Exploring Quantumness at Long-Baseline Neutrino Experiments

TL;DR

The paper addresses whether long-baseline neutrino oscillations exhibit quantum behavior that violates classical macrorealism, tested via Leggett–Garg inequalities. It develops a data-driven LGI framework using energy-triplet strings, multiple sign configurations ($K_3^{Q++},K_3^{Q+-},K_3^{Q-+},K_3^{--}$) and their classical FC/EF analogs, a RMS $z$-score metric, and split-Gaussian sampling to handle asymmetric uncertainties; it computes LGI violations for MINOS, NOvA, T2K, and DUNE and compares across experiments. Key contributions include explicit quantum and classical string expressions in terms of survival probabilities, a robust energy-triplet construction that accounts for bin widths, uncertainty propagation via split-Gaussian sampling, and quantitative significances showing strong quantumness, notably ~$14\sigma$ for T2K and $>5\sigma$ for NOvA and DUNE projections. The results provide a rigorous framework for probing quantumness in macroscopic propagation and offer guidance for future experiments and analyses in neutrino physics.

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 $5σ$.

Figures (9)

• Figure 1: $K_3^{Q++}$ (left panel) and $K_3^{\mathrm{max}}$ (right panel) for the neutrino energies accessible at the NOvA experiment. The axes correspond to neutrino energies $E_{31}$ and $E_{21}$ (see \ref{['sec:application_energy']}), with the shaded region denoting the disallowed values of $E_{32}$ (corresponding to invalid energy triplet choices). The colorful regions denote $K_3 > 1$ values, where the nonclassical behavior of the NOvA experiment may be expected.
• Figure 2: Schematic diagram representing the overlap between the generated energy bin $(\widetilde{E}_{31}^L, \widetilde{E}_{31}^R)$ and $k^{th}$ experimental energy bin $(E_{k}^L, E_{k}^R)$. The gray shaded area corresponds to the overlapping region where its left and right boundaries are defined by $I_L =\max(E_{k}^L, \, \widetilde{E}_{31}^L)$ and $I_R =\min(E_{k}^R, \, \widetilde{E}_{31}^R)$, respectively.
• Figure 3: Schematic diagram representing the overlap between the generated energy bin $(\widetilde{E}_{31}^L, \widetilde{E}_{31}^R)$ and two experimental energy bins ($m$ and $n$).
• Figure 4: Probability density function obtained through a split-Gaussian sampling of an asymmetric mock oscillation probability distribution, with mean $\mu = 0.5$, and upper and lower standard deviations given by $\sigma_+ = 0.1$, and $\sigma_- = 0.05$, for $10^6$ MC samples.
• Figure 5: Fraction of energy triplets that violate the Leggett--Garg inequality (LGI) for the four considered long-baseline experiments. The red histograms correspond to the quantum scenario and show that a large fraction of triplets exceeds the classical bound. The cyan histograms represent the classical factorized correlator (FC) method, employed for all 4 LG strings. The gray histograms correspond to the classical exponential fit (EF) method. Comparing the three cases, the quantum distributions clearly exhibit LGI violations, while the classical cases remain concentrated at comparatively smaller values.