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 ${\mathcal{H}}_{\chi \chi }^{\mathrm{mode}}=C_{{\eta }_m}^2$ and ${\mathcal{H}}_{{\xi }_m{\xi }_m}^{\mathrm{mode}}=C_{{\eta }_m}^2/(1-{\eta }_m^2)$, 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 $({\theta }_{23},{\delta }_{\mathrm{CP}},{\xi }_{31},g)$ at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At ${\Gamma }_0=10^{-23}\mathrm{GeV}$, the fixed-coordinate ratio ${\mathcal{F}}_{\delta \delta }^{\mathrm{flav}}/{\mathcal{H}}_{\delta \delta }$ 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.

21 pages, 9 figures,