Wave-particle duality and entanglement in neutrino oscillation

TL;DR

This paper extends wave-particle complementarity to a quantum-triality framework for three-flavor neutrino oscillations by incorporating detector--propagation entanglement within a density-matrix formalism. It derives explicit expressions for predictability, visibility, and I-concurrence-based entanglement, showing that $\mathcal{P}^2 + \mathcal{V}^2 + \mathcal{E}^2 = 1$, with $\mathcal{P}^2 = 2(P_{\mu\mu}^2+P_{\mu e}^2+P_{\mu\tau}^2) - 1$, $\mathcal{V}^2 = 2(P_{\mu\mu}P_{\mu e}+P_{\mu\mu}P_{\mu\tau})$, and $\mathcal{E}^2 = 2(P_{\mu\mu}P_{\mu e}+P_{\mu\mu}P_{\mu\tau}+2P_{\mu e}P_{\mu au})$. Applying this to DUNE and T2K with GLoBES, the study shows the triality balance persists across vacuum and matter regimes, and at the first oscillation maximum both particle- and wave-like information can be accessed via $\mathcal{P}^2$ and $\mathcal{E}^2$ while $\mathcal{V}^2$ captures additional coherence distributed across the system. The results highlight how quantum correlations extend wave--particle duality to multipartite neutrino systems and offer a unified interpretation of oscillations grounded in quantum information theory.

Abstract

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.

Figures (2)

• Figure 1: Three-flavor neutrino oscillations as a natural realization of triality. The visibility $\mathcal{V}^{2}$, predictability $\mathcal{P}^{2}$, and entanglement $\mathcal{E}^{2}$ are shown as functions of neutrino energy for T2K with baseline of 295 km. The three quantities exchange dominance across the energy spectrum while preserving the exact triality relation. Entanglement monogamy emerges, with two flavors maximally correlated while the third decouples.
• Figure 2: Triality condition in the three-flavor case at a DUNE baseline. Oscillation dynamics generate regimes of high visibility (wave-like behavior), strong predictability (particle-like behavior), and maximal entanglement (mixed states). The interplay among the three quantities demonstrates flavor monogamy,i.e., whenever two flavors are maximally entangled, the third is excluded. The residual plot verifies $\mathcal{P}^2 + \mathcal{V}^2 + \mathcal{E}^2 = 1$ across the full energy range.