Conjecture that entanglement-assisted Shannon capacity equals the Lovász theta function

Let $G$ be a graph, and let $\Theta_*(G)$ be its entanglement-assisted Shannon capacity. Let $\vartheta(G)$ be the Lovász theta function. Entanglement-assisted capacity conjecture. For every graph $G$,

$$\Theta_*(G)=\vartheta(G).$$

The theta function is known to be monotone for the entanglement-assisted cohomomorphism preorder and therefore gives an upper bound on $\Theta_*(G)$. The source reports that equality remains conjectural.