A min-entropy uncertainty relation for finite size cryptography
Abstract
Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are thereby relations in terms of the smooth min-entropy for BB84 and six-state encodings. Previously, strong uncertainty relations were obtained which are valid in the limit of large block lengths. Here, we prove a new uncertainty relation in terms of the smooth min-entropy that is only marginally less strong, but has the crucial property that it can be applied to rather small block lengths. This paves the way for a practical implementation of many cryptographic protocols. As part of our proof we show tight uncertainty relations for a family of Renyi entropies that may be of independent interest.
Cite
@article{arxiv.1205.0842,
title = {A min-entropy uncertainty relation for finite size cryptography},
author = {Nelly Huei Ying Ng and Mario Berta and Stephanie Wehner},
journal= {arXiv preprint arXiv:1205.0842},
year = {2014}
}
Comments
5+6 pages, 1 figure, revtex. new version changed author's name from Huei Ying Nelly Ng to Nelly Huei Ying Ng, for consistency with other publications