Quantum key distribution system against the probabilistic faint after-gate attack

In practical quantum key distribution (QKD) systems, a single photon-detector (SPD) is one of the most vulnerable components. Faint after-gate attack is a universal attack against the detector. However, the original faint after-gate attack can be discovered by monitoring the photocurrent. This paper presents a probabilistic generalization of the attack, which we refer to as probabilistic faint after-gate attack, by introducing probability control modules. Previous countermeasures for photocurrent monitoring may fail in detecting the eavesdropper under some specific probabilities. To mitigate this threat, we provide a method to determine the detectable boundary in the limitation of precision of photocurrent monitoring, and investigate the security of QKD systems under such boundaries using the weak randomness model.