A parallel repetition theorem for entangled two-player one-round games under product distributions

We show a parallel repetition theorem for the entangled value ${\omega }^{\ast }(G)$ of any two-player one-round game $G$ where the questions $(x,y) \in $\mathcal{X}$\times$\mathcal{Y}$$ to Alice and Bob are drawn from a product distribution on $\mathcal{X}\times \mathcal{Y}$. We show that for the $k$-fold product $G^k$ of the game $G$ (which represents the game $G$ played in parallel $k$ times independently), $ \omega^(G^k) =\left(1-(1-\omega^(G))^3\right)^{\Omega\left(\frac{k}{\log(|$\mathcal{A}$| \cdot |$\mathcal{B}$|)}\right)} $,where$$\mathcal{A}$$and$$\mathcal{B}$$ represent the sets from which the answers of Alice and Bob are drawn.