Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pauli graph and finite projective lines/geometries   The commutation relations between the generalized Pauli operators of N-qudits
(i. e., N p-level quantum systems), and the structure of their maximal sets of
commuting bases, follow a nice graph theoretical/geometrical pattern. One may
identify vertices/points with the operators so that edges/lines join commuting
pairs of them to form the so-called Pauli graph P_{p^N} . As per two-qubits (p
= 2, N = 2) all basic properties and partitionings of this graph are embodied
in the geometry of the symplectic generalized quadrangle of order two, W(2).
The structure of the two-qutrit (p = 3, N = 2) graph is more involved; here it
turns out more convenient to deal with its dual in order to see all the
parallels with the two-qubit case and its surmised relation with the geometry
of generalized quadrangle Q(4, 3), the dual of W(3). Finally, the generalized
adjacency graph for multiple (N > 3) qubits/qutrits is shown to follow from
symplectic polar spaces of order two/three. The relevance of these mathematical
concepts to mutually unbiased bases and to quantum entanglement is also
highlighted in some detail.

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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat