Entanglement distribution in Bhabha scattering with an entangled spectator particle

We analyze how entanglement is generated and distributed in a Bhabha scattering process $(e^{-}{e}^{+}\to e^{-}{e}^{+})$ at tree level. In our setup an electron $A$ scatters with a positron $B$, which is initially entangled with another electron $C$ (spectator), that does not participate directly to the process. We find that the QED scattering generates and distributes entanglement in a nontrivial way among the three particles; the correlations in the output channels $AB$, $AC$, and $BC$ are studied in detail as functions of the scattering parameters and of the initial entanglement weight. Although derived in a specific case, our results exhibit some general features of other similar QED scattering processes, for which the extension of the present analysis is straightforward.