Push-down automata as sequential generators of highly entangled states

We exploit the duality between quantum channels and sequentially generated states to construct families of highly entangled states that undergo phase transitions. These highly entangled states can be sequentially generated by collecting the emitted radiation from an open quantum system. In the dual perspective, the open system is regarded as a quantum-state-generating machine. A nontrivial class of such machines are quantum push-down automata, which can be used to create highly entangled states including the Motzkin state parametrically faster than adiabatic evolution. We construct generalizations of the Motzkin state that can be efficiently sequentially generated.