Parameterized Multipartite Entanglement and Genuine Entanglement Measures Based on q -Concurrence.

We study genuine multipartite entanglement (GME) and multipartite k -entanglement based on q -concurrence. Well-defined parameterized GME measures and measures of multipartite k -entanglement are presented for arbitrary dimensional n -partite quantum systems. Our GME measures show that the GHZ state is more entangled than the W state. Moreover, our measures are shown to be inequivalent to the existing measures according to entanglement ordering. Detailed examples show that our measures characterize the multipartite entanglement finer than some existing measures, in the sense that our measures identify the difference of two different states while the latter fail.