In our paper, we concentrate on the Z-eigenvalue inclusion theorem and its application in the geometric measure of entanglement of multipartite pure states. We present a new Z-eigenvalue inclusion theorem by virtue of the division and classification of tensor elements, and tighter bounds of Z-spectral radius of weakly symmetric nonnegative tensors are obtained. As applications, we present some theoretical upper and lower bounds of entanglement for symmetric pure state with nonnegative amplitudes for two kinds of geometric measures with different definitions, respectively.

中文翻译：

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张量的Z-特征值包含定理和多部分纯态纠缠的几何度量

在本文中，我们集中于Z-特征值包含定理及其在多部分纯态纠缠的几何度量中的应用。通过张量元素的划分和分类，我们提出了一个新的Z-特征值包含定理，并且获得了弱对称非负张量的Z-谱半径的更严格边界。作为应用，我们针对两种具有不同定义的几何量度，分别给出了具有非负振幅的对称纯态的纠缠的理论上界和下界。