The Entanglement of Elastic and Inelastic Scattering

TL;DR

This paper introduces a new measure called scattering entropy to quantify entanglement in projectile-target interactions, showing that entanglement correlates with inelastic interaction strength and approaches maximum in high-energy proton-proton scattering.

Contribution

It proposes a novel entanglement measure based on the unitarity of the S-matrix and demonstrates its effectiveness through simple models and analysis of experimental data.

Findings

Entanglement increases with inelastic interaction strength.

Maximum entanglement corresponds to the classical black disk model.

High-energy $pp$ scattering data shows near-maximal entanglement above 1 GeV.

Abstract

The entanglement properties of systems in which elastic and inelastic reactions occur in projectile-target interactions is studied. A new measure of entanglement, the scattering entropy, based on the unitarity of the $S-$matrix (probability conservation), is suggested. Using simple models for both low- and high-energy interactions, the amount of entanglement is found to track with the strength of the inelastic interaction. The familiar example of the classical ``black disk", total absorption, model is found to correspond to maximum entanglement. An analysis of high-energy $pp$ scattering data shows that entanglement is near maximum for lab energies greater than about 1 GeV, showing that the total absorption model is a reasonable starting point for understanding the data.