Abstract
The Leggett–Garg inequality (LGI), derived under the assumption of realism, acts as the temporal Bell inequality. It is studied in electromagnetic and strong interaction like photonics, superconducting qubits and nuclear spin. 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 times. A study of the updated data of the Daya Bay experiment unambiguously depicts an obvious cluster of data over the classical bound of LGtI and shows a 6.1sigma significance of the violation of them.
Highlights
Nonclassical features of the quantum system have experienced extensive study since the inception of quantum mechanics
The unique feature of Bell’s inequality (BI) is its testable formula from the consequence of the famous hypothesis called local realism (LR)
The LR believers assume that any observable value of an object, even if not detected, must have a definite value and that results of any individual measurement of the observables remain unaffected if they have a space-like separation
Summary
Nonclassical features of the quantum system have experienced extensive study since the inception of quantum mechanics. Due to the oscillation of neutrino flavors, it offers an ideal source to test quantum mechanics in the case of the weak interaction and from a macroscopic point of view. J. C (2017) 77:775 two-level states, a series of quantum-information theory calculations [15,16,17,18] have been applied on neutrino flavor oscillation in the last several years. C (2017) 77:775 two-level states, a series of quantum-information theory calculations [15,16,17,18] have been applied on neutrino flavor oscillation in the last several years These quantum correlations can be directly linked to the probabilities of flavor oscillation, which leads to violation of the classical boundary limits when assuming the neutrino oscillation mixing angle is not vanishing. We will investigate whether the Daya Bay reactor neutrino experiment can observe the violation of LGIs
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