Quantum estimation in neutrino oscillations

TL;DR

This paper applies Quantum Estimation Theory to neutrino oscillations, analyzing the precision limits of measuring mixing parameters and the role of entanglement, with implications for experimental neutrino physics.

Contribution

It computes the Quantum Fisher Information for neutrino mixing angles and examines the effectiveness of flavor measurements and entanglement in parameter estimation.

Findings

Mass measurements achieve optimal precision according to QFI.

Flavor measurements are optimized at specific neutrino times-of-flight.

Single-particle entanglement does not enhance measurement precision.

Abstract

Neutrino oscillations are at the forefront of advances in Physics beyond the Standard Model. Increasing accuracy in measurements of the neutrino mixing matrix is an important challenge in current experiments. It depends on parameters that do not directly correspond to observables of the neutrino system. This type of estimation problem is handled by Quantum Estimation Theory (QET) via the Fisher Information (FI) and the Quantum Fisher Information (QFI). In this work, we analyze two-flavor neutrino oscillations within the framework of QET. We compute the QFI for the mixing angle $\theta$ and show that mass measurements are the ones that achieve optimal precision. We also study the FI associated with flavor measurements and show that they are optimized at specific neutrino times-of-flight. Therefore, although the usual population measurement does not realize the precision limit set by the QFI, it can in principle be implemented with the best possible sensitivity to $\theta $. We study how these quantifiers relate to the single-particle, mode entanglement. We demonstrate that this form of entanglement does not enhance neither of them. In particular, this shows that in single-particle settings, entanglement is not directly connected with the optimal precision in metrological tasks.