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arXiv · 1104.0202

Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture

Ulrich Seyfarth·Kedar S. Ranade
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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.

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Ulrich Seyfarth, Kedar S. Ranade. 2011-04-01. Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture. https://doi.org/10.1063/1.4723825

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