The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an $n$-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of $m$-qubit couplings with $m\ge [(n+1)/2]$. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.

• Received 3 May 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.260502