Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning

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. [1,2] 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 1 . 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. arXiv:1112.3396v1 [quant-ph]

Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases

“…This allows us to map our protocol to the key rates, thus arriving at the standard MUB protocol. By increasing the dimension d, we obtain an increase in the secret key rate which has been theoretically observed in recent pa-pers [18,19], resulting in higher key generation rates for dimension d = 4. Similarly the Shannon mutual information increases, demonstrating an improvement in the information capacity.…”

“…The limit on the tolerable error rate that is safe for secret key generation can be improved by implementing a full set of (d + 1) MUBs [19,24]. Using a full set of MUBs results in an increase in the tolerable error rate in which we can still extract a reasonable secret key without compromising the security of the protocol.…”

“…(9) The total average error rate is the total error obtained as an average over the different MUBs, L [19] and is defined as…”

Key-rate enhancement using qutrit states for quantum key distribution with askew aligned sources

“…Then this entanglement version of 3d-MDI-QKD becomes same with 3-dimensional case of d-dimensional entanglement based protocol proposed in [29]. Security analysis of the ddimensional entanglement based protocol has been studied in the previous works, against individual attack [29] (Eve monitors states separately) and against collective attack [30,31] (Eve monitors several states jointly). According to the results, the secret key rate of 3d-MDI-QKD per sifted key against collective attack is evaluated as…”

“…High dimensional quantum states are applied in QKD protocol as well. There were researches for proving security of QKD using d-dimensional quantum system which is generalized version of original QKD protocol [27][28][29][30][31][32]. These results show that QKD using high dimensional quantum states has higher upper bound on the error rate that ensures unconditional security of the channel.…”