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.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.

arXiv:1602.00041Physical Review LettersJul 26, 2016150 citations

New test of neutrino oscillation coherence with Leggett–Garg inequality

Xingzhi Wang, Bo-Qiang Ma

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 $10\sigma$ 10σ , and of over 90 $\%$ % of theoretical predictions, while the KamLAND data exhibit violation of $1.9\sigma$ 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.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 $$10\sigma $$ 10σ , and of over 90 $$\%$$ % of theoretical predictions, while the KamLAND data exhibit violation of $$1.9\sigma $$ 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.

arXiv:2201.10597The European Physical Journal CFeb 1, 202220 citations

Quantifying quantum coherence in experimentally observed neutrino oscillations

Xue‐Ke Song, Yanqi Huang, Jiajie Ling +1 more

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.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.

arXiv:1806.00715Physical Review ANov 26, 201859 citations

Leggett-Garg Inequalities for testing quantum mechanics of neutrino oscillations

Sebastian Shetters

This project examines the quantum mechanical nature of neutrino oscillations through the Leggett-Garg Inequality (LGI), a test for temporal correlations that distinguishes quantum mechanics from classical hidden-variable theories. Using data from the MINOS experiment, which measures neutrino survival probabilities across a 735 km baseline, two methods were employed to calculate LGI violations: a conventional approach and an overlap method. While both are valid, the overlap method is theoretically more accurate as it incorporates uncertainties in energy. The conventional method identified 80 triplets with 62 LGI violations, while the overlap method identified 780 triplets with an average of 528 LGI violations. These results demonstrate significant LGI violations, affirming quantum coherence in neutrino oscillations and challenging classical macrorealism. This study advances our understanding of quantum behavior in macroscopic systems, offering robust evidence for the quantum mechanical framework of neutrino physics.This project examines the quantum mechanical nature of neutrino oscillations through the Leggett-Garg Inequality (LGI), a test for temporal correlations that distinguishes quantum mechanics from classical hidden-variable theories. Using data from the MINOS experiment, which measures neutrino survival probabilities across a 735 km baseline, two methods were employed to calculate LGI violations: a conventional approach and an overlap method. While both are valid, the overlap method is theoretically more accurate as it incorporates uncertainties in energy. The conventional method identified 80 triplets with 62 LGI violations, while the overlap method identified 780 triplets with an average of 528 LGI violations. These results demonstrate significant LGI violations, affirming quantum coherence in neutrino oscillations and challenging classical macrorealism. This study advances our understanding of quantum behavior in macroscopic systems, offering robust evidence for the quantum mechanical framework of neutrino physics.

May 1, 20250 citations

Leggett-Garg test inequality with spin and flavour neutrino oscillations in a constant magnetic field

I. A. Monroy, S. D. Madrid

The Leggett-Garg inequality (LGI), an analogue of Bellś inequality involving correlations of measurements of one observable on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. In this work, we investigate its implications in the context of neutrino flavour ( $ν_{e}^{L}\leftrightarrowν_μ^{L}$ ) and spin ( $ν_{e}^{L}\leftrightarrowν_{e}^{R}$ ) oscillations in the presence of a constant transverse magnetic field. For systems with strong magnetic fields, we show that, for both cases, there are length regions $ΔL$ where the LGI is violated, as quantified by the correlator functions $K_{3}$ and $K_{4}$ .The Leggett-Garg inequality (LGI), an analogue of Bellś inequality involving correlations of measurements of one observable on a system at different times, stands as one of the hallmark tests of quantum mechanics against classical predictions. In this work, we investigate its implications in the context of neutrino flavour ($ν_{e}^{L}\leftrightarrowν_μ^{L}$) and spin ($ν_{e}^{L}\leftrightarrowν_{e}^{R}$) oscillations in the presence of a constant transverse magnetic field. For systems with strong magnetic fields, we show that, for both cases, there are length regions $ΔL$ where the LGI is violated, as quantified by the correlator functions $K_{3}$ and $K_{4}$.

quant-pharXiv:2606.04412Acta Physica Polonica BJun 4, 20260 citations

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

Ricardo Zamora Barrios, M. A. Acero

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.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.

arXiv:2401.00240Dec 30, 20230 citations

10\sigma

10σ , and of over 90

\%

% of theoretical predictions, while the KamLAND data exhibit violation of

1.9\sigma

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.

ν_{e}^{L}\leftrightarrowν_μ^{L}

) and spin (

ν_{e}^{L}\leftrightarrowν_{e}^{R}

) oscillations in the presence of a constant transverse magnetic field. For systems with strong magnetic fields, we show that, for both cases, there are length regions

ΔL

where the LGI is violated, as quantified by the correlator functions

K_{3}

and

K_{4}