Min-entropy uncertainty relation for finite-size cryptography
Ng, Nelly Huei Ying.
Date of Issue2012
School of Physical and Mathematical Sciences
Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are therefore relations in terms of the smooth min-entropy for Bennett-Brassard 1984 (BB84) and six-state encodings. The smooth min-entropy Hminε(X/B) quantifies the negative logarithm of the probability for an attacker B to guess X, except with a small failure probability ε. Previously, strong uncertainty relations were obtained which are valid in the limit of large block lengths. Here, we prove an alternative 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 Rényi entropies that may be of independent interest.
Physical review A
© 2012 American Physical Society. This paper was published in Physical Review A and is made available as an electronic reprint (preprint) with permission of American Physical Society. The paper can be found at the following official DOI: [10.1103/PhysRevA.86.053620]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.