Clifford-group-restricted eavesdroppers in quantum key distribution

Abstract

Quantum key distribution (QKD) promises provably secure cryptography, even to attacks from an all-powerful adversary. However, with quantum computing development lagging behind QKD, the assumption that there exists an adversary equipped with a universal fault-tolerant quantum computer is unrealistic for at least the near-future. Here, we explore the effect of restricting the eavesdropper's computational capabilities on the security of QKD and find that improved secret key rates are possible. Specifically, we show that for a large class of discrete variable protocols higher key rates are possible if the eavesdropper is restricted to a unitary operation from the Clifford group. Further, we consider Clifford-random channels consisting of mixtures of Clifford gates. We numerically calculate a secret-key-rate lower bound for BB84 with this restriction and show that, in contrast to the case of a single restricted unitary attack, the mixture of Clifford-based unitary attacks does not result in an improved key rate.