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**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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