Tate's full faithfulness conjecture for motives

Let $F$ be a number field and let $\operatorname{Rep}_{{\mathbb Q}_\ell}(G_F)$ be the category of $\ell$-adic representations of $G_F=\operatorname{Gal}(\overline F/F)$. Consider the functor from motives over $F$ with rational coefficients to their étale $\ell$-adic realizations. Tate's conjecture. The functor

$$(\cdot)_\ell:{\mathcal M}(F)_{\mathbb Q}\longrightarrow \operatorname{Rep}_{{\mathbb Q}_\ell}(G_F)$$

is fully faithful.