For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in a pure tripartite state. Furthermore, we find the lower bound and actual values of the entanglement of purification for different classes of tripartite and higher-dimensional bipartite mixed states. Thereafter, we show that if entanglement of purification is not additive on tensor product states, it is actually subadditive. Using these results, we identify some states which are additive on tensor products for entanglement of purification. The implications of these findings on the quantum advantage of dense coding are briefly discussed, whereby we show that for tripartite pure states, it is strictly monogamous and if it is nonadditive, then it is superadditive on tensor product states.
Tighter monogamy and polygamy relations in multiparty quantum systems
School of Mathematics and Science, Hebei GEO University（河北地质大学数学与科学学院）；Intelligent Sensor Network Engineering Research Center of Hebei Province, Hebei GEO University（河北省智能传感器网络工程研究中心）
General Monogamy and polygamy properties of quantum systems
一夫一妻制和一夫多妻制是纠缠的重要性质，它们刻画了多体系统的纠缠分布。分别基于$α$次$(0\leqα\leq γ)$幂纠缠测度和$β$次$(β\geq δ)$幂辅助纠缠测度研究了一般的一夫一妻和一夫多妻关系.我们说明了这些一夫一妻制和一夫多妻制的关系比文章[Quantum Inf Process 19，101]中的不等式更紧密，因此可以更精确地描述满足更强约束的纠缠态的纠缠分布。对于特定的纠缠度量，如并发和凸顶扩展负性，通过应用这些关系，可以得到相应的一夫一妻制和一夫多妻制不等式，这些不等式将文章[Quantum Inf Process 18，23]和[Quantum Inf Process 18，105]中现有的不等式作为特例。更多细节在实施例中呈现。
纠缠一夫多妻和纠缠一夫一妻一样，是多体量子态的一个基本性质。研究了一般$n$ -量子比特态的多偶性与并发度$C$和形成纠缠度$E$的关系.我们将[Phys. Rev. A 90，024304（2014）]中的结果从参数区域$α\leq0$扩展到$α\leqα_0$，其中$C$为$0<α_0\leq2$，$E$为$0<α_0\leq\sqrt{2}$。
The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy
Institute of Theoretical Physics and Astrophysics, University of Gdańsk（格但斯克大学理论物理与天体物理研究所）；International Centre for Theory of Quantum Technologies, University of Gdansk（格但斯克大学量子技术理论国际中心）；Faculty of Physics, Ludwig Maximilian University（慕尼黑路德维希-马克西米利安大学物理学院）
我们通过几个纠缠单调来研究是否所有的最大纠缠态都是纯的。在两体情况下，我们发现导致纠缠熵作为纠缠度量的唯一性的相同条件，排除了最大混合纠缠态的存在。在多体情况下，我们的结论使我们能够推广一夫一妻的纠缠的想法：我们建立了\textit{polygamy of entanglement}，表示如果一个一般的状态是最大的纠缠相对于某种多体纠缠，那么它必然是任何其他系统的因式分解。
G_q-concurrence and entanglement constraints in multiqubit systems
School of Mathematical Sciences, Hebei Normal University（河北师范大学数学科学学院）；College of Physics, Hebei Key Laboratory of Photophysics Research and Application, Hebei Normal University（河北师范大学物理学院）
