  Quantum key distribution is widely thought to offer unconditional security in
communication between two users. Unfortunately, a widely accepted proof of its
security in the presence of source, device and channel noises has been missing.
This long-standing problem is solved here by showing that, given fault-tolerant
quantum computers, quantum key distribution over an arbitrarily long distance
of a realistic noisy channel can be made unconditionally secure. The proof is
reduced from a noisy quantum scheme to a noiseless quantum scheme and then from
a noiseless quantum scheme to a noiseless classical scheme, which can then be
tackled by classical probability theory.
