We provide security bounds against coherent attacks for two families of quantum key distribution protocols that use $d$-dimensional quantum systems. In the asymptotic regime, both the secret key rate for fixed noise and the robustness to noise increase with $d$. The finite key corrections are found to be almost insensitive to $d\lesssim 20$.

• Received 6 April 2010

DOI:https://doi.org/10.1103/PhysRevA.82.030301