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Superior monogamy and polygamy relations and estimates of concurrence

Feb 5, 2025
14 pages
Published in:
  • Eur.Phys.J.Plus 140 (2025) 2, 101
  • Published: Feb 5, 2025
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Abstract: (Springer)
It is well known that any well-defined bipartite entanglement measure E\mathcal {E} obeys γ\gamma th-monogamy relations Eq. (1.1) and assisted measure Ea\mathcal {E}_{a} obeys δ\delta th-polygamy relations Eq. (1.2). Recently, we presented a class of tighter parameterized monogamy relation for the α\alpha th (α≥γ)(\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: tighter monogamy relation for the α\alpha th (0≤α≤γ0\le \alpha \le \gamma ) power of any bipartite entanglement measure E\mathcal {E} based on Eq. (1.1);tighter polygamy relation for the β\beta th (β≥δ \beta \ge \delta ) power of any bipartite assisted entanglement measure Ea\mathcal {E}_{a} based on Eq. (1.2);tighter polygamy relation for the ω\omega th (0≤ω≤δ0\le \omega \le \delta ) power of any bipartite assisted entanglement measure Ea\mathcal {E}_{a} based on Eq. (1.2). In the second part, using the tighter polygamy relation for the ω\omega th (0≤ω≤20\le \omega \le 2) power of CoA, we obtain good estimates or bounds for the ω\omega th (0≤ω≤20\le \omega \le 2) power of concurrence for any N-qubit pure states ∣ψ⟩AB1⋯BN−1|\psi \rangle _{AB_{1}\cdots B_{N-1}} under the partition AB1AB_{1} and B2⋯BN−1B_{2}\cdots B_{N-1}. Detailed examples are given to illustrate that our findings exhibit greater strength across all the region.tighter monogamy relation for the α\alpha th (0≤α≤γ0\le \alpha \le \gamma ) power of any bipartite entanglement measure E\mathcal {E} based on Eq. (1.1);tighter polygamy relation for the β\beta th (β≥δ \beta \ge \delta ) power of any bipartite assisted entanglement measure Ea\mathcal {E}_{a} based on Eq. (1.2);tighter polygamy relation for the ω\omega th (0≤ω≤δ0\le \omega \le \delta ) power of any bipartite assisted entanglement measure Ea\mathcal {E}_{a} based on Eq. (1.2).
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