On the geometry of a class of N-qubit entanglement monotones
On the geometry of a class of N-qubit entanglement monotones
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一类 N 量子位纠缠单调的几何
DOI：
10.1088/0305-4470/38/41/016
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
P. Lévay
中科院分区：
文献类型：
--
作者：
P. Lévay
定义了一类在随机局域操作和经典通信下不变的N比特纠缠单调数（SLOCC）。这类纠缠单调包括著名的例子的并发，3-纠缠和一些最近介绍的四，五和N-量子比特SLOCC不变量。这些不变量的构造是基于希尔伯特空间的二分划分，其形式为L = 2N−n ≥ l = 2n。这样的划分可以给出CL中l-平面的Grassmannian Gr（L，l）的一个很好的几何解释，其可以通过Plucker嵌入实现为适当维数的复射影空间中的二次多项式的零轨迹。这些不变量用格拉斯曼的Plucker坐标表示。
A family of N-qubit entanglement monotones invariant under stochastic local operations and classical communication (SLOCC) is defined. This class of entanglement monotones includes the well-known examples of the concurrence, the 3-tangle and some of the four-, five- and N-qubit SLOCC invariants introduced recently. The construction of these invariants is based on bipartite partitions of the Hilbert space in the form with L = 2N−n ≥ l = 2n. Such partitions can be given a nice geometrical interpretation in terms of Grassmannians Gr(L, l) of l-planes in CL that can be realized as the zero locus of quadratic polynomials in the complex projective space of suitable dimension via the Plucker embedding. The invariants are neatly expressed in terms of the Plucker coordinates of the Grassmannians.