MUBs, polytopes, and finite geometries

Details MUBs, polytopes, and finite geometries MUBs, polytopes, and finite geometries

2004-06-23

arxiv.org/abs/quant-ph/0406174v2

Physics

Quantum Physics

15 pages; talk at the Vaxjo conference on probability and physics

Scientific paper

10.1063/1.1874558

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 questions about a convex polytope, but not in any obvious way the same question.

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