  The study of leakage measures for privacy has been a subject of intensive
research and is an important aspect of understanding how privacy leaks occur in
computer systems. Differential privacy has been a focal point in the privacy
community for some years and yet its leakage characteristics are not completely
understood. In this paper we bring together two areas of research --
information theory and the g-leakage framework of quantitative information flow
(QIF) -- to give an operational interpretation for the epsilon parameter of
local differential privacy. We find that epsilon emerges as a capacity measure
in both frameworks; via (log)-lift, a popular measure in information theory;
and via max-case g-leakage, which we introduce to describe the leakage of any
system to Bayesian adversaries modelled using ``worst-case'' assumptions under
the QIF framework. Our characterisation resolves an important question of
interpretability of epsilon and consolidates a number of disparate results
covering the literature of both information theory and quantitative information
flow.
