Quantum Information Theory
Kvantinformationsteori

FMFN35, 7.5 credits, A (Second Cycle)

Valid for: 2025/26
Faculty: Faculty of Engineering LTH
Decided by: PLED F/Pi
Date of Decision: 2025-04-10
Effective: 2025-05-05

General Information

Depth of study relative to the degree requirements: Second cycle, in-depth level of the course cannot be classified
Elective for: F4, F4-kv, MFOT1, MNAV2, N4
Language of instruction: The course will be given in English on demand

Aim

The general aim of the course is that the students should acquire knowledge of theoretical concepts and methods in quantum theory and quantum information.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

• describe the main directions in quantum information and how these relate to one another,
• demonstrate good theoretical understanding of states, measurements and transformations in quantum theory.
• give an account of basic quantum information protocols such as teleportation,super-dense encoding and entanglement swapping.
• demonstrate good theoretical understanding of quantum mechanical entanglement and non-locality.
• name and on a general level explain basic concepts and results in quantum cryptography and other relevant application fields of quantum information.

Competences and skills
For a passing grade the student must

• apply different mathematical representation forms of quantum transformations.
• calculate probability distributions based on general density matrices, measurements and structures on the Hilbert space.
• design simple examples of entanglement criteria.
• discuss conceptual aspects of non-locality and its relevance for information applications.
• use Bell inequalities for simple quantitative calculations of non-locality.
• describe communication- and entanglement-based methods for quantum encryption and qualitatively analyse their safety aspects.

Judgement and approach
For a passing grade the student must

• Give an account of the importance of theoretical ideas and methods in quantum information both for conceptualizing quantum physics and for applications in quantum technology.

Contents

The course covers the following theoretical concepts in quantum information:

• mathematical representation theory for quantum mechanical states, measurements and transformations
• entropy and information concepts
• paradigmatic quantum protocols: teleportation, super-dense encoding and entanglement swapping
• initial discussion of quantum mechanical entanglement, especially its detection, quantification and classification
• non-locality: hidden variables, systematic analysis of Bell inequalities and non-locality beyond quantum physics
• BB84 and E91 quantum encryption protocols
• quantum metrology: The Cramér-Rao theorem and quantum Fisher information.

Examination details

Grading scale: TH - (U, 3, 4, 5) - (Fail, Three, Four, Five)
Assessment:

Assessment takes place in the form of an oral examination at the end of the course.

Students who do not pass a regular assessment will be offered another opportunity

for assessment soon thereafter.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Modules
Code: 0124. Name: Examination.
Credits: 7.5. Grading scale: TH - (U, 3, 4, 5). Assessment: Oral exam. The module includes: According to the lectures.

Admission

Assumed prior knowledge: Quantum mechanics corresponding to FMFN01 Quantum Mechanics, Advanced Course 1.
The number of participants is limited to: No

Reading list

• Wilde, Mark, 1980-: Quantum information theory. Cambridge : Cambridge University Press, 2017, ISBN: 9781316809976. Supplementary reading.
• Nielsen, Michael A., 1974-: Quantum computation and quantum information. Cambridge : Cambridge Univers. Press, 2000, ISBN: 0521632358. Supplementary reading.
• Courses lecture notes.
• lecture notes by J. Preskill.
  http://theory.caltech.edu/~preskill/ph229/

Contact

Teacher: Armin Tavakoli, armin.tavakoli@teorfys.lu.se
Examinator: Armin Tavakoli, armin.tavakoli@teorfys.lu.se
Course homepage: https://canvas.education.lu.se

Further information

The course is in full coordinated with FYST82, Physics: Quantum Information Theory, which is a course given at the Faculty of Science.