  We consider multi-qubit systems and relate quantitatively the problems of
generating cluster states with high value of concurrence of assistance, and
that of generating states with maximal bipartite entanglement. We prove an
upper bound for the concurrence of assistance. We consider dynamics of spin-1/2
systems that model qubits, with different couplings and possible presence of
magnetic field to investigate the appearance of the discussed entanglement
properties. We find that states with maximal bipartite entanglement can be
generated by an XY Hamiltonian, and their generation can be controlled by the
initial state of one of the spins. The same Hamiltonian is capable of creating
states with high concurrence of assistance with suitably chosen initial state.
We show that the production of graph states using the Ising Hamiltonian is
controllable via a single-qubit rotation of one spin-1/2 subsystem in the
initial multi-qubit state. We shown that the property of Ising dynamics to
convert a product state basis into a special maximally entangled basis is
temporally enhanced by the application of a suitable magnetic field. Similar
basis transformations are found to be feasible in the case of isotropic XY
couplings with magnetic field.
