  The security of quantum key distribution protocols is guaranteed by the laws
of quantum mechanics. However, a precise analysis of the security properties
requires tools from both classical cryptography and information theory. Here,
we employ recent results in non-asymptotic classical information theory to show
that one-way information reconciliation imposes fundamental limitations on the
amount of secret key that can be extracted in the finite key regime. In
particular, we find that an often used approximation for the information
leakage during information reconciliation is not generally valid. We propose an
improved approximation that takes into account finite key effects and
numerically test it against codes for two probability distributions, that we
call binary-binary and binary-Gaussian, that typically appear in quantum key
distribution protocols.
