Revealing precision bounds on neutrino oscillation parameters with quantum estimation theory

Quantum estimation theory provides ultimate precision bounds on parameter estimation, independent of experimental setups. In this article, we apply this theoretical framework to neutrino oscillations, aiming to clarify some subtle issues and reveal the maximum achievable precision of oscillation parameters. First, taking the example of two-flavor oscillations, we clarify how the quantum Fisher information (QFI) depends on the choice of bases when the basis transformation itself involves the parameters in question. Then, for three-flavor oscillations, we compute the QFI matrix for electron and muon neutrino states in the flavor basis and derive analytical expressions and numerical results for both diagonal and off-diagonal elements. The implications of off-diagonal correlations for multiparameter estimation are discussed, and the quantum Cram\'{e}r-Rao bounds on the precision of oscillation parameters for typical reactor and long-baseline accelerator neutrino experiments are obtained. Our results establish a theoretical benchmark for the ultimate precision achievable in future neutrino oscillation experiments.