Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyse and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an 'entanglement purification' procedure which, because it requires only a few quantum Controlled-Not and singlequbit operations, could be implemented using technology that is currently being developed. The scheme allows an arbitrarily small bound to be placed on the information that any eavesdropper may extract from the encrypted 1

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Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting non--classical properties. We describe a simple quantum logic gate, the quantum controlled--NOT, and analyse some of its applications. We discuss two possible physical realisations of the gate; one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole--dipole interaction.Comment: 5 pages, RevTeX, two figures in a uuencoded, compressed fil

A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method. The quantum computation solves the problem with certainty in exponentially less time than any classical deterministic computation.

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