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arXiv:2401.00240

Evaluation of the Leggett-Garg inequality by means of the neutrino oscillations observed in reactor and accelerator experiments

Ricardo Zamora Barrios, M. A. Acero

Published Dec 30, 2023• 0 citations
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Abstract

We revisit the study of the violation of the Leggett-Garg inequality in neutrino oscillation data as a mean to test some of the fundamental aspects of quantum mechanics. In particular, we consider the results of the Daya Bay and RENO reactor experiments, and the MINOS and NOvA accelerator experiments. We find that DB and MINOS exhibit a strong manifestation of Leggett-Garg violation, whereas for RENO and NOvA data, the indication is weaker. Considering the particular baselines and energy ranges explored by each experiment, our results demonstrate that the Leggett-Garg violation is more evident for smaller baseline-to-energy ratios in all the data sets studied, a relevant aspect to consider when looking for evidence of quantum mechanical decoherence in neutrino oscillations.

DOI
10.48550/arxiv.2401.00240

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We revisit the study of the violation of the Leggett-Garg inequality in neutrino oscillation data as a mean to test some of the fundamental aspects of quantum mechanics. In particular, we consider the results of the Daya Bay and RENO reactor experiments, and the MINOS and NOvA accelerator experiments. We find that DB and MINOS exhibit a strong manifestation of Leggett-Garg violation, whereas for RENO and NOvA data, the indication is weaker. Considering the particular baselines and energy ranges explored by each experiment, our results demonstrate that the Leggett-Garg violation is more evident for smaller baseline-to-energy ratios in all the data sets studied, a relevant aspect to consider when looking for evidence of quantum mechanical decoherence in neutrino oscillations.
Abstract Leggett–Garg inequality (LGI) is a time analogue of Bell’s inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett–Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of over 10σ10\sigma 10σ 10σ , and of over 90 %\%% % of theoretical predictions, while the KamLAND data exhibit violation of 1.9σ1.9\sigma 1.9σ 1.9σ , being of 58 %\%% % of the theoretical prediction. The present work is the first to have considered the energy uncertainties in neutrino coherence tests.
Neutrino oscillation represents an intriguing physical phenomenon where the quantumness can be maintained and detected over a long distance. Previously, the nonclassical character of neutrino oscillation was tested with the Leggett-Garg inequality, where a clear violation of the classical bound was observed [J. A. Formaggio et al., Phys. Rev. Lett. 117, 050402 (2016)]. However, there are several limitations in testing neutrino oscillations with the Leggett-Garg inequality. In particular, the degree of violation of the Leggett-Garg inequality cannot be taken as a ``measure of quantumness.'' Here, we focus on quantifying the quantumness of experimentally observed neutrino oscillation, using the tools of the recently developed quantum resource theory. We analyzed ensembles of reactor and accelerator neutrinos at distinct energies from a variety of neutrino sources, including Daya Bay (0.5 and 1.6 km), KamLAND (180 km), MINOS (735 km), and T2K (295 km). The quantumness of the three-flavored neutrino oscillation is characterized within a $3\ensuremath{\sigma}$ range relative to the theoretical prediction. It is found that the maximal coherence was observed in the neutrino source from the KamLAND reactor. However, even though the survival probability of the Daya Bay experiment did not vary significantly (it dropped about 10%), the coherence recorded can reach up to 40% of the maximal value. These results represent the longest distance over which quantumness was experimentally determined for quantum particles other than photons.
The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6 σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.
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 6.1σ6.1\sigma 6.1σ significance of the violation of them.
The Leggett-Garg inequality, an analogue of Bell's inequality involving correlations of measurements on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. The phenomenon of neutrino oscillations should adhere to quantum-mechanical predictions and provide an observable violation of the Leggett-Garg inequality. We demonstrate how oscillation phenomena can be used to test for violations of the classical bound by performing measurements on an ensemble of neutrinos at distinct energies, as opposed to a single neutrino at distinct times. A study of the MINOS experiment's data shows a greater than 6σ violation over a distance of 735 km, representing the longest distance over which either the Leggett-Garg inequality or Bell's inequality has been tested.
Violations of classicality can be probed through measurements performed on a system at different times, as proposed by Leggett and Garg. Specifically, violations of Leggett-Garg inequalities suggest the presence of quantum effects in macroscopic systems. Long-baseline neutrino experiments provide some of the longest available propagation distances over which such tests can be performed. Previous studies of Leggett-Garg tests in the neutrino sector have largely focused on showing that the oscillation probabilities can violate classical bounds for certain parameter choices. In this work, we develop a more complete and data-driven framework that treats both the distributions representing the classical and quantum behavior, as well as the experimental uncertainties. We consider MINOS, T2K, NOvA, as well as the upcoming DUNE, and present the respective statistical significance for distinguishing quantum behavior from classical scenarios at these long-baseline neutrino experiments. Among them, we find that T2K yields the most significant violation of classicality, at the level of ∼14σ\sim 14 σ∼14σ, with NOvA and projections for DUNE also resulting in a significance of more than 5σ5σ5σ.