  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.
