English

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

Mathematical Physics 2007-10-31 v1 math.MP Quantum Physics

Abstract

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

Keywords

Cite

@article{arxiv.0710.5642,
  title  = {Circulant matrices, gauss sums and mutually unbiased I. The prime number case},
  author = {M. Combescure},
  journal= {arXiv preprint arXiv:0710.5642},
  year   = {2007}
}