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arXiv · 1205.0842

A min-entropy uncertainty relation for finite size cryptography

Nelly Huei Ying Ng·Mario Berta·Stephanie Wehner
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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.

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Nelly Huei Ying Ng, Mario Berta, Stephanie Wehner. 2012-05-04. A min-entropy uncertainty relation for finite size cryptography. https://doi.org/10.1103/physreva.86.042315

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