Finite-key analysis for practical implementations of quantum key distribution

The lists of bits processed in quantum key distribution are necessarily of finite length. The need for finite-key unconditional security bounds was recognized long ago, but the theoretical tools have become available only very recently. We provide finite-key unconditional security bounds for two practical implementations of the Bennett–Brassard 1984 coding: prepareand-measure implementations without decoy states and entanglement-based implementations. A finite-key bound for prepare-and-measure implementations with decoy states is also derived under a simplified treatment of the statistical fluctuations. The presentation is tailored to allow direct application of the bounds in experiments. Finally, the bounds are also evaluated on a priori reasonable expected values of the observed parameters. 1 Author to whom any correspondence should be addressed. New Journal of Physics 11 (2009) 045024 1367-2630/09/045024+20$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft