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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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https://hal.archives-ouvertes.fr/hal-00005539
Contributor : Metod Saniga <>
Submitted on : Tuesday, November 8, 2005 - 11:46:49 AM
Last modification on : Thursday, November 12, 2020 - 9:42:04 AM
Long-term archiving on: : Thursday, September 23, 2010 - 3:50:32 PM

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

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