Improved Finite-Key Security Analysis of Measurement-Device-Independent Quantum Key Distribution Against a Trojan-Horse Attack

Measurement-device-independent quantum key distribution (MDI QKD) is a promising method for remote key sharing that can eliminate all detector side-channel attacks. However, current security proofs often overlook the potential information leakages from the legitimate users' devices. In a quantum version of Trojan-horse attack (THA), a malicious eavesdropper can inject bright light into the sources of a MDI QKD system and then analyze the back-reflected light to obtain their setting choices, thereby compro-mising the final security. Here, we derive the finite-key security bounds of decoy-state MDI QKD in the presence of THA, which significantly outperform previous analyses in terms of the secret-key rate and transmission distance. Specifically, we analyze a symmetric three-intensity decoy-state MDI QKD pro-tocol and an efficient four-intensity decoy-state MDI QKD protocol. Our results represent a fundamental step in guaranteeing the implementation security of quantum communication systems.