  We consider a pure 2m-qubit initial state to evolve under a particular
quantum me- chanical spin Hamiltonian, which can be written in terms of the
adjacency matrix of the Johnson network J(2m;m). Then, by using some techniques
such as spectral dis- tribution and stratification associated with the graphs,
employed in [1, 2], a maximally entangled GHZ state is generated between the
antipodes of the network. In fact, an explicit formula is given for the
suitable coupling strengths of the hamiltonian, so that a maximally entangled
state can be generated between antipodes of the network. By using some known
multipartite entanglement measures, the amount of the entanglement of the final
evolved state is calculated, and finally two examples of four qubit and six
qubit states are considered in details.
