Some attempts at proving the non-existence of a full set of mutually unbiased bases in dimension 6

Details Some attempts at proving the non-existence of a full set of mutually unbiased bases in dimension 6 Some attempts at proving the non-existence of a full set of mutually unbiased bases in dimension 6

2010-12-14

arxiv.org/abs/1012.3147v1

Physics

Mathematical Physics

19 pages

Scientific paper

Complete sets of mutually unbiased bases are only known to exist in prime-power dimensions. We will describe a few approaches to the problem proving the (non)-existence of four mutually unbiased bases in dimension 6. These will include the notions of Grassmannian distance, quadratic matrix programming, semidefinite relaxations to polynomial programming, as well as various tools from algebraic geometry.

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