发表机构
LPMS, Faculty of Sciences, Ibn Tofail University; LPHE–Modeling and Simulation, Faculty of Sciences, Mohammed V University in Rabat; Centre of Physics and Mathematics, CPM, Faculty of Sciences, Mohammed V University in Rabat; College of Computing and Mathematical Sciences, Department of Applied Mathematics and Sciences and Center for Cyber-Physical Systems (C2PS), Khalifa University of Science and Technology（伊本·图费利大学理学院; 拉巴特穆罕默德五世大学理学院; 拉巴特穆罕默德五世大学理学院物理与数学中心; 阿联酋哈利法大学科学技术学院计算与数理科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文区分两种中微子振荡退相干模型，推导双味态量子资源精确表达式，并在三味基准下评估多参数QFIM与味FIM的不相容性，指出单能量测量FIM秩亏，提供态级信息几何基准。
AI 中文摘要
中微子振荡为开放系统动力学、量子资源和参数估计提供了一个干涉测量设置。我们区分了两个常被混淆的统计族：传播基退相干使用生存因子$\eta_p$在味投影前抑制干涉，改变味概率；有效味模退相干仅抑制单粒子双模态的离对角相干性，同时固定其布居数。对于双味模态，我们推导了精确的并发度、形成纠缠度和局部量子不确定性，并将单侧投影失谐简化为单参数优化。对于$0<P<1$和$0<\eta_m<1$，$(P,\chi,\eta_m)$中的QFIM是对角的，其中$\mathcal{H}^{\rm mode}_{\chi\chi}=C_{\eta_m}^2$和$\mathcal{H}^{\rm mode}_{\xi_m\xi_m}=C_{\eta_m}^2/(1-\eta_m^2)$，其中$\xi_m=-\ln\eta_m$。对于传播基退相干，基匹配的QFI和味FI将动力学信息损失与测量不可达性分开，针对混合角、质量平方分裂和退相干率。一个单色三味基准评估了在DUNE-like、T2HK-like和ESSnuSB-inspired点处$(\theta_{23},\delta_{\rm CP},\xi_{31},g)$的混合态QFIM、味FIM和SLD不相容性。在$\Gamma_0=10^{-23}\\,\mathrm{GeV}$时，固定坐标比率$\mathcal{F}^{\rm flav}_{\delta\delta}/\mathcal{H}_{\delta\delta}$分别约为$0.010$、$0.013$和$0.105$；所有三个点都显示出强烈的$\theta_{23}$--$\xi_{31}$不相容性。单能量味测量仅提供两个独立概率，因此其四参数FIM秩亏：这些对角比率是条件诊断，而非联合四参数灵敏度。这些是态级信息几何基准，而非事件级灵敏度预测。
英文摘要
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.
Comments21 pages, 9 figures,
