Entanglement properties of locally maximally entangleable states

Full text: Locally maximally entangleable states (LMES) are a class of multi partite quantum states characterized by 2n-1 real phases, where n is the number of qubits. Prominent examples of LMES are graph states and stabilizer states. They can be prepared by applying general phase gates to a product state. One can associate any LMES to a weighted hypergraph, identifying each of these phase gates acting non-trivially on a subset of qubits to a weighted hyperedge connecting a subset of vertices. In this regard, they can be understood as a generalization of (weighted) graph states. The hypergraph, or equivalently the 2n-1 phases, determine the entanglement. We investigated the entanglement of LME states, ie their usefulness as a resource when the parties are separated and their manipulation is restricted to local operations and classical communication (LOCC). We discuss local unitary (LU) and stochastic LOCC equivalence of these states. In some cases, LU equivalence can be reduced to the much simpler case of equivalence under the action of local Pauli gates, which simplifies the characterization of LU-equivalent classes. We also present the convertibility of LMESs under local operations and classical communication (LOCC) to characterize the set of states that can be deterministically obtained from them. (author)