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

Abstract

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 $\mathcal{H}^{\rm mode}_{χχ}=C_{η_m}^2$ and $\mathcal{H}^{\rm mode}_{ξ_mξ_m}=C_{η_m}^2/(1-η_m^2)$, where $ξ_m=-\lnη_m$. 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 $(θ_{23},δ_{\rm CP},ξ_{31},g)$ at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At $Γ_0=10^{-23}\,\mathrm{GeV}$, the fixed-coordinate ratio $\mathcal{F}^{\rm flav}_{δδ}/\mathcal{H}_{δδ}$ 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.