Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conic approach to quantum graph parameters using linear optimization
  over the completely positive semidefinite cone   We investigate the completely positive semidefinite cone $\mathcal{CS}_+^n$,
a new matrix cone consisting of all $n\times n$ matrices that admit a Gram
representation by positive semidefinite matrices (of any size). In particular
we study relationships between this cone and the completely positive and doubly
nonnegative cones, and between its dual cone and trace positive non-commutative
polynomials.
  We use this new cone to model quantum analogues of the classical independence
and chromatic graph parameters $\alpha(G)$ and $\chi(G)$, which are roughly
obtained by allowing variables to be positive semidefinite matrices instead of
$0/1$ scalars in the programs defining the classical parameters. We can
formulate these quantum parameters as conic linear programs over the cone
$\mathcal{CS}_+^n$. Using this conic approach we can recover the bounds in
terms of the theta number and define further approximations by exploiting the
link to trace positive polynomials.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol