Intelligent Vehicle Control and Integrated Design Technology, Hefei, 230601, People’s Republic of China

    Fei Ming

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  1. Fei Ming
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Correspondence to Fei Ming.

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Ming, F., Fang, BL., Hu, X. et al. Uncertainty relations for quantum coherence using wave packet approach in neutrino oscillations. Eur. Phys. J. Plus 139, 229 (2024). https://doi.org/10.1140/epjp/s13360-024-05005-5

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