Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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,  study relationships beten this cone and the completely positive and the doubly nonnegative cone, and beten its dual cone and trace positive noncommutative polynomials.  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.  can formulate these quantum parameters as conic linear programs over the cone ${\mathcal{CS}_{+}^n}$. Using this conic approach  can recover the bounds in terms of the theta number and define further approximations by exploiting the link to trace positive polynomials.
['Monique Laurent', 'Teresa Piovesan']
I am writing a research paper on a idea Conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone
[{"from": "human", "value": "I am writing a research paper on a idea Conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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,  study relationships beten this cone and the completely positive and the doubly nonnegative cone, and beten its dual cone and trace positive noncommutative polynomials.  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.  can formulate these quantum parameters as conic linear programs over the cone ${\\mathcal{CS}_{+}^n}$. Using this conic approach  can recover the bounds in terms of the theta number and define further approximations by exploiting the link to trace positive polynomials."}]