Entropy Accumulation With Improved Second-Order Term
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Publication:5211524
DOI10.1109/TIT.2019.2929564zbMATH Open1433.94042arXiv1805.11652OpenAlexW3100554412WikidataQ127456021 ScholiaQ127456021MaRDI QIDQ5211524
Publication date: 28 January 2020
Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)
Abstract: The entropy accumulation theorem states that the smooth min-entropy of an -partite system is lower-bounded by the sum of the von Neumann entropies of suitably chosen conditional states up to corrections that are sublinear in . This theorem is particularly suited to proving the security of quantum cryptographic protocols, and in particular so-called device-independent protocols for randomness expansion and key distribution, where the devices can be built and preprogrammed by a malicious supplier. However, while the bounds provided by this theorem are optimal in the first order, the second-order term is bounded more crudely, in such a way that the bounds deteriorate significantly when the theorem is applied directly to protocols where parameter estimation is done by sampling a small fraction of the positions, as is done in most QKD protocols. The objective of this paper is to improve this second-order sublinear term and remedy this problem. On the way, we prove various bounds on the divergence variance, which might be of independent interest.
Full work available at URL: https://arxiv.org/abs/1805.11652
Cryptography (94A60) Measures of information, entropy (94A17) Authentication, digital signatures and secret sharing (94A62)
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