We investigate the possibility to obtain higly multipartite-entangled states
as nondegenerate eigenstates of Hamiltonians that involve only short-range and
few-body interactions. We study small-size systems (with a number of qubits
ranging from three to five) and search for Hamiltonians with a Maximally
Multipartite Entangled State (MMES) as a nondegenerate eigenstate. We then find
conditions, including bounds on the number of coupled qubits, to build a
Hamiltonian with a Greenberger-Horne-Zeilinger (GHZ) state as a nondegenerate
eigenstate. We finally comment on possible applications.Comment: 15 pages, 3 figures. Proceedings of IQIS 2013 to appear on IJQ
