中微子振荡的操作量子估计理论：可识别性、可达性与谱精度界限
Operational quantum estimation theory for neutrino oscillations: identifiability, attainability, and spectral precision bounds
AI总结：
该研究构建中微子振荡的操作量子估计框架，分离态、测量与事件信息，分析QFI的秩、联合可达性，通过DUNE GLoBES验证并揭示局部界限与全局实验灵敏度的关联。
AI中文摘要：
量子费希尔信息（QFI）界定了测量选择前态编码的精度，但未确立可识别性、联合可达性或探测器灵敏度。我们针对三味中微子振荡构建了一个操作框架，将态、测量与重建事件信息分离开。在固定基线、能量、源味及物质分布下，传播后的态是纯qutrit，其六坐标QFI的秩至多为4；可分辨的宽带分量能恢复秩，因为聚合核等于其活跃核的交集。我们利用量子曲率、精确纯态Holevo成本及数值原始-对偶括号分析联合可达性，并将信息通过味投影、探测器响应、泊松采样及扰动轮廓传播。公共DUNE GLoBES配置的独立实现，将参考谱的相对误差重现至3.87×10^-16，轮廓似然曲率重现至3.26×10^-6；在声明的标度与容差下，其264个分箱的事件信息在所有176个已记录物理点的数值秩为6，而保留任意四个规则总和的秩至多为4，最弱记录在声明的实际阈值处有效秩为5；条件似然试点还显示有限网格覆盖不足及对辅助测量集合的依赖性。该框架可识别局部量子或费希尔界限何时不支持全局实验灵敏度主张。
英文摘要：
Quantum Fisher information (QFI) bounds state-encoded precision before measurement choice but does not establish identifiability, joint attainability, or detector sensitivity. We develop an operational framework for three-flavor oscillations that separates state, measurement, and reconstructed-event information. At fixed baseline, energy, source flavor, and matter profile, the propagated state is a pure qutrit, so its six-coordinate QFI has rank at most four. Resolved broadband components can restore rank because the aggregate kernel equals the intersection of their active kernels. We analyze joint attainability using quantum curvature, exact pure-state Holevo costs, and numerical primal-dual brackets, and propagate information through flavor projection, detector response, Poisson sampling, and nuisance profiling. An independent implementation of the public DUNE GLoBES configuration reproduces the reference spectra to relative error $3.87\times10^{-16}$ and the profiled likelihood curvature to $3.26\times10^{-6}$. Under the declared scaling and tolerance, its 264-bin event information has numerical rank six at all 176 documented physics points, whereas any four retained rule totals have rank at most four. The weakest record has effective rank five at the declared practical threshold. A conditional likelihood pilot also shows finite-grid overcoverage and dependence on the auxiliary-measurement ensemble. The framework identifies when local quantum or Fisher bounds do not support global experimental-sensitivity claims.
