  We consider the cloning of sequences of qubits prepared in the states used in
the BB84 or 6-state quantum cryptography protocol, and show that the
single-qubit fidelity is unaffected even if entire sequences of qubits are
prepared in the same basis. This result is of great importance for practical
quantum cryptosystems because it reduces the need for high-speed random number
generation without impairing on the security against finite-size attacks.
