Measuring QED cross sections via entanglement

We considered a QED scattering (AB→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 was evaluated and we noted coherence (off-diagonal) terms were created, which led to non-null values for ⟨σₓ⟩ and ⟨σy⟩ that are, in principle, measurable in a Stern-Gerlach apparatus. We chose a particular QED scattering (e⁺e^-→μ⁺μ^-) and found that ⟨σₓ⟩ and ⟨σy⟩ are proportional to the total cross section (σₜₒₜₐₗ) 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 information IAC and IBC, and noticed an increase (decrease) in IAC (IBC), which indicates that, after $AB$ interact, the total amount of correlations (quantum+classical) is distributed among the 3 subsystems.