NMAK22000U Analysis in Quantum Information Theory

Volume 2023/2024

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
MSc Programme in Quantum Information Science


The purpose of this course is to give the analytic background behind quantum information theory in the framework of operators on Hilbert spaces and functional analysis, including the following topics:

  • completely positive and completely bounded maps
  • operator systems and spaces
  • Choi representation and Kraus operators
  • Stinespring's representation theorem
  • tensor products
  • quantum measurements and related sets of correlations
  • entanglement
  • Schmidt decompositions
  • factorizable channels and applications in quantum information theory
Learning Outcome

After completing the course the student will have:

knowledge about the subjects mentioned in the description of the content,

skills to solve problems concerning the material covered, and

the following competences:

  • understand and master the functional analytic approach to quantum information theory,
  • be able to work rigorously with the concepts taught in the course,
  • use analysis tools to study and solve concrete problems in quantum information theory.

Lecture notes and/or textbook.

Some familiarity with Hilbert spaces and operators on Hilbert spaces, and basic knowledge of functional analysis. The course FunkAn can possibly be followed in parallel.
Academic qualifications equivalent to a BSc degree are recommended.
4 hours of lectures and 3 hours of exercises per week for 8 weeks.
  • Category
  • Hours
  • Lectures
  • 32
  • Preparation
  • 125
  • Theory exercises
  • 24
  • Exam
  • 25
  • Total
  • 206
Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Continuous assessment
Type of assessment details
3 written assignments, each of which counts equally towards the final grade
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship

Oral, 30 minutes with 30 minutes preparation time.

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.