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Mathematical Introduction to Quantum Information Processing

Module MA5057

This Module is offered by TUM Department of Mathematics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Basic Information

MA5057 is a semester module in English language at Master’s level which is offered irregular.

This Module is included in the following catalogues within the study programs in physics.

  • Catalogue of non-physics elective courses
  • Specialization Modules in Elite-Master Program Theoretical and Mathematical Physics (TMP)
Total workloadContact hoursCredits (ECTS)
270 h 90 h 9 CP

Content, Learning Outcome and Preconditions


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.

Learning Outcome

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.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 4 Mathematical Introduction to Quantum Information Processing [MA5057] Wolf, M. Mon, 10:15–11:45, MI 00.06.011
Fri, 10:15–11:45, MI 03.08.011
UE 2 Mathematical Introduction to Quantum Information Processing (Exercise Session) [MA5057] Wolf, M. Fri, 12:15–13:45, MI 00.09.022

Learning and Teaching Methods

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.




Lecture notes and further literature will be provided.

Module Exam

Description of exams and course work

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.

Exam Repetition

The exam may be repeated at the end of the semester.

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