Quantum states prepared by practical entanglement swapping

Entanglement swapping between photon pairs is a fundamental building block in schemes using quantum relays and quantum memories to overcome the range limits of long distance quantum key distribution. We develop a closed-form solution for the actual quantum states prepared by practical entanglement swapping, which takes into account experimental deficiencies due to inefficient detectors, detector dark counts and multi-photon-pair contributions of parametric down conversion sources. We investigate how the entanglement present in the final state of the remaining modes is affected by the practical imperfections. To test the predictions of our theory, comparison with experimental entanglement swapping is provided.