Entanglement in the Symmetric Sector of n Qubits
Entanglement in the Symmetric Sector of n Qubits
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DOI：
10.1103/physrevlett.106.180502
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发表时间：
2011-05-03
影响因子：
8.6
通讯作者：
Mosseri, R.
中科院分区：
文献类型：
--
作者：
Ribeiro, P.;Mosseri, R.
讨论了n个量子比特对称态的纠缠特性。马约拉纳表示将一个通用的这样的状态映射到球面上的n个点的系统中。纠缠不变量，无论是在本地幺正（LU）或随机本地操作和经典通信（SLOCC），然后可以解决的马约拉纳点的相对位置。在LU的情况下，可以从指向这些点的径向向量的内积构建一个过完备的不变量集;这是详细记录的三量子比特的情况。在SLOCC的情况下，相关的莫比乌斯变换的交比被证明起着核心作用，这里以四个量子位为例。最后，作为一个附带结果，我们还分析了对称和一般情况下的最大纠缠3量子比特态的流形。
We discuss the entanglement properties of symmetric states of n qubits. The Majorana representation maps a generic such state into a system of n points on a sphere. Entanglement invariants, either under local unitaries (LU) or stochastic local operations and classical communication (SLOCC), can then be addressed in terms of the relative positions of the Majorana points. In the LU case, an overcomplete set of invariants can be built from the inner product of the radial vectors pointing to these points; this is detailed for the well-documented three-qubits case. In the SLOCC case, a cross ratio of related Mobius transformations are shown to play a central role, exemplified here for four qubits. Finally, as a side result, we also analyze the manifold of maximally entangled 3 qubit state, both in the symmetric and generic case.