Tripartite Entanglement as a Probe of Neutrino Mass Hierarchy, CP Violation, and Non-Standard Interactions

Abstract

We investigate global tripartite quantum entanglement in three-flavor neutrino oscillations as a tool for probing the neutrino mass hierarchy and CP violation. Using the linear entropy formalism, we compute the global entanglement entropy for an initial electron neutrino state as a function of L/E, comparing Normal Ordering (NO) and Inverted Ordering (IO) across CP phases 0, 90, 120 and 180, in vacuum and in constant-density matter rho = 2.8g/cm^3, L = 1300km). We define the hierarchy sensitivity diagnostic dell S and show that MSW matter effects amplify dell S by roughly a factor of two relative to vacuum, with peak sensitivity at L/E approx 655km/GeV (approx 2GeV at the DUNE baseline). For antineutrinos the diagnostic is near-perfectly antisymmetric to the neutrino case at the MSW resonance, with deviations directly encoding dell CP. ANnother diagonostic defined here separates the matter hierarchy signal from the CP asymmetry signal in the tripartite entanglement. For non-standard interactions (NSI) parameterized by epsilon_{ee}, we find Dell S{max} is approx 0.113 + 0.105epsilon_{ee}, a linear and CP-phase-independent relation. The optimal L/E for hierarchy discrimination is stable at approx 655km/GeV for all epsilon_{ee}less than or equal to 0.2, providing a robust, NSI-independent energy recommendation for DUNE.