Probing Quantum Foundations in Long-Baseline Neutrino Oscillations: Wave Packet Approach from MINOS Data to DUNE Predictions

Abstract: We investigate neutrino flavor oscillations in the wave packet formalism, extending the standard planewave treatment to incorporate the finite spatial coherence of neutrino mass eigenstates.We derive the full three flavor oscillation probability with MSW matter effects, decoherence, and localization suppression governed by the wave packet width, benchmarking against MINOS disappearance data and extending to DUNE predictions under the same parameters. To quantify how sharply the oscillation data constrain the wave packet width, we compute the classical Fisher information FC as a function of neutrino energy for both MINOS and DUNE, and show that its sensitivity is concentrated precisely in the low-energy regime where the wave-packet and plane-wave predictions diverge. Beyond the oscillation probability analysis, we compute wave particle entanglement complementarity quantities within a quantum information theoretic framework and explore the complete triality description involving entanglement, predictability, and visibility as functions of neutrino energy for both experiments such as MINOS and DUNE. We show that even when the oscillation probability is numerically indistinguishable from the planewave result, the wave packet structure leaves observable imprints in these triality measures. Our results demonstrate that the wave packet approach provides a theoretically consistent and experimentally motivated framework for probing quantum foundations in long-baseline atmospheric neutrino oscillation experiments.