多部分 Rains 纠缠的泛滥
Flood of multipartite Rains entanglement
AI总结：
该研究将两部分 Rains 相对熵推广为多部分 Rains 等纠缠度量，证明其单调性，建立纯态蒸馏速率上界，定义多部分 max-Rains 纠缠并推导对偶规划，还给出计算 Rains 纠缠的算法。
AI中文摘要：
多部分纠缠具有诸如 genuine multipartite entanglement（GME，真多部分纠缠）的激活以及不等价纠缠类别的存在等现象，而现有的两部分纠缠度量在该领域没有唯一的推广。在本研究中，我们将 Rains、monsoon、hurricane 和 squall 纠缠定义为两部分 Rains 相对熵的推广，并建立了这些纠缠度量的各种性质。我们还证明，Rains 纠缠在完全保留部分转置正定性的选择性量子操作下是单调的。我们在标准和概率近似蒸馏场景中，针对从任意态蒸馏出固定纯态的单次和渐近速率，建立了单字母上界。在我们定义的纠缠度量中，单次纯态蒸馏速率的最紧上界由 Rains 纠缠给出。然而，GME 的激活（或等价地，可分性的张量不稳定性）使得 Rains 纠缠的单次上界能否扩展为单字母渐近上界尚不明确。相反，我们利用 hurricane 和 squall 纠缠建立了渐近纯态蒸馏速率的上界，由此可得到 GHZ 和 W 可蒸馏纠缠的上界。此外，我们定义了多部分 max-Rains 纠缠，将其表示为半定规划，并推导了其对偶规划。最后，我们分析了这些度量在量子两两独立网络中的表现，并建立了用于计算 Rains 纠缠的条件梯度（Frank-Wolfe）算法。
英文摘要：
Multipartite entanglement admits phenomena such as the activation of genuine multipartite entanglement (GME) and the existence of inequivalent classes of entanglement, and existing bipartite entanglement measures have no unique generalization to this regime. In this work, we define the Rains, monsoon, hurricane, and squall entanglement as generalizations of the bipartite Rains relative entropy, and we establish various properties of these entanglement measures. We also prove that the Rains entanglement is monotone under selective quantum operations that completely preserve the positivity of the partial transpose. We establish single-letter upper bounds on the one-shot and asymptotic rates at which a fixed pure state can be distilled from an arbitrary state in both the standard and probabilistic approximate distillation scenarios. Among the entanglement measures we define, the tightest upper bound on the one-shot pure-state distillation rate is in terms of the Rains entanglement. However, the activation of GME (or, equivalently, the tensor instability of biseparability) makes it unclear if the one-shot bound in terms of the Rains entanglement can be extended to a single-letter asymptotic bound. Instead, we establish upper bounds on the asymptotic pure-state distillation rate in terms of the hurricane and squall entanglement. Upper bounds on the GHZ- and W-distillable entanglement follow as a consequence. Additionally, we define the multipartite max-Rains entanglement, write it as a semidefinite program, and derive a dual program for it. Finally, we analyze these measures for quantum pairwise independent networks, and we establish a conditional gradient (Frank-Wolfe) algorithm for computing the Rains entanglement.
