Preparing GHZ and $W$ states on a long-range Ising spin model by global controls

Entanglement, a unique quantum resource with no classical counterpart, stays at the heart of quantum information. The GHZ and $W$ states are two inequivalent classes of multipartite entangled states which can not be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and $W$ states via global controls on a long-range Ising spin model. For the GHZ state, general solutions is analytically obtained for an arbitrary-size spin system, while for $W$ state, we find a standard way to prepare the $W$ state that is analytically illustrated in 3- and 4-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search only increases linearly with the size of the system.