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. By considering three-flavor oscillation along with the possible entanglement between the detector and the propagation states, we extend beyond the usual wave-particle duality and arrive at a more complete triality description involving predictability, visibility, and entanglement. Using reduced density matrices and considering I-concurrence as an entanglement measure, we show that the total information carried by the system is conserved and naturally organized through the relation P 2 + V 2 + 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 DUNE and 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.