MUBs, Polytopes, and Finite Geometries

Ingemar Bengtsson
2005 AIP Conference Proceedings  
A complete set of N+1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = p^k, where p is a prime number. They mesh naturally with finite affine planes of order N, that exist when N = p^k. The existence of MUBs for other values of N is an open question, and the same is true for finite affine planes. I explore the question whether the existence of complete sets of MUBs is directly related to the existence of finite affine planes. Both questions can be shown to be geometrical
more » ... questions about a convex polytope, but not in any obvious way the same question.
doi:10.1063/1.1874558 fatcat:b27gblxyhzeo7owpkfkfm7a4p4