Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generation of mutually unbiased bases as powers of a unitary matrix in
  2-power dimensions   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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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: stat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph