Efficiently implementable codes for quantum key expansion
arXiv:quant-ph/0608029 · doi:10.1103/PhysRevA.75.010303
Abstract
The Shor-Preskill proof of the security of the BB84 quantum key distribution protocol relies on the theoretical existence of good classical error-correcting codes with the ``dual-containing'' property. A practical implementation of BB84 thus requires explicit and efficiently decodable constructions of such codes, which are not known. On the other hand, modern coding theory abounds with non-dual-containing codes with excellent performance and efficient decoding algorithms. We show that the dual-containing constraint can be lifted at a small price: instead of a key distribution protocol, an efficiently implementable key expansion protocol is obtained, capable of increasing the size of a pre-shared key by a constant factor.
4 pages, 1 figure. The new version has the title changed, the abstract, introduction and conclusion rewritten. To appear in PRA Rapid Communications