Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois Unitaries, Mutually Unbiased Bases, and MUB-balanced states   A Galois unitary is a generalization of the notion of anti-unitary operators.
They act only on those vectors in Hilbert space whose entries belong to some
chosen number field. For Mutually Unbiased Bases the relevant number field is a
cyclotomic field. By including Galois unitaries we are able to remove a
mismatch between the finite projective group acting on the bases on the one
hand, and the set of those permutations of the bases that can be implemented as
transformations in Hilbert space on the other hand. In particular we show that
there exist transformations that cycle through all the bases in every dimension
which is an odd power of an odd prime. (For even primes unitary MUB-cyclers
exist.) These transformations have eigenvectors, which are MUB-balanced states
(i.e. rotationally symmetric states in the original terminology of Wootters and
Sussman) if and only if d = 3 modulo 4. We conjecture that this construction
yields all such states in odd prime power dimension.

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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph