Generalised entropy accumulation

TL;DR

This paper generalizes the entropy accumulation theorem to a broader class of processes with a natural non-signalling condition, enabling more versatile cryptographic security proofs.

Contribution

It introduces a more general entropy accumulation theorem that relaxes previous restrictions on side information, broadening its applicability in cryptography.

Findings

First multi-round security proof for blind randomness expansion

Simplified analysis of the E91 quantum key distribution protocol

New variants of Uhlmann's theorem and chain rules for Renyi divergence

Abstract

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.