Rigidity and a common framework for mutually unbiased bases and k ‐nets

  title={Rigidity and a common framework for mutually unbiased bases and 
k ‐nets},
  author={Sloan Nietert and Zsombor Szil'agyi and Mih{\'a}ly Weiner},
  journal={Journal of Combinatorial Designs},
  pages={869 - 892}
Many deep connections have been observed between collections of mutually unbiased bases (MUBs) and combinatorial designs called k ‐nets (and in particular, between collections of MUBs and finite affine planes). Here we introduce the notion of a k ‐net over a C * ‐algebra, providing a common framework for both objects. In the commutative case, we recover (classical) k ‐nets, while the choice of M d ( C ) leads to collections of MUBs. In this framework, we derive a rigidity property which hence… 
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