Two types of dynamic quantum state secret sharing based on tensor networks states

Abstract 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.