# Measuring a QED cross section via a witness particle

## TL;DR

This paper proposes a method to measure the QED scattering cross section using a witness particle entangled with a third particle, revealing measurable coherence effects linked to the scattering process.

## Contribution

It introduces a novel approach to infer the total scattering cross section through coherence measurements on an entangled witness particle in a QED process.

## Key findings

- Coherence terms relate to the total cross section.
- Measurable $\sigma_x$ and $\sigma_y$ are proportional to the cross section.
- Correlation distributions among particles change after scattering.

## Abstract

We consider a QED scattering ($AB\rightarrow AB$), in which $B$ is initially entangled with a third particle ($C$) that does not participate directly in the scattering. The effect of the scattering over $C$'s final state is evaluated and we note coherence (off-diagonal) terms are created, which lead to non null values for $\langle \sigma_x\rangle$ and $\langle \sigma_y\rangle$ that are, in principle, measurable in a Stern-Gerlach apparatus. We chose a particular QED scattering ($e^+e^-\rightarrow\mu^+\mu^-$) and found that $\langle \sigma_x\rangle$ and $\langle \sigma_y\rangle$ are proportional to the total cross section ($\sigma_{\text{total}}$) of the $AB$ scattering, besides being maximal if $BC$'s initial state is taken as a Bell basis. Furthermore, we calculated the initial and final mutual informations $I_{AC}$ and $I_{BC}$, and noticed an increase (decrease) in $I_{AC}$ ($I_{BC}$), which indicates that, after $AB$ interact, the total amount of correlations (quantum $+$ classical) are distributed among the $3$ subsystems.