Quantum computation in correlation space and extremal entanglement

Recently, a framework was established to systematically construct novel universal resource states for measurement-based quantum computation using techniques involving finitely correlated states. With these methods, universal states were found which are in certain ways much less entangled than the original cluster state model, and it was hence believed that with this approach many of the extremal entanglement features of the cluster states could be relaxed. The new resources were constructed as "computationally universal" states--i.e. they allow one to efficiently reproduce the classical output of each quantum computation--whereas the cluster states are universal in a stronger sense since they are "universal state preparators". Here we show that the new resources are universal state preparators after all, and must therefore exhibit a whole class of extremal entanglement features, similar to the cluster states.