Quantum estimation in neutrino oscillations

In this work, we analyze two-flavor neutrino oscillations within the framework of quantum estimation theory (QET). We compute the quantumFischer information (QFI) for the mixing angle theta and show that mass measurements are the ones that achieve optimal precision. We also study the Fischer information (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 investigate how these quantifiers relate to the single-particle, mode entanglement in neutrino oscillations. We demonstrate that this form of entanglement does not enhance either of them. In particular, our results show that in single-particle settings, entanglement is not directly connected with the enhancement of precision in metrological tasks.