Generation of mutually unbiased bases as powers of a unitary matrix in 2-power dimensions

Details Generation of mutually unbiased bases as powers of a unitary matrix in 2-power dimensions Generation of mutually unbiased bases as powers of a unitary matrix in 2-power dimensions

2007-03-12

arxiv.org/abs/math/0703333v2

Mathematics

Representation Theory

9 pages, some earlier questions resolved

Scientific paper

Let q be a power of 2. We show by representation theory that there exists a q x q unitary matrix of multiplicative order q+1 whose powers generate q+1 pairwise mutually unbiased base in C^q. When q is a power of an odd prime, there is a q x q unitary matrix of multiplicative order q+1 whose first (q+1)/2 powers generate (q+1)/2 pairwise mutually unbiased bases. We also show how the existence of these matrices implies the existence of a special type of orthogonal decomposition with respect to the Killing form of the special linear and symplectic Lie algebras.

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