Superior monogamy and polygamy relations and estimates of concurrence

Abstract

Abstract It is well known that any well-defined bipartite entanglement measure $$\mathcal {E}$$ E obeys $$\gamma $$ γ th-monogamy relations Eq. (1.1) and assisted measure $$\mathcal {E}_{a}$$ E a obeys $$\delta $$ δ th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the $$\alpha $$ α th $$(\alpha \ge \gamma )$$ ( α ≥ γ ) 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: tighter monogamy relation for the $$\alpha $$ α th ( $$0\le \alpha \le \gamma $$ 0 ≤ α ≤ γ ) power of any bipartite entanglement measure $$\mathcal {E}$$ E based on Eq. (1.1); tighter polygamy relation for the $$\beta $$ β th ( $$ \beta \ge \delta $$ β ≥ δ ) power of any bipartite assisted entanglement measure $$\mathcal {E}_{a}$$ E a based on Eq. (1.2); tighter polygamy relation for the $$\omega $$ ω th ( $$0\le \omega \le \delta $$ 0 ≤ ω ≤ δ ) power of any bipartite assisted entanglement measure $$\mathcal {E}_{a}$$ E a based on Eq. (1.2). In the second part, using the tighter polygamy relation for the $$\omega $$ ω th ( $$0\le \omega \le 2$$ 0 ≤ ω ≤ 2 ) power of CoA, we obtain good estimates or bounds for the $$\omega $$ ω th ( $$0\le \omega \le 2$$ 0 ≤ ω ≤ 2 ) power of concurrence for any N-qubit pure states $$|\psi \rangle _{AB_{1}\cdots B_{N-1}}$$