Outage Probability Conjecture for MISO channels

Let

$$\mathcal{D}(t):=\{ {\mathbf{Q}}\in\mathbb{C}^{t\times t}\mid {\mathbf{Q}}\geq 0,\operatorname{tr}({\mathbf{Q}})\leq 1\}$$

and let $(H_i)_{1\leq i\leq t}$ be independent and identically distributed as $\mathcal{N}_{\mathbb{C}}(0,1)$. Write ${\mathbf{H}}=(H_1,\dots,H_t)$ and let $\mathcal{U}(t)$ denote the group of $t\times t$ unitary matrices. For every $x\in\mathbb{R}_+$, there exists $k\in\{1,\dots,t\}$ such that

Outage Probability Conjecture for MISO.

$$\operatorname*{\arg\,\min}_{{\mathbf{Q}}\in\mathcal{D}(t)}\mathbb{P}\{{\mathbf{H}}{\mathbf{Q}}{\mathbf{H}}^*\leq x\} =\left\{ {\mathbf{U}}\operatorname{diag}\left(\underbrace{\frac{1}{k},\dots,\frac{1}{k}}_{k},\underbrace{0,\dots,0}_{t-k}\right){\mathbf{U}}^*: {\mathbf{U}}\in\mathcal{U}(t)\right\}.$$

The source states that this MISO case was proved by Abbe et al.; consequently this is a solved special case of the general outage probability conjecture.