Nonsplit quantum unique ergodicity conjecture for Bianchi Maaß forms

Let $E$ be an imaginary quadratic field of class number $1$, let $\Gamma$ be the relevant arithmetic subgroup, and let $(\phi_j)$ be an orthonormal basis of Bianchi Maaß cusp forms on $\mathrm{SL}_2(\mathcal{O}_E)\backslash\mathbb{H}^3$, with spectral parameter $t_j$. Restrict $\phi_j$ from $\mathbb{H}^3$ to $\Gamma\backslash\mathbb{H}$ and define the signed measure $d\mu_j(z)\coloneqq\phi_j(z)\,d\mu(z)$. For $H\in C_b(\Gamma\backslash\mathbb{H})$, let $\mathcal{D}_j(H)$ be the discrepancy defined from this signed measure as in the Hilbert case, and set

$$C(\phi_j)\coloneqq(3+|t_j|)^4.$$

Nonsplit Bianchi quantum unique ergodicity conjecture. If $H\in C_b(\Gamma\backslash\mathbb{H})$ is fixed, then

$$\lim_{C(\phi_j)\to\infty}C(\phi_j)^{\frac18}\mathcal{D}_j(H)=0.$$

This is the imaginary-quadratic, or Bianchi, analogue of the preceding nonsplit conjecture. It predicts quantitative dissipation of the restrictions to the modular surface as the analytic conductor grows, and the statement remains open.