Quantum Estimation Theory Limits in Neutrino Oscillation Experiments

Measurements of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing parameters have entered a precision era, enabling increasingly stringent tests of neutrino oscillations. Within the framework of quantum estimation theory, we investigate whether flavor measurements, the only observables currently accessible experimentally, are optimal for extracting the oscillation parameters. We compute the Quantum Fisher Information (QFI) and the classical Fisher Information (FI) associated with ideal flavor projections for all oscillation parameters, considering accelerator muon (anti)neutrino and reactor electron antineutrino beams propagating in vacuum. Two main results emerge. First, flavor measurements saturate the QFI at the first oscillation maximum for θ₁₃, θ₂₃, and θ₁₂, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for δ_CP. In particular, only a small fraction of the available information on δ_CP is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESSνSB, a planned facility. Second, the QFI associated with δ_CP is approximately one order of magnitude smaller than that of the mixing angles, indicating that the neutrino state intrinsically encodes less information about CP violation. Nevertheless, this quantum bound lies well below current experimental uncertainties, implying that the present precision on δ_CP is not fundamentally limited. Our results provide a quantitative framework to disentangle fundamental from practical limitations and establish a benchmark for optimizing future neutrino facilities.