On the Closure of the Completely Positive Semidefinite Cone and Linear Approximations to Quantum Colorings

@inproceedings{Burgdorf2015OnTC,
  title={On the Closure of the Completely Positive Semidefinite Cone and Linear Approximations to Quantum Colorings},
  author={Sabine Burgdorf and Monique Laurent and Teresa Piovesan},
  booktitle={TQC},
  year={2015}
}
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… 

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