Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Studies of symmetries that give special quantum states the "right to
  exist"   In this thesis we study symmetric structures in Hilbert spaces known as
symmetric informationally complete positive operator-valued measures
(SIC-POVMs), mutually unbiased bases (MUBs), and MUB-balanced states. Our tools
include symmetries such as the Weyl-Heisenberg (WH) group symmetry, Clifford
unitaries, Zauner symmetry, and Galois-unitaries (g-unitaries), which are
non-linear operators defined to generalize the notion of anti-unitaries.

30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga