Hjelmslev Geometry of Mutually Unbiased Bases
Abstract
Description
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.
4 pages, 1 figure; extended list of references, figure made more illustrative and in colour; v3 - one more figure and section added, paper made easier to follow, references updated
4 pages, 1 figure; extended list of references, figure made more illustrative and in colour; v3 - one more figure and section added, paper made easier to follow, references updated