**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.