Superior monogamy and polygamy relations and estimates of concurrence

• URL: http://arxiv.org/abs/2503.00694v1
• Date: Sun, 02 Mar 2025 02:25:34 GMT
• Title: Superior monogamy and polygamy relations and estimates of concurrence
• Authors: Yue Cao, Naihuan Jing, Kailash Misra, Yiling Wang,
• Abstract summary: We present a class of tighter parameterized monogamy relation for the $alpha$th $(alphageqgamma)$ power based on Eq. (1.1)<n>This study provides a family of tighter lower (resp. upper) bounds of the monogamy (resp. polygamy) relations in a unified manner.
• Score: 6.408200192709026
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is well known that any well-defined bipartite entanglement measure $\mathcal{E}$ obeys $\gamma$th-monogamy relations Eq. (1.1) and assisted measure $\mathcal{E}_{a}$ obeys $\delta$th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the $\alpha$th $(\alpha\geq\gamma)$ 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 $\alpha$th ($0\leq \alpha\leq \gamma$) power of any bipartite entanglement measure $\mathcal{E}$ based on Eq. (1.1); (ii) tighter polygamy relation for the $\beta$th ($ \beta \geq \delta$) power of any bipartite assisted entanglement measure $\mathcal{E}_{a}$ based on Eq. (1.2); (iii) tighter polygamy relation for the $\omega$th ($0\leq \omega \leq \delta$) 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 $\omega$th ($0\leq \omega \leq 2$) power of CoA, we obtain good estimates or bounds for the $\omega$th ($0\leq \omega \leq 2$) power of concurrence for any $N$-qubit pure states $|\psi\rangle_{AB_{1}\cdots B_{N-1}}$ 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.

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