Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hierarchy of Spin Operators, Quantum Gates, Entanglement, Tensor Product
  and Eigenvalues   {\bf Abstract.} We show that two hierarchies of spin Hamilton operators admit
the same spectrum. Both Hamilton operators play a central role for quantum
gates in particular for the case spin-$\frac12$ and the case spin-1. The
spin-$\frac12$, spin-1, spin-$\frac32$ and spin-2 cases are studied in detail.
Entanglement and mutually unbiased bases of the eigenvectors is discussed. Two
triple Hamilton operators are also investigated. Both are also admitting the
same spectrum.

29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol