Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication

We investigate a general class of quantum key distribution (QKD) protocols using one-way classical communication. We show that full security can be proven by considering only collective attacks. We derive computable lower and upper bounds on the secret-key rate of those QKD protocols involving only entropies of two-qubit density operators. As an illustration of our results, we determine new bounds for the Bennett-Brassard 1984, the 6-state, and the Bennett 1992 protocols. We show that in all these cases the first classical processing that the legitimate partners should apply consists in adding noise.