  We introduce and study the entanglement breaking rank of an entanglement breaking channel. We show that the entanglement breaking rank of the channel $\mathfrak Z: M_d \to M_d$ defined by \begin{align*} \mathfrak Z(X) = \frac{1}{d+1}(X+\text{Tr}(X)\mathbb I_d) \end{align*} is $d^2$ if and only if there exists a symmetric informationally-complete POVM in dimension $d$. 
Entanglement Breaking Rank and the existence of SIC POVMs