4EU+: Quantum Information and Quantum Many-Body Theory

7 March - 28 June 2024. 


The course is not mandatory in any master's education but is part of the 4EU+ Alliance. The course is given in collaboration with the University of Warsaw, the University of Milan, the University of Geneva, Heidelberg University, Sorbonne University and Charles University.

Target Groups

Master students and PhD students. The course is open to all interested students, as well as students outside the 4EU+ Alliance. Travel grants are, however, only available to students from within the alliance. Priority will be given to students from our partner universities, the University of Milan, the University of Warsaw, the University of Geneva, Heidelberg University, Sorbonne University and Charles University.


Expected minimal requirements: Linear algebra some elementary quantum knowledge, e.g., elementary quantum computing or elementary quantum mechanics.


Registration before 1 March 2024. 

Master students enrolled at the University of Copenhagen must apply to the Study Board to transfer the course credits as part of their master's programme. The course responsible can help with the application to the Study Board. Please contact Albert Werner or Jan Philip Solovej.


Spring and Block 4. 7 March - 28 June 2024.


The course will consist of three phases:
  • Phase 1: 7 March - 2 May 2024
    Online lectures
     (approximately one two-hour lecture every other week, in total 7 lectures)
  • Phase 2: 2-31 May 2024. Students work on assignments which will be presented at a poster session at the physical meeting.
  • Phase 3: 24-28 June 2024. Physical Master Class in Copenhagen (Approximately 24 hours of lectures plus 5 hours of exercises).


We are currently witnessing the second quantum revolution and with it the advent of quantum technological devices for information processing purposes. Understanding these systems and their capabilities as well as developing robustalgorithms for them, requires a fundamental understanding of complex quantum many-body systems as well as ways tocharacterize their properties efficiently. Within this course, we will help the participants to obtain proficiency in allof these aspects of quantum theory. A tentative list of topics includes:

  • Entanglement/Non-Locality:
    Lecture 1: States, Measurement, Tensor Product, Maximally Entangled State
    Lecture 2: Tensor Product (contd.), Density Matrices, Reduced States, Entropy, Entanglement Entropy.
    Lecture 3: Bell-inequalities, Bell’s Theorem, Non-local Games/Protocols.

  • Quantum Spin-System
    Lecture 1: Spin Hamiltonians, Spin-½ Heisenberg Model, SU(2), Ground States, Ground State Energy
    Lecture 2: Free Energy, Thermodynamic Limit, Thermal State
    Lecture 3: Symmetry Breaking, Mermin-Wagner
    Lecture 4: AKLT, Matrix Product States

For each of these topics, we will provide introductory lectures to get students acquainted with the topics before entering into the in-person phase, where experts and practitioners of these fields will give further insight.

Learning Outcome

The goal is to provide the students with a blended learning approach to the course content on the mathematics of quantum theory with special emphasis on complex quantum many-body systems and quantum information theory. The main intended learning outcomes include an overview of the latest developments in those fields. Furthermore, the course will help the participants to develop competencies to engage in self-organized cross-university and interdisciplinary collaborations via online groupwork as well as to give and receive peer-feedback on results. Inviting external experts in the field will also give young researchers in the field the opportunity to grow their professional network considerably. 

Registration before 1 March 2024

Contact Persons

University of Copenhagen: 
Associate Professor Albert Werner and Professor Jan Philip Solovej, Department of Mathematical Sciences (Project Coordinator)

University of Milan:
Professor Niels BenedikterDipartimento di Matematica

University of Warsaw:
Assistant Professor Marcin Napiórkowski, Faculty of Physics

University of Geneva: 
Assistant Professor Géraldine HaackDepartment of Applied Physics 
Professor Nicholas Brunner, Department of Applied Physics

Heidelberg University:
Professor Manfred Salmhofer, Department of Physics

Sorbonne University:
Frédéric GrosshansCNRS Researcher at LIP6

Associate Professor Marco Túlio Quintino, Department of Engineering and LIP6

 Charles University: 
Professor Martin Loebl, Department of Applied Mathematics