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 $\eta_p$ 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 $0<\eta_m<1$, the QFIM in $(P,\chi,\eta_m)$ is diagonal, with $\mathcal{H}^{\rm mode}_{\chi\chi}=C_{\eta_m}^2$ and $\mathcal{H}^{\rm mode}_{\xi_m\xi_m}=C_{\eta_m}^2/(1-\eta_m^2)$, where $\xi_m=-\ln\eta_m$. 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 $(\theta_{23},\delta_{\rm CP},\xi_{31},g)$ at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At $\Gamma_0=10^{-23}\,\mathrm{GeV}$, the fixed-coordinate ratio $\mathcal{F}^{\rm flav}_{\delta\delta}/\mathcal{H}_{\delta\delta}$ is approximately $0.010$, $0.013$, and $0.105$, respectively; all three points show strong $\theta_{23}$--$\xi_{31}$ 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.