  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.
