Mathematical Introduction to Quantum Information Processing

Quantum computation, quantum communication, and quantum cryptography are all high-level forms of quantum information processing. This course will introduce and analyze the basic building blocks of quantum information processing from a mathematical perspective. Beginning with the abstract foundations of quantum theory, the course will deal with quantum measurement theory, the description, steering and application of quantum evolutions, quantum statistical inference, and quantum tomography. One of the main aims of the course is to develop a better understanding of the fundamental limits of quantum information processing concerning speed, disturbance, precision, heat production and the use of other resources.

After successful completion of the module, students are able to analyze and describe quantum statistical experiments on abstract grounds. They master in particular the use of the quantum instruments framework for describing measurements and evolutions. Moreover, they know and understand the basic operational concepts, opportunities, and limitations of quantum information processing.

MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Structures 2, any course that contains an introduction to Hilbert spaces and linear operators (e.g. MA3001 Functional Analysis, but much less is required).
Recommended but not essential: Introductory course on Probability Theory.

The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should animate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

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Lecture notes and further literature will be provided.

The exam will be in written (60 minutes) or oral (25 minutes) form, depending on the number of participants. Students demonstrate that they have gained a deeper knowledge of definitions and main mathematical tools and results concerning the mathematics of quantum information processing. The students are expected to be able to derive and explain basic methods, concepts, and properties and to apply them to specific examples.