Quantum key distribution with several intercept–resend attacks via a depolarizing channel

Abstract

The disturbance effect of a depolarizing channel on the security of the quantum key distribution of the four-state BB84 protocol, with multiple sequential intercept–resend attacks of many eavesdroppers, has been studied. The quantum bit error rate and the mutual information are computed for an arbitrary number N of eavesdroppers. It is found that the quantum error rate decreases with increasing the depolarizing parameter p characterizing the noise of the channel. For p < 0.165, there exists a special value ptr of p below which the information is secure and otherwise the information is not secure. The value of ptr decreases with increasing the number of attacks. In contrast, for p ⩾ 0.165, the information is not secure independently of the number of eavesdroppers. Phase diagrams corresponding to the secure—unsecure information are also established.