Prior knowledge on quantum information science (e.g. a course on quantum computing) is helpful but not necessary; familiarity with complex numbers and linear algebra is sufficient.
We introduce and study the mathematics of quantum information science, which brings together quantum mechanics and theoretical computer science, with a focus on information theoretic (instead of computational) aspects in this course.
In the first few lectures, we discuss the so-called density-operator formalism of quantum mechanics and study the relevant mathematical concepts: density operators, partial trace, purification, CPTP maps, and the Schatten norms. After that, the focus will be on measures of quantum information, i.e., ways to quantify the information content of quantum states. This is done by means of studying a quantum-version of the classical Renyi entropies. We analyze the crucial properties of these information measures and discuss (on some examples) their operational significance.
From a technical perspective and to some extent, the course can be seen as a non-commutative extension of classical probability- and information-theory. Along the way, we will touch upon different mathematical concepts, e.g., covering some elements of matrix analysis.
The goal of the course is to familiarize the students with the basic concepts of quantum information theory, and to offer an in-depth understanding of certain selected topics within the field. After successful completion of the course, the student should be able to read research articles in the field.
Mode of instruction
Lectures, homework exercises, and some home study
The examination consists of homework and an oral (retake) exam. The homework counts as a practical. There is no retake for it and it is evaluated on the basis of pass/fail. A pass is required to take part in the exam. The homework does not count towards the final grade, which is based only on the exam.
Lecture notes will be provided (online) during the course. No additional literature is needed.
Information on the course will be made available on a dedicated course website.