  We prove the security of the Bennett-Brassard (BB84) quantum key distribution
protocol for an arbitrary source whose averaged states are basis-independent, a
condition that is automatically satisfied if the source is suitably designed.
The proof is based on the observation that, to an adversary, the key extraction
process is equivalent to a measurement in the sigma_x-basis performed on a pure
sigma_z-basis eigenstate. The dependence of the achievable key length on the
bit error rate is the same as that established by Shor and Preskill for a
perfect source, indicating that the defects in the source are efficiently
detected by the protocol.
