On Rényi entropy in quantum information theory

Abstract

Quantum systems are systems of small physical objects such as particles. Quantum theory uses mathematics to describe and predict the behaviour of a quantum system. We can ask ourselves which fields of mathematics are used in quantum mechanics. However, quantum mechanics entails a variety of subjects which are quite broad. Therefore, we will focus on mathematically describing concepts in quantum information theory. Quantum mechanical information quantities such as von Neumann entropy and Rényi entropy are of importance within quantum information theory. To further narrow the subject we will focus on the mathematical concepts needed to describe entropy in a finite representation space. We will see that linear algebra, probability theory and analysis are the fields of mathematics which will most frequently be called upon.