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 <sigma(x)> and <sigma(y)> that arc, in principle, measurable in a Stern-Gerlach apparatus. We chose a particular QED scattering (e(+)e(- )-> mu(+)mu(-)) and found that <sigma(x)> and <sigma(y)> are proportional to the total cross section (sigma(total)) 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 I-AC: and I-BC, and noticed an increase (decrease) in I-AC (I-BC), which indicates that, after AB interact, the total amount of correlations (quantum + classical) is distributed among the 3 subsystems.