Quantum cryptography ("QC") isn't a method of encryption; it's a method of generating a random shared secret (random bits known to Alice and Bob but not to the eavesdropper). Actually, if Alice and Bob don't already have a shared secret, or at least some way of authenticating each other, then they are vulnerable to a man-in-the-middle attack even if they use QC, so sometimes QC is said to be a way of expanding an existing shared secret to a longer one. You can use the long shared secret as a one-time pad, which is a (classical) provably secure encryption technique, to send the actual message over a conventional communication line.
We already have a way of expanding a short shared secret to a long one, and using it as a "one-time pad", without QC: it's called a stream cipher. The reason people are interested in QC, despite its being vastly slower and more expensive, is that the bits you get from it are true quantum randomness, whereas stream cipher bits are pseudorandom, and no one has ever managed to prove that a one-time pad with pseudorandom numbers is secure (this is related to P =? NP).
There are proofs that an eavesdropper can't learn the random bits produced by QC. However, these proofs rely not only on the correctness of quantum mechanics but also on far less plausible assumptions about the QC hardware and limitations on the actions that the eavesdropper is allowed to take. Real-world QC systems have been successfully attacked by violating those assumptions. So QC is "unconditionally secure if certain conditions are met", and I'm not sure that those conditions can ever be met in reality.