  The $U_q(A^{(1)}_n)$-zero range processes introduced recently by Mangazeev,
Maruyama and the authors are integrable discrete and continuous time Markov
processes associated with the stochastic $R$ matrix derived from the well-known
$U_q(A_n^{(1)})$ quantum $R$ matrix. By constructing a representation of the
relevant Zamolodchikov-Faddeev algebra, we present, for $n=2$, a matrix product
formula for the steady state probabilities in terms of $q$-boson operators.
