Abstract

Due to the non-commutativity of quantum mechanics there are infinitely many possible quantum generalisations of classical divergences like the Kullback-Leibler (KL) and Renyi divergences. In this talk I want to review how one can decide which of these generalisations is the “right” one using the context of quantum hypothesis testing. For that I first briefly review the setup of classical binary hypothesis testing and Stein’s Lemma, which gives operational meaning to the KL-divergence. After then recalling some quantum basics I talk about the quantum Stein’s Lemma and comment on its proof using quantum Renyi divergences. If time permits, I will then briefly talk about the Hoeffding and Han-Kobayashi regimes of binary hypothesis testing, which give operational meaning to the Renyi divergences, and comment how the corresponding quantum generalisations give rise to the “right” quantum generalisation of the Renyi divergences.