Circulant matrices, gauss sums and mutually unbiased I. The prime number case

Understand

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 $d \times d$ 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.