Air Force Research Laboratory, Information Directorate, Rome, NY, 13441, USA.
Sci Rep. 2023 Mar 21;13(1):4601. doi: 10.1038/s41598-023-31273-9.
In this paper, we explore the value of measures of mixedness in witnessing entanglement. While all measures of mixedness may be used to witness entanglement, we show that all such entangled states must have a negative partial transpose (NPT). Where the experimental resources needed to determine this negativity scale poorly at high dimension, we compare different measures of mixedness over both Haar-uniform and uniform-purity ensembles of joint quantum states at varying dimension to gauge their relative success at witnessing entanglement. In doing so, we find that comparing joint and marginal purities is overwhelmingly (albeit not exclusively) more successful at identifying entanglement than comparing joint and marginal von Neumann entropies, in spite of requiring fewer resources. We conclude by showing how our results impact the fundamental relationship between correlation and entanglement and related witnesses.
在本文中，我们探讨了混合度测度在见证纠缠中的价值。虽然所有的混合度测度都可以用来见证纠缠，但我们表明，所有这样的纠缠态都必须具有负部分转置（NPT）。在需要确定这种负性的实验资源在高维下表现不佳的情况下，我们比较了不同的混合度测度在不同维数的哈厄均匀和均匀纯度联合量子态的哈厄均匀和均匀纯度联合量子态上的相对成功，以衡量它们在见证纠缠方面的相对成功。在这样做的过程中，我们发现，尽管需要更少的资源，但比较联合和边际纯度在识别纠缠方面比比较联合和边际冯·诺依曼熵更成功。最后，我们展示了我们的结果如何影响相关性和纠缠以及相关见证之间的基本关系。
