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arXiv:quant-ph/9809039 · Annual Symposium on Foundations of Computer Science

Quantum cryptography with imperfect apparatus

Dominic Mayers, Andrew Chi-Chih Yao

Published Nov 27, 2002• 380 citations

Abstract

Quantum key distribution, first proposed by C.H. Bennett and G. Brassard (1984), provides a possible key distribution scheme whose security depends only on the quantum laws of physics. So far the protocol has been proved secure even under channel noise and detector faults of the receiver but is vulnerable if the photon source used is imperfect. In this paper we propose and give a concrete design for a new concept, self-checking source, which requires the manufacturer of the photon source to provide certain tests; these tests are designed such that, if passed, the source is guaranteed to be adequate for the security of the quantum key distribution protocol, even though the testing devices may not be built to the original specification. The main mathematical result is a structural theorem which states that, for any state in a Hilbert space, if certain EPR-type equations are satisfied, the state must be essentially the orthogonal sum of EPR pairs.

DOI: 10.1109/sfcs.1998.743501

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We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. Our proof applies when both the source and the detector have small basis-dependent flaws, as is typical in practical implementations of the protocol. We derive a general lower bound on the asymptotic key generation rate for weakly basis-dependent eavesdropping attacks, and also estimate the rate in some special cases: sources that emit weak coherent states with random phases, detectors with basis-dependent efficiency, and misaligned sources and detectors.

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