Generalised entropy accumulation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year :

Generalised entropy accumulation


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.

Dates and versions

hal-03750961 , version 1 (13-08-2022)





Tony Metger, Omar Fawzi, David Sutter, Renato Renner. Generalised entropy accumulation. 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), Oct 2022, Denver, United States. ⟨10.1109/FOCS54457.2022.00085⟩. ⟨hal-03750961⟩
57 View
0 Download



Gmail Facebook Twitter LinkedIn More