Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some non-standard ways to generate SIC-POVMs in dimensions 2 and 3   The notion of Symmetric Informationally Complete Positive Operator-Valued
Measures (SIC-POVMs) arose in physics as a kind of optimal measurement basis
for quantum systems. However the question of their existence is equivalent to
that of the existence of a maximal set of \emph{complex equiangular lines}.
That is to say, given a complex Hilbert space of dimension $d$, what is the
maximal number of (complex) lines one can find which all make a common (real)
angle with one another, in the sense that the inner products between unit
vectors spanning those lines all have a common absolute value? A maximal set
would consist of $d^2$ lines all with a common angle of
$\arccos{\frac{1}{\sqrt{d+1}}}$. The same question has been posed in the real
case and some partial answers are known. But at the time of writing no unifying
theoretical result has been found in the real or the complex case: some
sporadic low-dimensional numerical constructions have been converted into
algebraic solutions but beyond this very little is known. It is conjectured
that such structures always arise as orbits of certain fiducial vectors under
the action of the Weyl (or generalised Pauli) group. In this paper we point out
some new construction methods in the lowest dimensions ($d=2$ and $d=3$). We
should mention that the SIC-POVMs so constructed are all unitarily equivalent
to previously known SIC-POVMs.

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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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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: solv-int
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The categories of this paper are: ao-sci