On the closure of the completely positive semidefinite cone and linear approximations to quantum colorings

Understand

We investigate structural properties of the completely positive semidefinite cone $\mathcal{CS}_+^n$, consisting of all the $n \times n$ symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size.

• This cone has been introduced to model quantum graph parameters as conic optimization problems.
• Recently it has also been used to characterize the set $\mathcal Q$ of bipartite quantum correlations, as projection of an affine section of it.
• We have two main results concerning the structure of the completely positive semidefinite cone, namely about its interior and about its closure.