Entanglement, steering, and separability in Compton-scattered annihilation photons

This work analyzes quantum correlations of photon pairs initially prepared in a Bell state, where one photon undergoes Compton scattering from a stationary, unpolarized electron. The evolved two-photon density matrix is analytically derived and spectrally decomposed. Concurrence and the Clauser-Horne-Shimony-Holt (CHSH) inequality evaluations identify angular regions demonstrating quantum steering correlations, entanglement without steering, and complete separability. The Peres conjecture is applied to interpret regions of entanglement lacking steering, emphasizing their limited practicality for quantum-information tasks. These results provide details potentially useful for employing Compton-scattered annihilation photons in various quantum protocols.