Entanglement-breaking channels are a quantum memory resource

Entanglement-breaking channels (equivalently, measure-and-prepare channels) are quantum operations noted for their ability to destroy multipartite spatial quantum correlations. Inspired by this property, they have also been widely employed in defining notions of “classical memory,” under the assumption that such channels effectively act as a classical resource. In this paper, we show that this assumption is false. By means of multitime correlations, we conclusively show that entanglement-breaking channels are still a quantum resource: A qudit going through an entanglement-breaking channel can generate genuinely nonclassical temporal correlations, i.e., that cannot be simulated by a classical system of same dimension. Our results imply that entanglement-breaking channels cannot generally be employed to characterize classical memory effects without additional assumptions.