Abstract
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 Refs. [Proc. R. Soc. London A 461, 207 (2005); Phys. Rev. Lett. 95, 080501 (2005)] for discrete variable protocols in -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, and mutually unbiased bases where is a prime, and show that for the protocols with 2 and mutually unbiased bases (MUBs) the optimal attack is an optimal cloner but, for the protocols with 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 Bennett-Brassard 1984 (BB84) protocol or the 6-state protocol.
- Received 26 January 2012
DOI:https://doi.org/10.1103/PhysRevA.85.052310
©2012 American Physical Society