Entanglement swapping with autonomous polarization-entangled photon pairs from a warm atomic ensemble

Entanglement swapping forms a key concept in the realization of scalable quantum networks and large-scale quantum communication. For the practical implementation of entanglement swapping, completely autonomous entanglement sources and a joint Bell-state measurement (BSM) between two independent photons are essential. Here, we experimentally demonstrate entanglement swapping between two independent polarization-entangled photon-pair sources obtained via spontaneous four-wave mixing (SFWM) in a Doppler-broadened atomic ensemble of ${^{87}}{\rm Rb}$⁸⁷Rb atoms. From the joint BSM, we estimate the ${\rm S}$S parameter in the Clauser-Horne-Shimony-Holt (CHSH) form of Bell's inequality and confirm the violation of the Bell-CHSH inequality by ${\rm S}={2.32} \pm {0.07}$S=2.32±0.07 with 4.5 standard deviations. We believe that this work is an important step toward realizing practical scalable quantum networks.