We provide a general formalism to characterize the cryptographic properties
of quantum channels in the realistic scenario where the two honest parties
employ prepare and measure protocols and the known two-way communication
reconciliation techniques. We obtain a necessary and sufficient condition to
distill a secret key using this type of schemes for Pauli qubit channels and
generalized Pauli channels in higher dimension. Our results can be applied to
standard protocols such as BB84 or six-state, giving a critical error rate of
20% and 27.6%, respectively. We explore several possibilities to enlarge these
bounds, without any improvement. These results suggest that there may exist
weakly entangling channels useless for key distribution using prepare and
measure schemes.Comment: 21 page