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 ...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(UEo A)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 ofαth(α≥0)for UE andβth(β≥0)for UEo A,respectively.The results show that the entanglement distribution characteristics of generalized W-class states satisfying stronger constraints can be described more accurately.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12175147,12075205,and T2121001)Zhejiang Provincial Natural Science Foundation of China(Grant No.Z24A050006)。
文摘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(UEo A)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 ofαth(α≥0)for UE andβth(β≥0)for UEo A,respectively.The results show that the entanglement distribution characteristics of generalized W-class states satisfying stronger constraints can be described more accurately.
