In this course, we introduce the mathematics of quantum mechanics from an information-theoretic perspective. In the first part, 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 so-called 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 interesting mathematical concepts, covering some elements of matrix analysis.
Prior knowledge on quantum information science (e.g. a course on quantum computing) is helpful by not necessary; familiarity with complex numbers and linear algebra is sufficient.
Form of the Class
Lectures, and possibly some home study.
Lecture notes are handed out during the course; no additional literature is necessary. BlackBoard is not used.
Take-home exercises are handed out roughly every two weeks; it is expected that the students do these exercises, but they are not graded and do not count towards the final grade.
The final grade will be determined by an oral exam after the semester.