Effect of weak randomness flaws on security evaluation of practical quantum key distribution with distinguishable decoy states

Quantum key distribution provides an unconditional secure key sharing method in theory, but the imperfect factors of practical devices will bring security vulnerabilities. In this paper, we characterize the imperfections of the sender and analyze the possible attack strategies of Eve. Firstly, we present a quantized model for distinguishability of decoy states caused by intensity modulation. Besides, considering that Eve may control the preparation of states through hidden variables, we evaluate the security of preparation in practical quantum key distribution (QKD) scheme based on the weak-randomness model. Finally, we analyze the influence of the distinguishability of decoy state to secure key rate, for Eve may conduct the beam splitting attack and control the channel attenuation of different parts. Through the simulation, it can be seen that the secure key rate is sensitive to the distinguishability of decoy state and weak randomness, especially when Eve can control the channel attenuation.