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Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes?

Abstract : This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an analogue of an arc in a (Desarguesian) projective plane of order d. Complete sets of MUBs thus correspond to (d+1)-arcs, i.e., ovals. The existence of two principally distinct kinds of ovals for d even and greater than four, viz. conics and non-conics, implies the existence of two qualitatively different groups of the complete sets of MUBs for the Hilbert spaces of corresponding dimensions.
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Contributor : Metod Saniga <>
Submitted on : Thursday, November 25, 2004 - 11:31:57 AM
Last modification on : Thursday, November 12, 2020 - 9:42:03 AM
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Metod Saniga, Michel Planat. Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes?. Chaos, Solitons and Fractals, Elsevier, 2005, 26, pp.1267 - 1270. ⟨hal-00002952v2⟩

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