Quantum estimation in QED scattering

We tackle the issue of estimating dynamical parameters in quantum electrodynamics. We numerically compute the quantum Fisher information matrix (QFIM) of physical parameters in electron-muon and Compton scattering at tree level. In particular, we consider the estimation of center-of-mass three-momentum magnitude and polar scattering angle through measurements on the internal degrees of freedom (helicity or polarization) of the scattered particles. Computations are carried out for pure and maximally mixed initial states. The QFIM values are then used to compute the quantum Cramér-Rao lower bounds on the estimations at hand. Further, we compare such ultimate bounds to the classical Fisher information of local polarization or helicity degrees of freedom.