We will give a high-level presentation of some recent works in Quantitative Information Flow which have brought results of interest for the wider communities of Information Theory and Quantum security. The first work is based on the notion of core-concavity, and it allows to generalize some axiomatic approach for Quantitative Information Flow to an axiomatic presentation of Information Theory for general entropy functions. Several fundamental Information Theoretical results can be proven in this framework. (Joint work with Arman Khouzani and Arthur Americo) The second contribution introduces quantum quantitative information flow, a leakage framework for quantum computation. The framework is a natural extension of gain functions and is based on Buscemi’s work on the theory of statistical comparison in quantum information, theory for which a quantum equivalent to the coriaceous theorem holds. (Joint work with Arthur Americo)

In this talk I will introduce the QIF approach to studying secure systems, focussing on the notion of refinement which provides a robust method of comparing systems wrt Bayesian threats. I will introduce a variety of new refinement orders inspired by QIF and DP which allow us to study threats to privacy using max-case notions. We will see how to apply these orders to the task of comparing DP mechanisms, raising the question of whether the order based on epsilon provides strong privacy guarantees.