Clifford group restricted eavesdroppers in quantum key distribution

TL;DR

This paper investigates how restricting an eavesdropper's quantum capabilities to Clifford group operations can enhance secret key rates in quantum key distribution, challenging the assumption of an all-powerful adversary.

Contribution

It introduces the concept of restricting eavesdroppers to Clifford group operations and analyzes its impact on QKD security and key rates, including numerical results for BB84.

Findings

Higher key rates are achievable with Clifford-restricted eavesdroppers.

Mixtures of Clifford gates do not improve key rates compared to single Clifford attacks.

Numerical lower bounds for BB84 show potential security benefits of restrictions.

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.