AI 中文总结
该研究针对二分纠缠度量及其辅助度量，引入由参数$m$索引的统一框架，推导出两个层次的精细不等式族，随着$m$增加边界收紧，推广并加强了现有关系，为量子相关领域应用提供了增强且灵活的工具。
AI 中文摘要
对于满足γ次幂一夫一妻制不等式的二分纠缠度量$\mathcal{E}$，以及服从δ次幂多配偶制不等式的辅助纠缠度量$\mathcal{E}_a$，我们引入了一个由参数$m\geq1$索引的统一可调框架。在此框架内，我们推导出两个层次的精细不等式族：一个对$\mathcal{E}$的收紧α次幂一夫一妻制关系，对所有$\alpha \geq m\gamma$有效；一个对$\mathcal{E}_a$的收紧β次幂多配偶制关系，适用于$(m - 1)\delta < \beta \leq m\delta$。随着$m$增加，边界逐渐收紧，在$m = 1$时恢复已知结果。我们通过分析比较和使用并发度及辅助并发度的数值评估表明，我们的结果推广并加强了现有的一夫一妻制和多配偶制关系。这种分层参数化方法为量子通信、量子网络和多体量子信息处理中的应用提供了增强且灵活的工具。
英文摘要
For a bipartite entanglement measure $\mathcal{E}$ that satisfies the $γ$th-power monogamy inequality (Eq.~\eqref{e:chap1-ineq1}), and for its assisted counterpart $\mathcal{E}_a$ that obeys the $δ$th-power polygamy inequality (Eq.~\eqref{e:chap1-ineq2}), we introduce a unified, tunable framework indexed by a parameter $m\geq1$. Within this framework, we derive two hierarchical families of refined inequalities: a tightened $α$-power monogamy relation for $\mathcal{E}$, valid for all $α\geq mγ$; a tightened $β$-power polygamy relation for $\mathcal{E}_a$, applicable for $(m-1)δ< β\leq mδ$. As $m$ increases, the bounds become progressively tighter, recovering known results at $m=1$. Notably, the optimal monogamy bound emerges as a piecewise function of $α$, with additional correction terms activated as $α$ crosses successive integer thresholds, thereby offering a sharper characterization of entanglement distribution. We demonstrate that our results generalize and strengthen existing monogamy and polygamy relations through analytical comparisons and numerical evaluations using concurrence and concurrence of assistance. This hierarchical, parameterized approach offers enhanced and flexible tools for applications in quantum communication, quantum networks, and multipartite quantum information processing.
Comments14pp
Journal refQuant. Information Process. (2026) 25:61 (16pp)
DOI：10.1007/s11128-026-05076-6
