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.