Educational materials

Here we collect some materials that are hopefully useful to students interested in the topic, and the quantum research community overall.


This monographs gives an introduction to measures of quantum information (divergences and entropies) and their properties and applications. It is aimed at graduate students interested in mathematical aspects of quantum information theory.

The published version is out of date, please consider the version on arXiv instead. Errata for current version on arXiv can be found under Errata.

Various Lectures and Tutorials

Tutorial on Quantum Information Theory

I gave a tutorial at QIP 2022 at CalTech titled “From one-shot to asymptotic quantum information theory”. The slides, with some corrections, are available here (pdf).

Masterclass on Entropy Inequalities

I taught a short course (two lectures) on “An Axiomatic Approach to Quantum Divergences” at the 2022 QMath Masterclass in Copenhagen. The lecture notes are available here (pdf), provided with the help of Yanglin Hu.

Introduction to Quantum Learning Theory

I gave a few introductory lectures on quantum learning theory as part of the course Advanced Topics in Quantum Information at ETH Zurich. Lecture notes are available here (pdf), provided with the help of Jan Seyfried.

Teaching at NUS