Quantum Fisher Information Revealing Parameter Sensitivity in Long-Baseline Neutrino Experiments

Abstract

Determination of the leptonic CP-violating phase $\hat{I}{´}_{\mathrm{CP}}$, the atmospheric mixing angle $\hat{I}{¸}_{23}$, and the mass-squared difference $\hat{I}”m_{31}^2$ constitutes a primary objective of current and next-generation long-baseline neutrino experiments. We employ QFI (QFI) to establish fundamental precision bounds on single-parameter estimation in three-flavor $\hat{I}{½}_{\hat{I}}¼\to \hat{I}{½}_e$ oscillations, treating the neutrino as an evolving pure quantum state. Computing QFI as a function of the baseline-to-energy ratio $L/E$ for benchmark parameter sets from NuFit-6.0, we find distinct sensitivity hierarchies and $L/E$-dependent structures. Specifically, $\hat{I}{´}_{\mathrm{CP}}$ and $\hat{I}{¸}_{23}$ exhibit bimodal QFI profiles with peaks at $L/E\sim 500$ and $1500km/GeV$, corresponding to the first and second oscillation maxima, reaching $F_Q(\hat{I}{´}_{\mathrm{CP}})\sim 0.15$ and $F_Q(\hat{I}{¸}_{23})\sim 15$, respectively. In contrast, $\hat{I}”m_{31}^2$ displays a unimodal structure peaking at $L/E\sim 1000$--$1200km/GeV$ with $F_Q(\hat{I}”m_{31}^2)\sim 3\times 10^6$, reflecting its role in setting the oscillation length scale.

17 pages, preprint