Location
online (email amgrad@uwaterloo.ca for link)
Candidate
Shreyas Natarajan | Applied Mathematics, University of Waterloo
Title
Quantum Rényi Divergence via Majorisation
Abstract
This short talk will be a literature review, exploring how the quantum Rényi divergences arise. They are measures of distance between quantum states - in other words they each introduce a geometry to the space of density operators. Like the standard Umegaki relative entropy, the quantum Rényi divergences are very important to quantum information theory; they are used in e.g. quantum hypothesis testing, decoupling bounds, and error exponents for CQ-channel coding, state-merging etc. There are different types of quantum Rényi divergence, which arise depending on the context, with vastly different properties and from different notions of quantum Radon-Nikodym derivative (i.e. dividing states). However, our understanding of what the different quantum Rényi divergences capture has been limited. In recent years, our understanding has significantly improved thanks to different notions of majorisation. Majorisation compares two tuples of quantum states based on the amount of information they contain. I will offer an introduction to the role of semi-ring theory in classifying quantum Rényi divergences based on majorisation (https://arxiv.org/pdf/2004.10587, https://arxiv.org/pdf/2509.18725 ), but I will also discuss some recent progress about the integral Rényi divergences (https://arxiv.org/pdf/2607.01712 ).