Superior monogamy and polygamy relations and estimates of concurrence

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Main Authors: Cao, Yue, Jing, Naihuan, Misra, Kailash, Wang, Yiling
Format: Preprint
Published: 2025
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author Cao, Yue
Jing, Naihuan
Misra, Kailash
Wang, Yiling
author_facet Cao, Yue
Jing, Naihuan
Misra, Kailash
Wang, Yiling
contents It is well known that any well-defined bipartite entanglement measure $\mathcal{E}$ obeys $γ$th-monogamy relations Eq. (1.1) and assisted measure $\mathcal{E}_{a}$ obeys $δ$th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the $α$th $(α\geqγ)$ power based on Eq. (1.1). This study provides a family of tighter lower (resp. upper) bounds of the monogamy (resp. polygamy) relations in a unified manner. In the first part of the paper, the following three basic problems are focused: (i) tighter monogamy relation for the $α$th ($0\leq α\leq γ$) power of any bipartite entanglement measure $\mathcal{E}$ based on Eq. (1.1); (ii) tighter polygamy relation for the $β$th ($ β\geq δ$) power of any bipartite assisted entanglement measure $\mathcal{E}_{a}$ based on Eq. (1.2); (iii) tighter polygamy relation for the $ω$th ($0\leq ω\leq δ$) power of any bipartite assisted entanglement measure $\mathcal{E}_{a}$ based on Eq. (1.2). In the second part, using the tighter polygamy relation for the $ω$th ($0\leq ω\leq 2$) power of CoA, we obtain good estimates or bounds for the $ω$th ($0\leq ω\leq 2$) power of concurrence for any $N$-qubit pure states $|ψ\rangle_{AB_{1}\cdots B_{N-1}}$ under the partition $AB_{1}$ and $B_{2}\cdots B_{N-1}$. Detailed examples are given to illustrate that our findings exhibit greater strength across all the region.
format Preprint
id arxiv_https___arxiv_org_abs_2503_00694
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Superior monogamy and polygamy relations and estimates of concurrence
Cao, Yue
Jing, Naihuan
Misra, Kailash
Wang, Yiling
Quantum Physics
Primary: 81P68, Secondary: 81P40
It is well known that any well-defined bipartite entanglement measure $\mathcal{E}$ obeys $γ$th-monogamy relations Eq. (1.1) and assisted measure $\mathcal{E}_{a}$ obeys $δ$th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the $α$th $(α\geqγ)$ power based on Eq. (1.1). This study provides a family of tighter lower (resp. upper) bounds of the monogamy (resp. polygamy) relations in a unified manner. In the first part of the paper, the following three basic problems are focused: (i) tighter monogamy relation for the $α$th ($0\leq α\leq γ$) power of any bipartite entanglement measure $\mathcal{E}$ based on Eq. (1.1); (ii) tighter polygamy relation for the $β$th ($ β\geq δ$) power of any bipartite assisted entanglement measure $\mathcal{E}_{a}$ based on Eq. (1.2); (iii) tighter polygamy relation for the $ω$th ($0\leq ω\leq δ$) power of any bipartite assisted entanglement measure $\mathcal{E}_{a}$ based on Eq. (1.2). In the second part, using the tighter polygamy relation for the $ω$th ($0\leq ω\leq 2$) power of CoA, we obtain good estimates or bounds for the $ω$th ($0\leq ω\leq 2$) power of concurrence for any $N$-qubit pure states $|ψ\rangle_{AB_{1}\cdots B_{N-1}}$ under the partition $AB_{1}$ and $B_{2}\cdots B_{N-1}$. Detailed examples are given to illustrate that our findings exhibit greater strength across all the region.
title Superior monogamy and polygamy relations and estimates of concurrence
topic Quantum Physics
Primary: 81P68, Secondary: 81P40
url https://arxiv.org/abs/2503.00694