Maximally genuine multi-qubit entangled states

We investigate the entanglement properties of graph states which correspond to connected graphs by calculating the two-qubit and genuine three-qubit entanglement. Using the operational definition of graph states, we prove that in connected graph states of N qubits, if N>2 there is no entanglement between any pair of qubits. Moreover, we show that if N>3 there is no genuine three-qubit entanglement among every three qubits. Based on these results, we then propose the definition of maximally genuine multi-qubit entangled states. The connected graph states of four qubits is one but not the only one class of maximally genuine four-qubit entangled states