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A min-entropy uncertainty relation for finite size cryptography

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Title A min-entropy uncertainty relation for finite size cryptography
Title of Series The Annual Conference on Quantum Cryptography (QCRYPT) 2012
Number of Parts 30
Author Ng, Nelly
Contributors Centre for Quantum Technologies (CQT)
National University of Singapore (NUS)
License CC Attribution - NonCommercial - NoDerivatives 2.5 Switzerland:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI 10.5446/36653
Publisher Eidgenössische Technische Hochschule (ETH) Zürich
Release Date 2012
Language English

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Subject Area Information technology
Abstract Apart from their foundational signicance, 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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