量子信息理论中与约化有关的纠缠判据的成立性
Thresholds for reduction-related entanglement criteria in quantum information theory
摘要：
我们考虑随机二分量子态，它是从随机的、均匀分布的、三分纯量子态中追踪一个子系统而得到的。我们计算阈值的尺寸被跟踪出的系统，使所产生的二分量子态满足约化准则在不同的渐近制度。我们认为，以及基础独立版本的减少标准（绝对减少标准），计算阈值为相应的特征值集。我们对绝对可分性研究中的其他相关集合也做了同样的事情，使用随机矩阵理论的技术。最后，我们收集和比较了已知的阈值对应于不同的纠缠标准，并得出了一个开放的问题列表。
英文摘要：
We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniques from random matrix theory. Finally, we gather and compare the known values for the thresholds corresponding to different entanglement criteria, and conclude with a list of open questions.
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