Fig. 1: Comparison of two-mode, one-mode and mode-pairing MDI-QKD schemes.

a Schematic diagram of a generic MDI-QKD scheme. The solid and dashed pulses yield successful and unsuccessful detection, respectively, at the measurement site. For b, c and d, each wave packet in the diagram represents two independent pulses emitted simultaneously by Alice and Bob. b In two-mode MDI-QKD schemes, the pairing of the blue pulses (as phase references) and orange pulses (as signals) is predetermined, necessitating coincidence detection. c In one-mode MDI-QKD schemes (e.g., twin-field quantum key distribution and its variants), there is no phase reference pulse, necessitating global phase locking. d In the mode-pairing MDI-QKD scheme, in accordance with the detection results, Alice and Bob pair the clicked pulses and assign them to be either reference or signal pulses, such that neither coincidence detection nor global phase locking is required.