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Quantum Cryptography on Noisy Channels: Quantum Versus Classical Key-Agreement Protocols

Nicolas Gisin and Stefan Wolf

When the 4-state or the 6-state protocol of quantum cryptography is carried out on anoisy (i.e., realistic) quantum channel, then the raw key has to be processed to reduce the information of an adversary Eve down to an arbitrarily low value, providing Alice and Bob with a secret key. In principle, quantum algorithms as well as classical algorithms can be used for this processing. A natural question is: up to which error rate on the raw key is a secret-key agreement at all possible? Under the assumption of incoherent eavesdropping, we find that the quantum and classical limits are precisely the same: as long as Alice and Bob share some entanglement both quantum and classical protocols provide secret keys.