Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture
Quantum Physics
2015-05-27 v2
Abstract
We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an irreducible characteristic polynomial that has a given Fibonacci index. For dimensions of the form 2^(2^k) we present a solution that shows an analogy to an open conjecture of Wiedemann in finite field theory. Finally, we discuss the equivalence of mutually unbiased bases.
Cite
@article{arxiv.1104.0202,
title = {Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture},
author = {Ulrich Seyfarth and Kedar S. Ranade},
journal= {arXiv preprint arXiv:1104.0202},
year = {2015}
}
Comments
11 pages, added chapter on equivalence