In this course, we give an introduction to the mathematics of quantum mechanics when viewed from an information-theoretic perspective. This means, we focus on the concept of “information” and how it changes when admitting quantum mechanics. For instance, as will be shown, quantum information cannot be copied in general – in contrast to its classical counter part. We will show several surprising consequences of the existence of quantum information and its properties. A highlight of this will be the existence of an “unbreakable” encryption scheme.
A list of topics is as follows: quantum states, entanglement, quantum teleportation, nonlocality and “pseudo-telepathy”, no-cloning theorem, entropy measures, privacy amplification, and quantum key distribution.
Prior knowledge of quantum mechanics may be helpful, but is certainly not necessary. Basic knowledge of complex linear algebra and probability theory is sufficient.