Viewing sets of mutually unbiased bases as arcs in finite projective planes

@article{Saniga2005ViewingSO,
  title={Viewing sets of mutually unbiased bases as arcs in finite projective planes},
  author={M. Saniga and M. Planat},
  journal={Chaos Solitons \& Fractals},
  year={2005},
  volume={26},
  pages={1267-1270}
}
Abstract This note is a short conceptual 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 as an analogue of an arc in a (finite) projective plane of order d . Complete sets of MUBs thus correspond to ( d  + 1)-arcs, i.e., ovals. In the Desarguesian case, the existence of two principally distinct kinds of ovals for d  = 2 n and n  ⩾ 3, viz. conics and non-conics… Expand
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