  We investigate the connection between the optimal collective eavesdropping
attack and the optimal cloning attack where the eavesdropper employs an optimal
cloner to attack the quantum key distribution (QKD) protocol. The analysis is
done in the context of the security proof in [Devetak and Winter, Proc. of the
Roy. Soc. of London Series A, 461, 207 (2005); Kraus, Gisin and Renner, Phys.
Rev. Lett. 95, 080501 (2005)] for discrete variable protocols in d-dimensional
Hilbert spaces. We consider a scenario in which the protocols and cloners are
equipped with symmetries. These symmetries are used to define a quantum cloning
scenario. We find that, in general, it does not hold that the optimal attack is
an optimal cloner. However, there are classes of protocols, where we can
identify an optimal attack by an optimal cloner. We analyze protocols with 2, d
and d+1 mutually unbiased bases where d is a prime, and show that for the
protocols with 2 and d+1 MUBs the optimal attack is an optimal cloner, but for
the protocols with d MUBs, it is not. Finally, we give criteria to identify
protocols which have different signal states, but the same optimal attack.
Using these criteria, we present qubit protocols which have the same optimal
attack as the BB84 protocol or the 6-state protocol.

Quantum Physics