Stokes-parameter representation for Compton scattering of entangled and classically correlated two-photon systems

A Stokes parameter representation for two-photon systems is developed to calculate cross sections for both entangled and classically correlated mixed states scattering off unpolarized and polarized Compton electrons. The cross section of Compton scattering for pairs of maximally entangled annihilation photons, generated by the disintegration of para-positronium, is compared with classical analogs. An analysis of the symmetrical properties and basis independence of these systems is conducted to elucidate the observed differences. We propose a method to establish an upper bound for identifying correlations influenced by entanglement. Furthermore, we calculate the cross section for Compton scattering of annihilation photons from spin-polarized electrons. A qualitative analysis reveals a contradiction to the contemporary assumption that Compton scattering acts as an entanglement kill switch. These findings contribute to a broader understanding of photon systems and their behavior in various scattering scenarios. Although the primary focus of this article is on Compton scattering, the formalism can be adapted to other interactions, provided that the Mueller matrix representation of the interaction is available.