Measurement-Device-Independent Quantum Key Distribution with Practical Spontaneous Parametric Down-Conversion Sources

Measurement-device-independent (MDI) quantum key distribution (QKD) closes all the loopholes in the detection side, which greatly improves the practical security of QKD. Spontaneous parametric downconversion (SPDC) sources play a significant role in MDI QKD by using the heralding strategies to achieve unique features, such as the passive-decoy method, which reduces side-channel information leakage from the source. However, photon pairs from realistic SPDC sources are often spectrally entangled. This lowers the Hong-Ou-Mandel (HOM) interference visibility, and thus increases the QKD error rate. Unfortunately, research efforts so far have not considered this effect quantitatively. This leads to an overestimation in the secure key rate; therefore their results cannot be applied to practical sources. In this article, we close this gap by decomposing the spectral entangled state into Schmidt eigenstates, then find their contributions to the secure key rate. In addition, our work allows an accurate optimization of pumping and filtering conditions to maximize the final key rate. We note that our model is general and can be applied to other quantum information processes involving HOM interference, such as quantum teleportation, entanglement swapping, and quantum computation.