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 \textsf{DUNE} and \textsf{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.