Abstract: Divergences are fundamental tools in information theory that quantify the differences between probability distributions or quantum states. Recently, we introduced a new definition for quantum f-divergences based on an integral representation. These have remarkable properties, making them more suitable for certain applications compared to previous definitions. Those include quantifying contraction, hypothesis testing, and differential privacy. However, their particular form also introduces new difficulties. In this talk we revisit the divergences and discuss alternative expressions for them that allow us to prove new properties and gain further insights into their structure. In particular, we can better compare them to other quantum f-divergences, which has applications to quantum state discrimination. This is joint work with Salman Beigi and Marco Tomamichel.
Bio: Christoph Hirche is a Junior-Professor at the Leibniz University Hannover, Germany. His current research focuses on entropic quantities in quantum information theory and their applications. Previously, he was a Marie Skłodowska-Curie Global Fellow at TU Munich in Germany and NUS in Singapore and a Postdoctoral Researcher at the University of Copenhagen in Denmark. He obtained his PhD from the Universitat Autonoma de Barcelona (Spain). Prior to his PhD, he obtained Bachelor and Master degrees in Physics from the Leibniz University Hannover.