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arXiv:2601.15375 · Journal of High Energy Physics

Exploring Quantumness at Long-Baseline Neutrino Experiments

Murshed Alam, Vedran Brdar, Dibya S. Chattopadhyay

hep-phhep-exquant-phSubmitted Jan 21, 2026• Announced Jan 23, 2026• 1 citation• Revised Jul 22, 2026 (v2)

v1 · Jan 21, 2026 v2 · Jul 22, 2026

Abstract

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 $\sim 14 σ$, with NOvA and projections for DUNE also resulting in a significance of more than $5σ$.

Journal reference: JHEP 06 (2026) 221
DOI: 10.1007/JHEP06(2026)221
Comments: 30 pages, 9 figures, 2 tables

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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

\sim 14 σ

, with NOvA and projections for DUNE also resulting in a significance of more than

5σ

.

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.

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.

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 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.

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.

Violation of LGtI inequalities in the light of NO

\nu

A and T2K anomaly

Abstract The recent anomaly observed in NO

\nu

ν A and T2K experiments in standard three-flavor neutrino oscillation could potentially signal physics extending beyond the standard model (SM). For the NSI parameters that can accommodate this anomaly, we explore the violation of Leggett–Garg type inequalities (LGtI) within the context of three-flavor neutrino oscillations. Our analysis focuses on LGtI violations in scenarios involving complex NSI with

\epsilon _{e\mu }

ϵ e μ or

\epsilon _{e\tau }

ϵ e τ coupling in long baseline accelerator experiments for normal and inverted mass ordering. LGtI violation is significantly enhanced in normal ordering (NO) for

\epsilon _{e\tau }

ϵ e τ scenario for T2K, NO

\nu

ν A, and DUNE experiment set-up. We find that for inverted ordering (IO), in the DUNE experimental set-up above 8.5 GeV, the LGtI violation can be an indication of

\epsilon _{e\tau }

ϵ e τ new physics scenario.