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Hjelmslev Geometry of Mutually Unbiased Bases

Metod Saniga·Michel Planat
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Abstract

The basic combinatorial properties of a complete set of mutually unbiased bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a prime and r a positive integer, are shown to be qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p^2 and rank r. The q vectors of a basis of H\_q correspond to the q points of a (so-called) neighbour class and the q+1 MUBs answer to the total number of (pairwise disjoint) neighbour classes on the conic.

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Metod Saniga, Michel Planat. 2005-11-08. Hjelmslev Geometry of Mutually Unbiased Bases. https://doi.org/10.1088/0305-4470/39/2/013

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