Generalised entropy accumulation
| Autor: | Metger, Tony, Fawzi, Omar, Sutter, David, Renner, Renato |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), Denver, CO, USA, 2022, pp. 844-850 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/FOCS54457.2022.00085 |
| Popis: | Consider a sequential process in which each step outputs a system $A_i$ 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 min-entropy of the outputs $A_1, \dots, A_n$ 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), 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 Renyi divergence and entropy, which might be of independent interest. Comment: 42 pages; v2 expands introduction but does not change any results; in FOCS 2022 |
| Databáze: | arXiv |
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