  We consider the asymptotic key rates achieved in the simplest quantum key
distribution protocols, namely the BB84 and the six-state protocols, when
non-uniform noise is present in the system. We first observe that higher qubit
error rates do not necessarily imply lower key rates. Secondly, we consider
protocols with advantage distillation and show that it can be advantageous to
use the basis with higher quantum bit error rate for the key generation. We
then discuss the relation between advantage distillation and entanglement
distillation protocols. We show that applying advantage distillation to a
string of bits formed by the outcomes of measurements in the basis with higher
quantum bit error rate is closely connected to the two-to-one entanglement
distillation protocol DEJMPS. Finally, we discuss the implications of these
results for implementations of quantum key distribution.
