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Title: Min-entropy uncertainty relation for finite-size cryptography
Authors: Ng, N.H.Y.
Berta, M.
Wehner, S. 
Issue Date: 2012
Citation: Ng, N.H.Y., Berta, M., Wehner, S. (2012). Min-entropy uncertainty relation for finite-size cryptography. Physical Review A - Atomic, Molecular, and Optical Physics 86 (4). ScholarBank@NUS Repository.
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 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. © 2012 American Physical Society.
Source Title: Physical Review A - Atomic, Molecular, and Optical Physics
ISSN: 10502947
DOI: 10.1103/PhysRevA.86.042315
Appears in Collections:Staff Publications

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