Quantum Physics in Higher-Dimensional Hilbert Spaces


date icon 27-Jul-10
time icon


Workshop Organizer: Časlav Brukner, Anton Zeilinger

Internationale Akademie Traunkirchen

Aim of the workshop

It was the intention of the Workshop to encourage scientific discussion on innovative ideas on testing foundations of quantum mechanics in Hilbert spaces of higher dimensions. This included a diverse range of approaches to the following problems:

  • Does a complete set of Mutually Unbiased Basis Sets (MUBs) and/or Symmetric, Informationally Complete, Positive Operator Valued Measures (SIC POVMs) exist in any dimension of the Hilbert space?
  • What would be the consequences for our understandings of structure of quantum theory in case of either answer?
  • What new theoretical and experimental perspectives to foundational issues can be expected from the research on MUBs and SIC POVMs?


The Workshop brought together many of the key scientists from all over the world working on the problems. The format of the Workshop was carried out with emphasis on discussions.


Senior Fellows

Name Summary
Marcus Appelby,
University of London
Ingemar Bengtsson,
University of Stockholm
Classification of complex Hadamard matrices
Steve Brierley,
University of York
QKD abstract
Caslav Brukner,
University of Vienna
MUBs in generalized probabilistic theories
Christopher Fuchs,
Perimeter Institute
Charting the Shape of Hilbert Space
Zhu Huangjun,
National University of Singapur
Jan-Ake Larsson,
Linköpings Universitet
SIC POVMs and the Discrete Affine Fourier Transform
Jay Lawrence,
Dartmouth College
Tomasz Paterek,
University of Singapore
Mutually unbiased bases and orthogonal latin squares
Stefan Weigert,
University of York
Mutually Unbiased Constellations
William Wootters,
Williams College
States with the Same Probability Distribution for Each Basis in a Complete Set of MUBs
Gerhard Zauner Quantum-Designs
Anton Zeilinger,
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences
Marek Zukowski,
University of Gdansk

Junior Fellows The workshop was open to a limited number of junior fellows.