The Quantum Channels of the Compton Scattering of an Entangled Pair of Photons

The Compton scattering of an entangled pair of photons is studied. Using the resulting reduced density matrix, we demonstrate how to derive the Kraus operators for the interaction from the underlying fundamental theory, quantum electrodynamics. The normalization of the final density matrix of the entangled photons after the interaction is crucial to obtaining the correct probabilities and correlations. The reduced density matrix of the photon, which does not participate in the interaction directly, remains unchanged. It indicates that quantum effects in quantum sensing using an entangled photon pair can be observed only through the correlations or superposition of the entire pair. We relate our results to the Stokes parameters for determining polarizations and investigating the entangled states of photons from electron-positron annihilation in astrophysical systems.