Hilbert-Schmidt distance and entanglement witnessing
Hilbert-Schmidt distance and entanglement witnessing
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DOI：
10.1103/physreva.102.012409
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发表时间：
2020-07-07
影响因子：
2.9
通讯作者：
Wiesniak, Marcin
中科院分区：
文献类型：
--
作者：
Pandya, Palash;Sakarya, Omer;Wiesniak, Marcin
吉尔伯特提出了一个算法界定一个给定的点和一个凸集之间的距离。我们应用吉尔伯特的算法，得到一个上界的希尔伯特-施密特距离之间的一个给定的状态和一组可分离的状态。虽然希尔伯特-施密特距离并不构成一个适当的纠缠度量，但它仍然可以用于见证纠缠。我们提供了几种基于吉尔伯特算法的方法，可以可靠地将给定状态定性为强纠缠或几乎可分离，同时计算效率高。该方法还输出连续改进的近似最接近的可分离状态的给定状态。我们用例子证明了该方法的有效性。
Gilbert proposed an algorithm for bounding the distance between a given point and a convex set. We apply the Gilbert's algorithm to get an upper bound on the Hilbert-Schmidt distance between a given state and the set of separable states. While Hilbert-Schmidt distance does not form a proper entanglement measure, it can nevertheless be useful for witnessing entanglement. We provide a few methods based on the Gilbert's algorithm that can reliably qualify a given state as strongly entangled or practically separable, while being computationally efficient. The method also outputs successively improved approximations to the closest separable state for the given state. We demonstrate the efficacy of the method with examples.