Subadditivity of mutual information for spin synchronization models

Let $(X,Y)$ be a spin synchronization model on a graph $G$, let $u \in V(G)$, and let $W \subset V(G)$. Let $I$ denote either the Chi-squared mutual information $I_2$ or the Kullback–Leibler mutual information $I_{KL}$.

Mutual-information subadditivity conjecture. The inequality

$$I(X_u; X_W \mid Y_{E(G)}) \leq \sum_{w \in W} I(X_u; X_w \mid Y_{E(G)})$$

should hold for arbitrary edge channels $Q$.

This is a proposed subadditivity principle relating information about a collection of spins to the sum of the pairwise informations. The source does not state that it is known or resolved.