Entropy accumulation

TL;DR

This paper demonstrates that entropy can accumulate in complex systems without independence assumptions, enabling simplified analysis of large systems and improving security bounds in device-independent cryptography.

Contribution

It generalizes entropy accumulation to non-independent systems using von Neumann entropy, extending the applicability of entropy-based analysis.

Findings

Entropy accumulation holds without independence assumptions.

Analysis of large systems reduces to studying individual parts.

Provides near-optimal security bounds in cryptography.

Abstract

We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$-partite system $A = (A_1, \ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The Asymptotic Equipartition Property implies that this is indeed the case to first order in $n$, under the assumption that the parts $A_i$ are identical and independent of each other. Here we show that entropy accumulation occurs more generally, i.e., without an independence assumption, provided one quantifies the uncertainty about the individual systems $A_i$ by the von Neumann entropy of suitably chosen conditional states. The analysis of a large system can hence be reduced to the study of its parts. This is relevant for applications. In device-independent cryptography, for instance, the approach yields essentially optimal security bounds valid for general attacks, as shown by Arnon-Friedman et al.