Abstract
We study the advantages to be gained in quantum key distribution (QKD) protocols by combining the techniques of local randomization, or noisy preprocessing, and structured (nonrandom) block codes. Extending the results of [Smith, Renes, and Smolin, {\em Physical Review Letters}, 100:170502] pertaining to BB84, we improve the best-known lower bound on the error rate for the 6-state protocol from 14.11% for local randomization alone to at least 14.59%. Additionally, we also study the effects of iterating the combined preprocessing scheme and find further improvements to the BB84 protocol already at small block lengths.
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