Wednesday, March 28, 2012

1104.0202 (Ulrich Seyfarth et al.)

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

Ulrich Seyfarth, 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.
View original: http://arxiv.org/abs/1104.0202

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