Quantum Information aims at exploiting quantum mechanics to
perform certain tasks (computation, measurements, communication,
etc.) more efficiently than what is allowed by classical physics.
The course will give an introduction to quantum information as well
as to some of the physical systems used to implement quantum
information processing. Special attention will be on quantum
optical systems (atoms, ions, and photons) and superconducting
In the course we will be dealing with the fundamental and often paradoxical structure of quantum mechanics. By working with these subjects, the participants will not only be brought up to date with a very active field of research, but will also gain a deeper understanding of quantum mechanics.
MSc Programme in Physics
After the course the students should be able to explain how the various quantum information protocols work and why they are better than any classical protocol. Furthermore the students should be able to describe how to implement quantum information protocols in practice and discuss some of the problems, which arise when one tries to do so.
More specifically the students should be able to:
- describe how the BB84 quantum cryptography protocol works and how it is implemented in practice.
- define entanglement for pure states, and describe how to use it for super dense coding, cryptography, and teleportation.
- explain how entanglement may be generated experimentally.
- explain what a quantum computer is and describe how the Deutsch and Grover algorithms and quantum simulation work on a quantum computer.
- discuss general requirements for practical implementation of quantum computation and describe how these requirements are fulfilled for ion traps and superconducting qubits.
- explain Bell's inequalities and their violation in quantum mechanics
- discuss how decoherence and imperfections appear and influence experiments and know how to describe it in terms of the density matrix.
- relate the various parts of the course together and apply the knowledge gained in the course in new situations.
After the course students should know the elementary concept from quantum information theory including qubits, pure and mixed states, Bloch sphere, entanglement, super dense coding, teleportation, quantum repeaters, Bell’s inequalities, entanglement purification, quantum error correction, and quantum computation algorithms (Deutsch, Grover, and quantum simulation). Furthermore they should know how one can implement quantum information processing in simple physical systems such as trapped ions and super conducting qubits.
The student will learn how the different logical structure of quantum mechanics, compared to classical mechanics, enables new possibilities for e.g. computation, measurements, and communication. Thereby the course will provide a deeper understanding of the quantum mechanics learned in previous courses. It will also provide the students with a background for further studies within quantum information, e.g. in a M.Sc. project
Lectures and exercises
Various notes and articles.
Academic qualifications equivalent to a BSc degree is
It is particularly important that you have a solid background in quantum mechanics, e.g. corresponding to a bachelor program in physics. Also it may be an advantage if you have followed a course on Optical Physics and Lasers but it is not strictly necessary.
- 7,5 ECTS
- Type of assessment
Oral examination, 30 minWithout preparation time
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
More internal examiners
Criteria for exam assessment
see learning outcome
Single subject courses (day)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 1
- No restriction
- Study Board of Physics, Chemistry and Nanoscience
- The Niels Bohr Institute
- Faculty of Science
- Anders Søndberg Sørensen (15-6471676875763176727568717668714371656c316e7831676e)
Phone 35 32 52 40, Mobile 24 66 13 77
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Courseinformation of students