Investigation of entanglement deterioration due to multi-photon pairs using photon number resolving detector

Polarization-entangled photon pairs generated by spontaneous parametric down-conversion are pivotal for quantum information applications, but multi-photon pair emissions can degrade entanglement quality and threaten communication security. Here, we present a comprehensive theoretical and experimental study of how multi-photon pair generation affects the Bell parameter in a Sagnac-based polarization-entangled photon source. By employing photon number resolving (PNR) parallel superconducting nanowire single-photon detectors, we successfully isolate and quantify the impact of single, double, and triple photon pair events on the entanglement parameter. Our results reveal that increased multi-photon contributions lead to a marked reduction in the Bell parameter, with experimental data aligning closely with our theoretical predictions. This degradation arises primarily from accidental coincidences associated with multi-photon events. The findings underscore the critical role of PNR detection in mitigating vulnerability, such as photon number splitting attacks in entanglement-based quantum key distribution protocols, suggesting that minimizing multi-photon pair generation and real-time photon number resolution are essential for achieving robust, secure quantum communication.