A quantum network consists of multiple entanglement sources that distribute entangled quantum states to spatially dispersed nodes. This allows the quantum states in nodes to be processed locally. Tensors connected by a contraction can be regarded as tensor networks, in which quantum states are described by tensors. A tensor network state can also be expressed by a graph. Since the advent of quantum computing, people have paid more and more attention to the theory and application of tensor network states (TNS).

In this paper, we study a connection between tensor networks states and dynamic quantum state secret sharing (QSS) based on the Affleck–Kennedy–Lieb–Tasaki (AKLT) model and parametric families of tensor network states. The ground state of the AKLT model is a simple quantum state in the form of the matrix product state (MPS), which is one of the well-known tensor network states. The parametric family of tensor network states is represented by the multiplication of some matrices and the tensor network states. The diversity of MPS representations, matrix factorization and matrix multiplication, and the simple graphical representation of TNS provide excellent tools for building new applications in the field of QSS and information security in quantum networks. Moreover, our QSS schemes are dynamic because many-body states used in our schemes are represented by the matrix product state (MPS) and parametric families of tensor network states respectively, which can be dynamically adjusted.

量子网络由多个纠缠源组成，这些纠缠源将纠缠的量子态分布到空间分散的节点。这允许在本地处理节点中的量子态。通过收缩连接的张量可以看作是张量网络，其中量子态由张量描述。张量网络状态也可以用图表示。自从量子计算出现以来，人们越来越关注张量网络状态（TNS）的理论和应用。

在本文中，我们基于 Affleck-Kennedy-Lieb-Tasaki (AKLT) 模型和张量网络状态的参数族研究张量网络状态与动态量子状态秘密共享 (QSS) 之间的联系。AKLT模型的基态是矩阵乘积态（MPS）形式的简单量子态，是众所周知的张量网络态之一。张量网络状态的参数族由一些矩阵和张量网络状态的乘积表示。MPS 表示的多样性、矩阵分解和矩阵乘法以及 TNS 的简单图形表示为在量子网络中的 QSS 和信息安全领域构建新应用程序提供了极好的工具。而且，