Thanks Hurkyl. I'm still not sure I follow:
Quote by Hurkyl
Any pair of bases for the vector spaces V and W naturally yield (in the obvious way) a basis for their tensor product V @W.

Certainly, but this doesn't by itself imply anything about the separability of states of the form mentioned, does it?
The curious thing is that psi can (apparently) be written as a sum of tensor products with
two different pairs of basis sets ({Ai}, B{i}) and (A'{i}, B'{i}) each in H2. Is that more clear?
I think what he's saying about the 3particle system is not merely that it gets entangled  but we also focus our attention on just two of the particles (by taking a partial trace). Then, even if we started with a pure state, we (usually) now have a mixed state.

To make sure I understand: the overall state is still pure, but the reduced density matrix, being nearzero in the offdiagonals, makes the smaller system appear mixed?
I'm still inclined to believe the second claim made in the paper, but maybe I'll give it some deeper mathematical thought or take it to the lin alg section of this forum.
Thanks!