Hannover 2010 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 11: Quantum Information: Concepts and Methods II
Q 11.6: Talk
Monday, March 8, 2010, 17:45–18:00, E 214
Mutually unbiased bases generated by a single unitary operator — •Kedar Ranade1, Oliver Kern2, and Ulrich Seyfarth2 — 1Institut für Quantenphysik, Universität Ulm — 2Institut für Angewandte Physik, Technische Universität Darmstadt
In this talk, we discuss a method for constructing unitary operators which generate mutually unbiased bases on Hilbert spaces H = Cd for d being a power-of-two dimension (i. e. d = 2m, m ∈ N). Such operators U have order d+1, and the columns of U, U2, …, Ud+1 = 1 define mutually unbiased bases. The construction is based on finding a maximal commuting unitary operator basis of the matrix algebra associated to the Hilbert space and a Clifford group unitary transformation which maps the equivalence classes of a partition of this operator basis onto another. We explicitly construct unitary operators which generate mutually unbiased bases in all dimensions d = 2m for m ≤ 22.