Operational quantum estimation theory for neutrino oscillations: identifiability, attainability, and spectral precision bounds

Abstract

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.