Researchers have applied quantum estimation theory (QET) to determine the fundamental precision limits in measuring neutrino oscillation parameters. This theoretical framework allows for the establishment of maximum bounds on the accuracy with which these parameters can be determined, independent of specific experimental setups. The work aims to clarify subtle issues and provide a theoretical benchmark for future neutrino experiments.

The study first addressed two-flavor neutrino oscillations, analyzing how the quantum Fisher information (QFI) is affected by the choice of measurement bases when these bases themselves depend on the parameters to be estimated. Subsequently, the analysis was extended to three-flavor oscillations, computing the QFI matrix for electron and muon neutrino states in the flavor basis. Analytical expressions and numerical results were obtained for both diagonal and off-diagonal elements of this matrix.

The implications of off-diagonal correlations for multiparameter estimation were discussed. Finally, quantum Cramér-Rao bounds on the precision of oscillation parameters were derived, applying them to typical scenarios of reactor and long-baseline accelerator neutrino experiments. These results establish a theoretical benchmark that defines the ultimate precision achievable in determining neutrino oscillation parameters, serving as a guide for the design and optimization of future experimental campaigns.