Quantum states prepared by real-world entanglement swapping and implications for Quantum Key Distribution

Entanglement swapping between photon pairs is a fundamental building block in schemes using quantum relays or quantum repeaters to overcome the range limits of long distance quantum key distribution. We have developed a closed-form solution for the actual quantum states prepared by realistic 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. Using our theory, we investigate how the QBER and the Secret Key Rate are affected by the real-world imperfections in a QKD experiment based on a BBM92 protocol with a single practical entanglement swapping. In particular, we provide the optimal photon-pair production rate of parametric down conversion sources for a given distance between Alice and Bob.