Holomorphic quantum unique ergodicity conjecture for Siegel cusp forms

Let $\mathbb H_n$ denote the Siegel upper-half space of degree $n$, and let $S_k(\operatorname{Sp}_{2n}(\mathbb Z))$ be the space of holomorphic Siegel cusp forms of weight $k$ for $\operatorname{Sp}_{2n}(\mathbb Z)$. Let

$$\mathrm d\mu:= (\det Y)^{-n-1}\mathrm dX\,\mathrm dY$$

be the invariant measure on $\mathbb H_n$, and set $Y_n:=\operatorname{Sp}_{2n}(\mathbb Z)\backslash\mathbb H_n$. For $F\in S_k(\operatorname{Sp}_{2n}(\mathbb Z))$, define the finite measure $\mu_F$ by

$$\mu_F(\phi):=\int_{Y_n}|F(Z)|^2\phi(Z)(\det Y)^k\,\mathrm d\mu$$

for bounded measurable $\phi$, and define

$$D_F(\phi):=\frac{\mu_F(\phi)}{\mu_F(1)}-\frac{1}{\operatorname{vol}(Y_n)}\int_{Y_n}\phi(Z)\,\mathrm d\mu.$$

Holomorphic QUE conjecture. Fix a bounded continuous function $\phi$ on $\operatorname{Sp}_{2n}(\mathbb Z)\backslash\mathbb H_n$. If $F\in S_k(\operatorname{Sp}_{2n}(\mathbb Z))$ traverses a sequence of Hecke eigenforms, then

$$D_F(\phi)\longrightarrow 0$$

whenever $k\longrightarrow\infty$.

This is the natural higher-rank generalization of holomorphic quantum unique ergodicity. The supplied text gives no resolution status.