Multiparameter Quantum Estimation and Degeneracy Structure in Three-Flavor Neutrino Oscillations

Achieving precision measurements of neutrino oscillation parameters and resolving parameter degeneracies remain central challenges in neutrino physics. This work presents a systematic investigation of three-flavor neutrino oscillations within the framework of quantum estimation theory using the quantum Fisher information matrix (QFIM). The behavior of all six independent elements of the QFIM associated with the parameters theta23, deltaCP, and Delta(m31)^2 is analyzed, and the impact of parameter correlations on the quantum Cram\'er-Rao bound is studied. Furthermore, we demonstrate that parameter degeneracies in neutrino oscillation probabilities do not necessarily imply indistinguishability of the underlying quantum states. By employing quantum fidelity and the QFIM, we show that degenerate parameter sets can exhibit distinct quantum-information characteristics that remain hidden at the probability level, revealing quantum-state differences between probability-degenerate solutions.