Weak particle-system convergence conjecture

Let $\bm X^P$ be the continuous-time particle-system approximation and let $Z(t)$ be the true solution of the corresponding McKean–Vlasov equation. Let $G^P(x)=\frac{1}{P}\sum_{j=1}^P g(x_j)$. Weak particle-system convergence conjecture. The weak error satisfies

$$\left|\mathbb{E}\left[G^P\left(\bm X^P(T)\right)-g\left(Z(T)\right)\right]\right|\lesssim P^{-2}.$$

The usual non-QMC particle approximation is stated to have weak rate $\mathcal{O}(P^{-1})$, whereas numerical tests and a bound in the zero-diffusion case support the conjectured improved rate.