Quantum Entanglement Of Hypergraph States And Its Local Pauli Inequivalence

Quantum information is a certain.kind of physical information contained in the "state" which describes a quantum system in quantum mechanics. As an intersection of quantum mechanics and information science, quantum information is a fast developing frontier discipline nowadays, it involves mathematics, physics, computer science and communication.With the rapid development of quantum information theory, quantum entanglement as a strange phenomenon to challenge the theory of completeness among quantum mechanics, and has been used as an important information resources. Quantum entanglement means that the quantum state of the composite system can not be written as the product of the quantum state of the parts. It can accomplish tasks that can not be completed by classical information processing, or, it can improve the efficiency of information processing significantly. Graph states are multipartite quantum states with applications in quantum error correction and one way quantum computation. The properties of a graph state are closely related with the entanglement contained in it. The entanglement measure of graph states has made great progress. For the problem of entanglement measure of quantum states, only bipartite quantum systems have reached to a better solution. The entanglement measure for a multipartite pure state is still far from reach, a perfect solution for the enatnglenet of a mixed multipartite quantum system is even difficult. A hypergraph state is an extension of a graph state. It can be described by mathematical hypergraph and acts as an indispensable role in anti-noise non information leakage, quantum computing and quantum simulation. Moreover, it is widely used in quantum key distribution, remote transmission, reduced complexity of information transmission and image segmentation. The research of the entanglement of hypergraph states is far from mature. Some measures of entanglement have been proposed, including robustness of entanglement, the relative entropy of entanglement, and geometric measure. We use geometric measure to calculate the entanglement value of hypergraph states.The thesis is organized as follows:In the first few sections, we introduce an iterative algorithm for five qubit hypergraph states, and searched for its closest product states. The entanglement values are obtained by the iterative algorithm. Then, we deal with the general conditions on local unitary equivalence of hypergraph states in the subsequent section. Finally, we use the geometric measure and bipartite entanglement measure to verify whether two hypergraph states are local equivalence or not. We analyze the entanglement values and local inequivalence of5qubit hypergraph states with inner hyperedges, and acquire some meaningful results. At last we analyze the module and the phase angle of the closest product states.