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

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.

11 pages, added chapter on equivalence

References in corpus (6)

• Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
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Cited by in corpus (3)

• States that "look the same" with respect to every basis in a mutually unbiased set
• Structure of the sets of mutually unbiased bases with cyclic symmetry
• Cyclic Mutually Unbiased Bases and Quantum Public-Key Encryption