Improved security bounds against the Trojan-Horse attack in decoy-state quantum key distribution

In a quantum Trojan-horse attack (THA), eavesdroppers learn encoded information by injecting bright light into encoded or decoded devices of quantum key distribution (QKD) systems. These attacks severely compromise the security of non-isolated systems. Thus, analytical security bound was derived in previous studies. However, these studies achieved poor performance unless the devices were strongly isolated. Here, we present a numerical method for achieving improved security bound for a decoy-state QKD system under THAs. The developed method takes advantage of the well-established numerical framework and significantly outperforms previous analytical bounds regarding the achievable final key and secure transmitted distance. The results provide a new tool for investigating the efficient security bounds of THA in practical decoy-state QKD systems. This study constitutes an important step toward securing QKD with real-life components.