Conic Approach to Quantum Graph Parameters Using Linear Optimization Over the Completely Positive Semidefinite Cone

@article{Laurent2015ConicAT,
  title={Conic Approach to Quantum Graph Parameters Using Linear Optimization Over the Completely Positive Semidefinite Cone},
  author={Monique Laurent and Teresa Piovesan},
  journal={SIAM J. Optim.},
  year={2015},
  volume={25},
  pages={2461-2493}
}
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 the doubly nonnegative cone, and between its dual cone and trace positive noncommutative polynomials. We use this new cone to model quantum analogues of the classical independence and… 

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