Concavity conjecture for mutual information in a two-target vector Poisson channel

Let $X=[X_1\:X_2]^{\intercal}$ be a non-negative random vector whose components $X_1$ and $X_2$ are mutually independent and identically distributed. Let $Y=[Y_1\:Y_2\:Y_3]^{\intercal}\in\mathbb{Z}_+^3$ be jointly distributed with $X$, with conditional law as in (a). Under the time constraint

$$T=T_1+T_2+T_3,$$

Mutual-information concavity conjecture. The mutual information $I(X_1,X_2;Y_1,Y_2,Y_3)$ is concave in $(T_1,T_2,T_3)$. The conjecture concerns the sensing-time allocation in the two-target vector Poisson channel and is motivated by extensive computational experiments, while the paper gives no proof and notes that the conditional third mutual-information term can itself be non-concave.