Superior monogamy and polygamy relations and estimates of concurrence

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 $(\alpha \ge \gamma )$ 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 ($0\le \alpha \le \gamma$) power of any bipartite entanglement measure $\mathcal{E}$ based on Eq. (1.1); (ii) tighter polygamy relation for the $\beta$th ($\beta \ge \delta$) power of any bipartite assisted entanglement measure ${\mathcal{E}}_a$ based on Eq. (1.2); (iii) tighter polygamy relation for the $\omega$th ($0\le \omega \le \delta$) 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 ($0\le \omega \le 2$) power of CoA, we obtain good estimates or bounds for the $\omega$th ($0\le \omega \le 2$) power of concurrence for any $N$-qubit pure states $|\psi {⟩}_{A{B}_1\cdots B_{N-1}}$ under the partition $A{B}_1$ 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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Cited by in corpus (1)

• Unified monogamy and polygamy relations for multipartite systems