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≲20.Comment: 5 pages, 1 figure, version 3 corrects equations (9) and (11), and
slightly modifies the figure to reflect the change to equation (11
