Comparison of non-decoy single-photon source and decoy weak coherent pulse in quantum key distribution

Abstract: Advancements in practical single-photon sources (SPS) exhibiting high brightness and low $g^{(2)}(0)$ have garnered significant interest for their application in quantum key distribution (QKD). To assess their QKD performance, it is essential to compare them with the widely employed weak coherent pulses (WCPs) in the decoy state method. In this work, we analyze the non-decoy efficient BB84 protocol for an SPS, partially characterising its photon statistics by its $g^{(2)}(0)$ and mean photon number. We compare it to the 2-decoy efficient BB84 with WCPs within the finite-key analysis framework while optimizing the parameters of both protocols. Our findings indicate that the non-decoy SPS with a mean photon number of $\langle n \rangle = 0.5$ and $g^{(2)}(0) = 3.6\%$ can enhance the secure key generation over the 2-decoy WCP for block sizes under $4.66 \cdot 10^9$ sent signals ($29$ seconds of acquisition time) at a channel loss of $10$ dB ($52.5$ km of optical fibre). Additionally, we demonstrate an increase in the maximum tolerable channel loss for SPSs with mean photon number $\langle n \rangle \geq 0.0142$ at block sizes below $10^8$ sent signals ($0.62$ seconds of acquisition time). These results suggest that SPSs hold potential for key rate enhancement in short-range QKD networks, though further research is required to evaluate their key generation capabilities when integrated into the decoy method.