Entropy accumulation

Frederic Dupuis; Omar Fawzi; Renato Renner

doi:10.1007/s00220-020-03839-5

paper

Entropy accumulation

arXiv:1607.01796 · doi:10.1007/s00220-020-03839-5

Abstract

We ask the question whether entropy accumulates, in the sense that the operationally relevant total uncertainty about an $n$ -partite system $A = (A_{1}, \dots A_{n})$ 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.

44 pages; expandable to 48 pages

Entropy accumulation

Abstract

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