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arXiv · 2411.10740

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

Zhong-Xi Shen·Wen Zhou·Dong-Ping Xuan·Zhi-Xi Wang·Shao-Ming Fei
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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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Zhong-Xi Shen, Wen Zhou, Dong-Ping Xuan, Zhi-Xi Wang, Shao-Ming Fei. 2024-11-16. Unified monogamy relations for the generalized $W$-class states beyond qubits. https://doi.org/10.1088/1572-9494%2Fad766d

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