Circulant Matrices, Gauss Sums and Mutually Unbiased Bases, I. The Prime Number Case

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Abstract

In this paper, we consider the problem of Mutually Unbiased Bases in prime dimension d. It is known to provide exactly d + 1 mutually unbiased bases. We revisit this problem using a class of circulant d × d matrices. The constructive proof of a set of d + 1 mutually unbiased bases follows, together with a set of properties of Gauss sums, and of bi-unimodular sequences.

Keywords

Mutually unbiased bases , circulant matrices , Gauss sums
  • Monique Combescure Institut de Physique Nucléaire de Lyon (IPNL), 4 rue Enrico Fermi F-69622 Villeurbanne Cedex, France.
  • Pages: 73–86
  • Date Published: 2009-09-01
  • Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal

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Published

2009-09-01

How to Cite

[1]
M. Combescure, “Circulant Matrices, Gauss Sums and Mutually Unbiased Bases, I. The Prime Number Case”, CUBO, vol. 11, no. 4, pp. 73–86, Sep. 2009.

Issue

Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal

Section

Articles