Quantum Estimation in QED Scattering

TL;DR

This paper investigates the fundamental limits of estimating parameters in QED scattering processes by computing quantum Fisher information and comparing it to classical bounds, providing insights into measurement precision in quantum field interactions.

Contribution

It introduces a numerical approach to compute quantum Fisher information for scattering parameters in QED, analyzing the estimation bounds for internal degrees of freedom.

Findings

QFIM computed for electron-muon and Compton scattering.

Quantum Cramér-Rao bounds established for scattering parameters.

Comparison between quantum and classical Fisher information bounds.

Abstract

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 centre-of-mass three-momentum magnitude and polar scattering angle through measurements on the internal degrees of freedom (helicity or polarisation) 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 Cram\'er-Rao lower bounds on the estimations at hand. Further, we compare such ultimate bounds to the classical Fisher information of local polarisation or helicity degrees of freedom.