Generating a GHZ state in 2m-qubit spin network

We consider a pure 2m-qubit initial state to evolve under a particular quantum mechanical 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 distribution and stratification associated with the graphs employed in Jafarizadeh and Sufiani (2008 Phys. Rev. A 77 022315), a maximally entangled GHZ state is generated between the antipodes of the network. In fact, an algorithm is given for determining 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 entanglement of the final evolved state is calculated, and finally two examples of four-qubit and six-qubit states are considered in detail.