Quantum Estimation under Decoherence in Neutrino Oscillations: Quantum Resources, Flavor Accessibility, and Multiparameter Incompatibility

Neutrino oscillations offer an interferometric setting for open-system dynamics, quantum resources, and parameter estimation. We distinguish two often-conflated statistical families: propagation-basis dephasing uses a survival factor η p to damp interference before flavor projection, changing flavor probabilities; effective flavor-mode dephasing suppresses only off-diagonal coherence of a single-particle, two-mode state while fixing its populations. For the two-flavor mode state, we derive exact concurrence, entanglement of formation, and local quantum uncertainty, and reduce one-sided projective discord to a one-parameter optimization. For 0<P<1 and 0<η m<1, the QFIM in (P,χ,η m) is diagonal, with H mode χχ=C η m squared and H mode ξ mξ m=C η m 2/(1-η m 2), where ξ m=- η m. For propagation-basis dephasing, basis-matched QFI and flavor FI separate dynamical information loss from measurement inaccessibility for the mixing angle, mass-squared splitting, and dephasing rate. A monochromatic three-flavor benchmark evaluates the mixed-state QFIM, flavor FIM, and SLD incompatibility for (θ 23,δ CP,ξ 31,g) at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At Γ 0=10-23, GeV, the fixed-coordinate ratio F flav δδ/H δδ is approximately 0.010, 0.013, and 0.105, respectively; all three points show strong θ 23 -- ξ 31 incompatibility. A single-energy flavor measurement supplies only two independent probabilities, so its four-parameter FIM is rank deficient: these diagonal ratios are conditional diagnostics, not joint four-parameter sensitivities. These are state-level information-geometric benchmarks, not event-level sensitivity forecasts.