Wave-particle duality and entanglement in neutrino oscillation

We investigate wave–particle–entanglement complementarity in three-flavor neutrino oscillations within a quantum information–theoretic framework. Treating neutrino flavor evolution as an open quantum system and explicitly accounting for detector–propagation correlations, we extend the conventional wave–particle duality relation to a triality relation involving predictability, visibility, and entanglement. Using reduced density matrices and I-concurrence as a quantitative measure of entanglement, we demonstrate that the total information content of the system satisfies the relation ${\mathcal{P}}^2+{\mathcal{V}}^2+{\mathcal{E}}^2=1$. While predictability and visibility exhibit the expected complementary behavior, we show that entanglement encodes additional wave-like information that is not captured by visibility alone. We apply our formalism to realistic long-baseline neutrino experiments, namely $\mathsf{\text{DUNE}}$ and $\mathsf{\text{T2K}}$, and find that at the first oscillation maximum, a simultaneous characterization of the particle-like and wave-like nature of neutrinos becomes possible through the combined measurement of predictability and entanglement. Our results provide a unified operational interpretation of neutrino oscillations and highlight the role of quantum correlations in extending wave–particle duality to multipartite systems.