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

Seyfarth, Ulrich and Ranade, Kedar (2012):
Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture.
53, In: J. Math. Phys., (6), p. 62201, DOI: 10.1063/1.4723825,
[Article]

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.

Item Type: Article
Erschienen: 2012
Creators: Seyfarth, Ulrich and Ranade, Kedar
Title: Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture
Language: German
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.

Journal or Publication Title: J. Math. Phys.
Volume: 53
Number: 6
Uncontrolled Keywords: Secure Data;Quantenkryptographie
Divisions: LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research Darmstadt
LOEWE > LOEWE-Zentren
LOEWE
Date Deposited: 30 Dec 2016 20:23
DOI: 10.1063/1.4723825
Identification Number: TUD-CS-2012-0112
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