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

By Ulrich Seyfarth and Kedar S. Ranade


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.Comment: 11 pages, added chapter on equivalenc

Topics: Quantum Physics
Year: 2012
DOI identifier: 10.1063/1.4723825
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