Efficient twin-field quantum key distribution with heralded single-photon source

Twin-field quantum key distribution (TF-QKD) can overcome the fundamental rate-loss limit in the point-to-point QKD without a quantum repeater, so as to realize key distribution over long distance. In general, weak coherent pulse (WCP) emitted from the attenuated laser is often used as the photon source for TF-QKD and its variants, however, the key generation rate and transmission distance may be restricted for TF-QKD protocols using this type of photon source as it contains a large proportion of vacuum part. Another candidate of photon source within reach of current technology is the heralded single-photon source (HSPS). In this paper, we propose two TF-QKD variants with HSPS and provide the analytical derivation of upper bounds of yields separately with active and passive decoy-state methods. Numerical simulations show that the active decoy-state TF-QKD with HSPS (referred to as Protocol (1) achieves higher secret key rate and tolerates more large transmission loss than the original TF-QKD with WCP source. However, since the active modulation of decoy intensities may leak additional information to the eavesdropper Eve, thus we extend the result of Protocol 1 and further propose a passive decoy-state TF-QKD with HSPS (referred to as Protocol (2). The simulation results demonstrate that the performance of Protocol 2 is close to the original active TF-QKD protocol, and its security and flexibility are further improved.