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

• URL: http://arxiv.org/abs/2411.10740v1
• Date: Sat, 16 Nov 2024 08:44:50 GMT
• Title: Unified monogamy relations for the generalized $W$-class states beyond qubits
• Authors: Zhong-Xi Shen, Wen Zhou, Dong-Ping Xuan, Zhi-Xi Wang, Shao-Ming Fei,
• Abstract summary: We study monogamy relations with respect to 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 ($alphageq2$) power of UE.
• Score: 1.125136513287558
• License:
• 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.

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