Measurement-device-independent quantum key distribution with asymmetric sources

Measurement-device-independent quantum key distribution (MDI QKD), which eliminates all the attacks from the eavesdropper to the measurement party, has been one of the most promising technologies for the implementation of end-to-end quantum networks. In practice, the asymmetry of both sources and channels is generally inevitable. Therefore, we propose a theory to analyze the performance when any two MDI users in networks communicate using asymmetric sources in distinct single or multiple temporal modes. As a specific application, we model to obtain the key rate of MDI QKD with a weak-coherent pulse source and a spontaneous parametric down-conversion source, and compare the performance to the cases with symmetric (i.e., identical) sources. The result demonstrates that the actual performance does not degrade due to the asymmetry of sources. On the contrary, it maintains at a good level over the entire distance we study. This work provides a theoretical basis for analyzing and optimizing MDI-QKD networks with asymmetric sources, thus paving the way for the practical deployment of completely asymmetric MDI-QKD networks.