Unified entropy entanglement

The unified entropy as a generalization of the von Neumann entropy exhibits distinct diversity which contains the Tsallis entropy, the R'{e}nyi entropy, the von Neumann entropy as special cases. The unified-($r,t$) entropy entanglement with $0<r<1$ and 0< t≤ 1 was shown to be an entanglement monotone in literature. In this paper, we explore unified-($q,s$) entropy entanglement with $q>1$ and qs≥1 and show that it is also an entanglement monotone and that both of them are monogamous. Going further, we present a global multipartite entanglement measure (GlMEM) based on the unified entropy and it has two subclasses which are classified by the parameters $(q,s)$ and $(r,t)$. Consequently, from the view of the complete multipartite entanglement measure theory, we show that one of them is a complete multipartite entanglement monotone and is not only completely monogamous but also tightly completely monogamous, but the other one is even not complete. We also explore the genuine entanglement measures induced by the unified entropy and the relations with the bipartite entanglement and the global entanglement are discussed, respectively.