Hjelmslev Geometry of Mutually Unbiased Bases

Details Hjelmslev Geometry of Mutually Unbiased Bases Hjelmslev Geometry of Mutually Unbiased Bases

2005-06-22

arxiv.org/abs/math-ph/0506057v3

Journal of Physics A 39 (2006) 435-440

Physics

Mathematical Physics

4 pages, 1 figure; extended list of references, figure made more illustrative and in colour; v3 - one more figure and section

Scientific paper

10.1088/0305-4470/39/2/013

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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