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Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2006

Hjelmslev Geometry of Mutually Unbiased Bases

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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Dates and versions

hal-00005539 , version 1 (22-06-2005)
hal-00005539 , version 2 (26-07-2005)
hal-00005539 , version 3 (08-11-2005)

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Cite

Metod Saniga, Michel Planat. Hjelmslev Geometry of Mutually Unbiased Bases. Journal of Physics A: Mathematical and Theoretical, 2006, 39, pp.435-440. ⟨10.1088/0305-4470/39/2/013⟩. ⟨hal-00005539v3⟩
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