The linear constraint of secret key rate capacity is overcome by the tiwn-field quantum key distribution (QKD). However, the complex phase-locking and phase-tracking technique requirements throttle the real-life applications of twin-field protocol. The asynchronous measurement-device-independent (AMDI) QKD or called mode-pairing QKD protocol [PRX Quantum 3, 020315 (2022), Nat. Commun. 13, 3903 (2022)] can relax the technical requirements and keep the similar performance of twin-field protocol. Here, we propose an AMDI-QKD protocol with a nonclassical light source by changing the phase-randomized weak coherent state to a phase-randomized coherent-state superposition (CSS) in the signal state time window. Simulation results show that our proposed hybrid source protocol significantly enhances the key rate of the AMDI-QKD protocol, while exhibiting robustness to imperfect modulation of nonclassical light sources.
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