f-differential privacy (f-DP) is a recent definition for privacy which can offer improved predictions of “privacy loss”. It has been used to analyse specific privacy mechanisms, such as the popular Gaussian mechanism. In this paper we show how f-DP’s foundation in statistical hypothesis testing implies equivalence to the channel model of Quantitative Information Flow (QIF). We demonstrate this equivalence as a Galois connection between two partially-ordered sets, namely f-DP’s trade-off functions, and a class of information channels. This equivalence enables novel general composition theorems for f-DP, supporting improved analysis for complex privacy designs. We apply our results to the popular privacy amplification mechanisms of sub-sampling and purification, to produce novel f-DP profiles for these general privacy-enhancing algorithms.