Noise reduction caused by eavesdropping on six-state quantum key distribution over collective-noise channel

In this paper, we show that there are instances where eavesdropping causes noise reduction for a quantum key distribution (QKD) protocol. To witness these phenomena, we investigate a fault-tolerant six-state QKD protocol over a collective unitary noise channel. In this protocol, legitimate users send and receive two-qubit states that belong to the noiseless subspace being robust against collective unitary errors. We examine eavesdropper's intercept/resend and entangling probe attacks on this protocol. In general, the collective unitary noises lessen the probability that legitimate users share a random bit with the QKD protocol. However, we show that eavesdropping enlarges that probability in some specific scenarios although the effects of the collective unitary noise channel are strong enough. These phenomena make the legitimate users difficult to distinguish between noises and eavesdropper's malicious acts by monitoring the probability that they share the same random key.