Generalised Entropy Accumulation
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2024-11
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Journal Article
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yes
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Abstract
Consider a sequential process in which each step outputs a system Ai and updates a side information register E. We prove that if this process satisfies a natural “non-signalling” condition between past outputs and future side information, the minentropy of the outputs A1,..., An conditioned on the side information E at the end of the process can be bounded from below by a sum of von Neumann entropies associated with the individual steps. This is a generalisation of the entropy accumulation theorem (EAT) (Dupuis et al. in Commun Math Phys 379: 867–913, 2020), which deals with a more restrictive model of side information: there, past side information cannot be updated in subsequent rounds, and newly generated side information has to satisfy a Markov condition. Due to its more general model of side-information, our generalised EAT can be applied more easily and to a broader range of cryptographic protocols. As examples, we give the first multi-round security proof for blind randomness expansion and a simplified analysis of the E91 QKD protocol. The proof of our generalised EAT relies on a new variant of Uhlmann’s theorem and new chain rules for the Rényi divergence and entropy, which might be of independent interest.
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published
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405 (11)
Pages / Article No.
261
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Springer
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03781 - Renner, Renato / Renner, Renato
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185902 - QSIT - Quantum Science and Technology (SNF)
188541 - Information-theoretic limits to time measurements (SNF)
188541 - Information-theoretic limits to time measurements (SNF)
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Is new version of: http://hdl.handle.net/20.500.11850/593324