2 2 M ay 1 99 8 Quantum Computers Render Quantum Key Distribution Unconditionally Secure

Quantum cryptography has long been claimed to be useful for achieving many tasks that are impossible from the perspective of conventional cryptography. Arguably, the most important problem in quantum cryptography has been a rigorous proof of the security of quantum key distribution, the most wellknown application. This notoriously hard problem has eluded researchers for the last fifteen years and has become even more important after the recent surprising demonstration of the insecurity of many other quantum cryptographic schemes including quantum bit commitment. Here, we solve this long standing problem by showing that, given quantum computers, quantum key distribution over an arbitrarily long distance of a realistic noisy channel can be made unconditionally secure. The novel technique we use is reduction from a quantum scheme to a classical scheme. The security in realistic noisy environments is then proven by using the recent theory of fault-tolerant quantum