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Mutually Unbiased Bases for Continuous Variables

Quantum Physics 2009-11-13 v2

Abstract

The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N = 2, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.

Keywords

Cite

@article{arxiv.0802.0394,
  title  = {Mutually Unbiased Bases for Continuous Variables},
  author = {Stefan Weigert and Michael Wilkinson},
  journal= {arXiv preprint arXiv:0802.0394},
  year   = {2009}
}

Comments

5 pages, no figures, revised to be identical to published text

R2 v1 2026-06-21T10:09:17.158Z