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

## TL;DR

This paper reports an empirical test of the Leggett-Garg-type inequality violation using neutrino oscillation data from the Daya Bay experiment, demonstrating a significant deviation from classical bounds with 6.1 sigma confidence.

## Contribution

It provides the first experimental evidence of LGtI violation in neutrino oscillations, extending quantum temporal correlations tests to weakly interacting particles.

## Key findings

- Data exceeds classical LGtI bounds with 6.1 sigma significance.
- Neutrino oscillation data shows clear quantum temporal correlations.
- Supports the quantum nature of neutrino oscillations.

## Abstract

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.