Conjecture that quantum and entanglement-assisted Shannon capacities coincide

Let $G$ be a graph, and let $\Theta_q(G)$ and $\Theta_*(G)$ denote its quantum and entanglement-assisted Shannon capacities, respectively. Quantum capacity conjecture. For every graph $G$,

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

The equality asks whether maximally entangled states suffice to attain the maximal entanglement-assisted Shannon capacity. The source describes this as an open problem in quantum zero-error information theory.