Entanglement Entropy of Compton Scattering with a Witness

TL;DR

This paper investigates how entanglement entropy and mutual information evolve in Compton scattering involving a witness photon, revealing that entanglement is preserved and correlations can develop without direct interaction.

Contribution

It derives the reduced density matrices and entanglement entropy changes in Compton scattering with a witness particle, highlighting unitarity constraints and correlation formation.

Findings

Witness photon entanglement entropy remains unchanged after scattering.

Nonzero mutual information develops between electron and witness photon.

A ratio involving Thomson cross-section and scattering area appears in key quantities.

Abstract

Unitarity and the optical theorem are used to derive the reduced density matrices of Compton scattering in the presence of a witness particle. Two photons are initially entangled wherein one photon participates in Compton scattering while the other is a witness, i.e. does not interact with the electron. Unitarity is shown to require that the entanglement entropy of the witness photon does not change after its entangled partner undergoes scattering. The final mutual information of the electronic and witness particle's polarization is nonzero for low energy Compton scattering. This indicates that the two particles become correlated in spite of no direct interaction. Assuming an initial maximally entangled state, the change in entanglement entropy of the scattered photon's polarization is calculated in terms of Stokes parameters. A common ratio of areas occurs in the final reduced density matrix elements, von Neumann entropies, Stokes parameter, and mutual information. This common ratio consists of the Thomson scattering cross-section and an accessible regularized scattering area.