MAT4430 – Quantum Information Theory

Schedule, syllabus and examination date

Course content

Quantum information theory is an active field of research at the intersection of mathematics, physics, and computer science. In this introductory course, we focus on the mathematical side of the subject. We will start by introducing basic notions from probability theory and classical information theory, and then develop the mathematical foundation of quantum information theory including quantum states on Hilbert spaces, distance measures, the measurement formalism, quantum channels and their representations, no-go theorems, and entanglement. In the second part of the course, we will introduce the von Neumann entropy, study its basic properties, and discuss the Schumacher compression theorem giving this quantity an operational meaning. In the final part of the course, we will focus on the transmission of information over quantum channels. We will study the classical and quantum capacity of quantum channels and discuss their basic properties.

Learning outcome

After completing the course you will

  • Have good knowledge of the mathematical formalism of quantum information theory and be able to formalize basic problems arising in quantum physics
  • Have knowledge of the basic features of quantum theory such as superposition, entanglement, and the no-cloning theorem
  • Be familiar with tensor products of Hilbert spaces and operators, and be able to compute entropies and distance measures between quantum states
  • Acquire ability to convert between Choi, Kraus, and Stinespring dilations of quantum channels
  • Be able to explain the notions of qubits, measurement, entanglement, and the basic protocols of quantum information theory such as quantum teleportation and superdense coding
  • Be able to explain quantum information theoretic tasks such as compression or information transmission
  • Know about the capacities of quantum channels and their entropic characterizations.

Admission to the course

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

Teaching

4 hours of lectures/exercises every week for the duration of the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.

Examination

Final written exam which counts 100 % towards the final grade.

This course has 1 mandatory assignment that must be approved before you can sit the final exam.

Examination support material

No examination support material is allowed.

Language of examination

Courses taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

More about examinations at UiO

You will find further guides and resources at the web page on examinations at UiO.

Last updated from FS (Felles studentsystem) Oct. 14, 2026 8:27:48 PM

Facts about this course

Level
Master
Credits
10
Teaching
Spring
Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course.
Examination
Spring

Contact

Department of Mathematics