Unified Monogamy Relations of Multipartite Entanglement

Abstract

Unified-(q, s) entanglement (Uq,s) is a generalized bipartite entanglement measure, which encompasses Tsallis-q entanglement, Rényi-q entanglement, and entanglement of formation as its special cases. We first provide the extended (q; s) region of the generalized analytic formula of Uq,s. Then, the monogamy relation based on the squared Uq,s for arbitrary multiqubit mixed states is proved. The monogamy relation proved in this paper enables us to construct an entanglement indicator that can be utilized to identify all genuine multiqubit entangled states even the cases where three tangle of concurrence loses its efficiency. It is shown that this monogamy relation also holds true for the generalized W-class state. The αth power Uq,s based general monogamy and polygamy inequalities are established for tripartite qubit states.