A Decoy-like Protocol for Quantum Key Distribution: Enhancing the Performance with Imperfect Single Photon Sources

Quantum key distribution (QKD) relies on single photon sources (SPSs), e.g. from solid-state systems, as flying qubits, where security strongly requires sub-Poissonian photon statistics with low second-order correlation values \$g^{(2}(0)\$). However, achieving such low \$g^{(2)}(0)\$ remains experimentally challenging. We therefore propose a decoy-like QKD protocol that relaxes this constraint while maintaining security. This enables the use of many SPSs with \$g^{(2)}(0) > \$0.1, routinely achieved in experiments but rarely considered viable for QKD. Monte Carlo simulations and our experiment from defects in hexagonal boron nitride show that, under linear loss, \$g^{(2)}(0)\$ remains constant, whereas photon-number-splitting (PNS) attacks introduce nonlinear effects that modify the measured \$g^{(2)}(0)\$ statistics. Exploiting this \$g^{(2)}(0)\$ variation as a diagnostic tool, our protocol detects PNS attacks analogously to decoy-state methods. Both single- and two-photon pulses consequently securely contribute to the secret key rate. Our protocol outperforms the Gottesman--Lo--Lutkenhaus--Preskill (GLLP) framework under high channel loss across various solid-state SPSs and is applicable to the satellite-based communication. Since \$g^{(2)}(0)\$ can be extracted from standard QKD experiments, no additional hardware is required. The relaxed \$g^{(2)}(0)\$ requirement simplifies the laser system for SPS generation. This establishes a practical route toward high-performance QKD without the need for ultra-pure SPSs.