Unified monogamy relations for the generalized <i>W</i>-class states beyond qubits

Abstract The monogamy of entanglement stands as an indispensable feature within multipartite quantum systems. We study monogamy relations with respect to any partitions for the generalized W -class (GW) states based on the unified-( q , s ) entanglement (UE). We provide the monogamy relation based on the squared UE for a reduced density matrix of a qudit GW state, as well as tighter monogamy relations based on the α th ( α ≥ 2) power of UE. Furthermore, for an n -qudit system ABC 1 ... C n −2 , a generalized monogamy relation and an upper bound satisfied by the β th (0 ≤ β ≤ 1) power of the UE for the GW states under the partition AB and C 1 ... C n −2 are established. In particular, two partition-dependent residual entanglements for the GW states are analyzed in detail.