Genuine multipartite entanglement measure based on α-concurrence

Quantifying genuine entanglement is a crucial task in quantum information theory. Based on the geometric mean of bipartite alpha-concurrences among all bipartitions, we present a class of well-defined genuine multipartite entanglement (GME) measures G alpha C with one parameter alpha for arbitrary multipartite states. We show that the G alpha C is of continuity for any multipartite pure states. By utilizing the related symmetry, analytical results of G alpha C are derived for any n-qubit GHZ states and W states, which show that the GHZ states are more genuinely entangled than the W states. With explicit examples, we demonstrate that the G alpha C can distinguish different GME states that other GME measures fail to. These results justify the potential applications of G alpha C in characterizing genuine multipartite entanglements.