We consider a QED scattering ($AB\rightarrow AB$), 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 is evaluated and we note coherence (off-diagonal) terms are created, which lead to non null values for $\langle \sigma_x\rangle$ and $\langle \sigma_y\rangle$ that are, in principle, measurable in a Stern-Gerlach apparatus. We chose a particular QED scattering ($e^+e^-\rightarrow\mu^+\mu^-$) and found that $\langle \sigma_x\rangle$ and $\langle \sigma_y\rangle$ are proportional to the total cross section ($\sigma_{ \text{ total}}$) 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 informations $I_{ AC}$ 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) are distributed among the $3$ subsystems.
Categories: hep-th quant-ph