标题： 四量子比特对称Greenberger-Horne-Zeilinger对角态的纠缠准则层次结构 显示英文标题

标题： A hierarchy of entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger diagonal states

摘要： 通过一种两步优化方法的纠缠判据，我们分析地提出了一组对于四量子比特对称Greenberger-Horne-Zeilinger (GHZ) 对角态的必要且充分的纠缠准则。 该准则集包含四个准则。 其中两个与密度矩阵元素线性相关。 另外两个准则与密度矩阵元素非线性相关。 该准则集具有嵌套结构。 准则的一个适当子集对于状态的一个适当子集的纠缠是必要且充分的。 我们用一般的Werner态集及其超集高度对称的GHZ对角态集来说明准则集的嵌套结构，它们都是对称GHZ对角态集的子集。 显示英文摘要

摘要： With a two step optimization method of entanglement witness, we analytically propose a set of necessary and sufficient entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set contains four criteria. Two of them are linear with density matrix elements. The other two criteria are nonlinear with density matrix elements. The criterion set has a nest structure. A proper subset of the criteria is necessary and sufficient for the entanglement of a proper subset of the states. We illustrate the nest structure of criterion set with the general Werner state set and its superset the highly symmetric GHZ diagonal state set, they are subsets of the symmetric GHZ diagonal state set.