1205.0842 (Huei Ying Nelly Ng et al.)

A min-entropy uncertainty relation for finite size cryptography    [PDF]

Huei Ying Nelly Ng, Mario Berta, Stephanie Wehner

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.

View original: http://arxiv.org/abs/1205.0842