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.
@article{1454,
title = {Circulant Matrices, Gauss Sums and Mutually Unbiased Bases, I. The Prime Number Case},
journal = {CUBO, A Mathematical Journal},
volume = {11},
year = {2009},
language = {en},
url = {http://dml.mathdoc.fr/item/1454}
}
Combescure, Monique. Circulant Matrices, Gauss Sums and Mutually Unbiased Bases, I. The Prime Number Case. CUBO, A Mathematical Journal, Tome 11 (2009) . http://gdmltest.u-ga.fr/item/1454/