Monogamy and polygamy for the generalized W-class states using unified-(q, s) entropy

We describe the entanglement distribution and restricted shareability of the multipartite generalized W-class states and their reduced density matrix under arbitrary partitions by using monogamy and polygamy relation based on the unified-(q, s) entropy. Firstly, we provide an analytical formula of unified-(q, s) entanglement (UE) and an analytical lower bound of unified-(q, s) entanglement of assistance (UEoA) for a reduced density matrix of a generalized W-class state. Then, we use these two analytical formulas to derive the monogamy and polygamy inequalities for a reduced density matrix of a qudit generalized W-class (GW) state. We establish two partition-dependent residual entanglements based on the new monogamy relation, which is helpful to obtain a comprehensive analysis of entanglement dynamics of generalized W-class states. Further, we investigate tighter monogamy and polygamy relations based on the power of αth (α ≥ 0) for UE and βth (β ≥ 0) for UEoA, respectively. The results show that the entanglement distribution characteristics of generalized W-class states satisfying stronger constraints can be described more accurately.