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?

Program

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.

Participants

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	Group-symmetry
Jan-Ake Larsson, Linköpings Universitet	SIC POVMs and the Discrete Affine Fourier Transform
Jay Lawrence, Dartmouth College	Symmetries
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.