Unified monogamy relations for the generalized $W$-class states beyond qubits

TL;DR

This paper establishes new monogamy relations for generalized W-class quantum states using unified entanglement measures, providing tighter bounds and analyzing residual entanglements for multipartite systems.

Contribution

It introduces unified monogamy relations for GW states beyond qubits, including tighter bounds and residual entanglement analysis, extending previous monogamy results.

Findings

Derived monogamy relations based on squared UE for qudit GW states.

Established tighter monogamy bounds using the $eta$th power of UE.

Analyzed partition-dependent residual entanglements in GW states.

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 $\alpha$th ($\alpha\geq2$) power of UE. Furthermore, for an $n$-qudit system $ABC_1...C_{n-2}$, generalized monogamy relation and upper bound satisfied by the $\beta$th ($0\leq\beta\leq1$) power of 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.