Quantum Analysis of Polarization Entanglement Degradation Induced by Multiple-Photon-Pair Generation

Polarization-encoded entanglement remains the simplest platform for the generation, manipulation, and visualization of entangled-photon states. While quantum dots have the potential to emit on-demand polarization entanglement, spontaneous-parametric-down-conversion (SPDC) sources remain the leading method for the generation of polarization-entangled states. SPDC sources suffer from the potential to produce multiple photon pairs in a single pass of an experiment. These multiple pairs have been shown to have negative impacts on quantum experiments involving entanglement. In this work, we now provide a rigorous theoretical model for the loss of entanglement due to additional photon pairs. This is seen as a reduction in a possible measurement of the Clauser-Horne-Shimony-Holt (CHSH) parameter. We perform these calculations for two different methods for the generation of polarization entanglement involving SPDC. The results agree with other observations presented in the literature. We also find that, even for small mean photon numbers, the CHSH parameter is reduced linearly, demonstrating that multiple photon pairs have a critical impact on the entanglement in the system.