Cyclic mutually unbiased bases, Fibonacci polynomials and Wiedemann's conjecture
| Autor: | Seyfarth, Ulrich, Ranade, Kedar S. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.4723825 |
| Popis: | 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 equivalence |
| Databáze: | arXiv |
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