  We show how to implement quantum transport, generate entangled state and
achieve spatial entanglement distribution via topological Thouless pumping in
one-dimensional disordered lattices. We introduce the on-site disorders to
suppress the high-order resonant tunneling (which cause wavepacket dispersion)
and realize dispersionless Thouless pumping. The interplay between the on-site
disorders and the band topology enables robust unidirectional transport. We
also demonstrate how to prepare spatially entangled two-particle NOON state via
Hong-Ou-Mandel interference assisted by the Thouless pumping. The quantum
entanglement can be well preserved during the distribution between spatially
separated sites. Our system paves a way to wide applications of topology in
quantum information process.
