Quantum Estimation Theory Limits in Neutrino Oscillation Experiments

TL;DR

This paper uses quantum estimation theory to evaluate the optimality of flavor measurements in neutrino oscillation experiments, revealing their strengths and limitations for different parameters and guiding future experimental design.

Contribution

It provides a quantitative analysis of the information content in flavor measurements for neutrino parameters, highlighting their optimality for some and suboptimality for others like δ_CP.

Findings

Flavor measurements saturate QFI for mixing angles at the first oscillation maximum.

They are far from optimal for δ_CP, with sensitivity improving at the second maximum.

The quantum information about δ_CP is intrinsically limited compared to mixing angles.

Abstract

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 $\theta_{13}$, $\theta_{23}$, and $\theta_{12}$, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for $\delta_{CP}$. In particular, only a small fraction of the available information on $\delta_{CP}$ is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESS$\nu$SB, a planned facility. Second, the QFI associated with $\delta_{CP}$ 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 $\delta_{CP}$ 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.