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

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 $d \times d$ 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.
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Preprints, Working Papers, ...
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Cited literature [11 references]

http://hal.in2p3.fr/in2p3-00184035
Contributor : Sylvie Flores <>
Submitted on : Tuesday, October 30, 2007 - 1:12:34 PM
Last modification on : Tuesday, November 19, 2019 - 2:41:36 AM
Long-term archiving on: : Monday, April 12, 2010 - 12:59:50 AM

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• HAL Id : in2p3-00184035, version 1
• ARXIV : 0710.5642

### Citation

M. Combescure. Circulant matrices, gauss sums and mutually unbiased I. The prime number case. 2007. ⟨in2p3-00184035⟩

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