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arXiv 0909.1077quant-ph
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相位因子对三量子比特态几何纠缠度量的影响

Effect of Phase Factor in the Geometric Entanglement Measure of Three-Qubit States

Sayatnova Tamaryan, Hungsoo Kim, Mu-Seong Kim, Kap Soo Jang, DaeKil Park

摘要:

任何纯三量子比特态都是唯一的,只有一个相位和四个正参数。纠缠的几何度量作为状态参数的函数可以有不同的表达式。每个表达式都有自己的适用范围,因此整个状态参数空间被划分为子空间,这些子空间是相应表达式的定义范围。本文的目的是研究最一般的量子位交换对称三量子位态的适用域。首先,我们计算了具有固定相位的排列不变三比特态的非线性本征方程的本征值和最近可分态。其次,我们计算了几何纠缠度,推导了所有子空间的边界,并找到了高纠缠态和低纠缠态的分配。结果表明,当相位因子为$π/2$时,有三个适用的区域,而其他情况下只有两个区域。这三个领域的出现是由于额外的W态的出现。结果表明,大部分高纠缠态位于畴界附近,远离畴界的态纠缠度降低,最终到达产物态。从几何测度的角度来看,W态的近邻粒子比GHZ态的近邻粒子纠缠度更高。然而,GHz邻居的范围比W邻居的范围宽得多。

英文摘要:

Any pure three-qubit state is uniquely characterized by one phase and four positive parameters. The geometric measure of entanglement as a function of state parameters can have different expressions. Each of expressions has its own applicable domain and thus the whole state parameter space is divided into subspaces that are ranges of definition for corresponding expressions. The purpose of this paper is to examine the applicable domains for the most general qubit-interchange symmetric three-qubit states. First, we compute the eigenvalues of the non-linear eigenvalue equations and the nearest separable states for the permutation invariant three-qubit states with a fixed phase. Next, we compute the geometric entanglement measure, deduce the boundaries of all subspaces, and find allocations of highly and slightly entangled states. It is shown that there are three applicable domains when the phase factor is $π/2$ while other cases have only two domains. The emergence of the three domains is due to the appearance of the additional W-state. We show that most of highly entangled states reside near the boundaries of the domains and states located far from the boundaries become less-entangled and eventually go to the product states. The neighbors of W-state are generally more entangled than the neighbors of Greenberger-Horne-Zeilinger(GHZ) state from the aspect of the geometric measure. However, the range of the GHZ-neighbors is much more wider than the range of the W-neighbors.

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