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

Monique Combescure

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

Authors

Monique Combescure Institut de Physique Nucléaire de Lyon (IPNL), 4 rue Enrico Fermi F-69622 Villeurbanne Cedex, France.

Keywords:

Mutually unbiased bases, circulant matrices, Gauss sums

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.