Testing violation of the Leggett-Garg-type inequality in neutrino oscillations of the Daya Bay experiment

The Leggett-Garg inequality (LGI), derived under the assumption of realism, acts as the temporal Bell's inequality. It is studied in electromagnetic and strong interaction like photonics, superconducting qu-bits and nuclear spin. Until the weak interaction two-state oscillations of neutrinos affirmed the violation of Leggett-Garg-type inequalities (LGtI). We make an empirical test for the deviation of experimental results with the classical limits by analyzing the survival probability data of reactor neutrinos at a distinct range of baseline dividing energies, as an analog to a single neutrino detected at different time. A study of the updated data of Daya-Bay experiment unambiguously depicts an obvious cluster of data over the classical bound of LGtI and shows a $6.1\sigma$ significance of the violation of them.Comment: 11 pages, 6 figure