In this course, we give an introduction to the mathematics of quantum mechanics from an information-theoretic point of view. This means, we focus on the concept of “information” and how it changes when the rules of quantum mechanics apply. Indeed, quantum information behaves very differently to its classical counter part, and has surprising consequences and opens the door for exciting applications. For instance, towards the end of the course, we will discuss and prove the security of an “unbreakable” encryption scheme. From a technical perspective, the course can be seen as a non-commutative extension of probability theory.
A list of topics is as follows: quantum states, entanglement, quantum teleportation, nonlocality, purification, no-cloning, entropy, privacy amplification, and quantum key distribution.
Prior knowledge of quantum mechanics is not necessary; basic knowledge of linear algebra and probability theory is sufficient.
Lecture notes will be handed out; BlackBoard will not be used. The examination will be in the form of an oral exam after the semester.