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

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 μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document} 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.