Duality from integrability: annihilating random walks with pair deposition

We study a system of interacting random walks in one dimension that annihilate immediately when two particles meet on the same site. In addition, pairs of particles are created on neighbouring sites. A duality with independent two-level systems which arises from the integrability of the model is proved. The duality function is determinantal and has the form of a matrix product. We use this duality to compute the exact current distribution.