Analysis in Quantum Information Theory

Course content

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 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

MSc Programme in Mathematics

MSc Programme in Mathematics with a minor subject

MSc Programme in Quantum Information Science

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.

4 hours of lectures and 3 hours of exercises per week for 8 weeks.

Lecture notes and/or textbook.

Advanced Vector Spaces (AdVec).

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.

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

30-minute oral examination with 30 minutes preparation time

Criteria for exam assessment

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

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 32
  • Preparation
  • 125
  • Theory exercises
  • 24
  • Exam
  • 25
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 2
No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinators
  • Magdalena Elena Musat   (5-727a786679457266796d33707a336970)
  • Mikael Rørdam   (6-7875786a67734673677a6e34717b346a71)
Saved on the 14-02-2024

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