Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing maximal families of mutually unbiased bases   We show that maximal families of mutually unbiased bases are characterized in
all dimensions by partitioned unitary error bases, up to a choice of a family
of Hadamards. Furthermore, we give a new construction of partitioned unitary
error bases, and thus maximal families of mutually unbiased bases, from a
finite field, which is simpler and more direct than previous proposals. We
introduce new tensor diagrammatic characterizations of maximal families of
mutually unbiased bases, partitioned unitary error bases, and finite fields as
algebraic structures defined over Hilbert spaces.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: math
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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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: econ