Anthony Leverrier

We establish an analytical lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation of coherent states. Previously, such bounds were only available for protocols with a Gaussian modulation, and numerical bounds existed in the case of simple phase-shift-keying modulations. The latter bounds were obtained as a solution of a convex optimization problem and our new analytical bound matches them, up to numerical precision. The more relevant case of quadrature amplitude modulation (QAM) could not be analyzed with the previous techniques,due to their large number of coherent states. Our bound shows that relatively small constellation sizes, with say 64 states, are essentially sufficient to obtain a performance close to a true Gaussian modulation and are therefore an attractive solution for large-scale deployment of continuous-variable quantum key distribution. We also derive similar bounds when the modulation consists of arbitrary states, not necessarily pure.

Quantum key distribution (QKD) is a cryptographic primitive allowing two distant parties, Alice and Bob, to establish a secret key in an untrusted environment controlled by some eavesdropper, Eve. We introduce a new continuous-variable QKD protocol using a continuous but non-Gaussian modulation, allowing for an efficient reconciliation scheme and thus for improved performances. The modulation we consider crucially uses algebraic properties of the octonions, which can be seen as points on the unit sphere in R^8. We establish the security of this protocol against collective attacks, provided that the quantum channel is linear.