Design theory is a relatively new part of combinatorics, which has a noncommutative generalisation called quantum design theory. Many important problems in quantum information theory can be formulated in the framework of quantum design theory. First the most important concepts of classical design theory are introduced via a few simple examples. Finite projective planes, Latin squares, Hadamard matrices emerge naturally. Then the concepts of classical design theory are generalised to the quantum case. Here the most basic examples are MUBs (mutually unbiased bases) and SIC-POVMs (symmetric, informationally complete positive operator valued measures). Both the classical and the quantum design theory present many interesting, unsolved problems.

 

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