论文标题
通过Segre嵌入的超数据集对量子纠缠的表征
Characterization of quantum entanglement via a hypercube of Segre embeddings
论文作者
论文摘要
对量子状态可分离性的一个特别简单的描述自然而然地在复杂的代数几何形状的情况下，通过segre嵌入。这是一张描述如何采用投射希尔伯特空间的产品的地图。在本文中，我们表明，对于n个颗粒的纯态，可以通过尺寸N-1的定向超立方体来描述相应的Segre嵌入，其中所有边缘均为双金属型Segre Maps。此外，我们通过N-1边缘的图像的相交来描述原始Segre映射的图像，其目标是HyperCube的最后一个顶点。然后将这个纯粹的代数结果转移到物理学上。对于Segre HyperCube的最后一个边缘，我们引入了一个可观察到的可分离性的可观察性，并且与平方降低密度矩阵的痕迹有关。结果，HyperCube方法给出了一个关于测量纠缠的新观点，自然地将两部分与Q $>> 1的$ Q $分区相关联。我们针对众所周知的国家测试了我们的观察结果，表明这些国家提供了纠缠的良好措施。
A particularly simple description of separability of quantum states arises naturally in the setting of complex algebraic geometry, via the Segre embedding. This is a map describing how to take products of projective Hilbert spaces. In this paper, we show that for pure states of n particles, the corresponding Segre embedding may be described by means of a directed hypercube of dimension n-1, where all edges are bipartite-type Segre maps. Moreover, we describe the image of the original Segre map via the intersections of images of the n-1 edges whose target is the last vertex of the hypercube. This purely algebraic result is then transferred to physics. For each of the last edges of the Segre hypercube, we introduce an observable which measures geometric separability and is related to the trace of the squared reduced density matrix. As a consequence, the hypercube approach gives a novel viewpoint on measuring entanglement, naturally relating bipartitions with $q$-partitions for q>1. We test our observables against well-known states, showing that these provide well-behaved and fine measures of entanglement.
