The Entanglement Criteria Of Five Qubit Greenberger-horne-zeilinger Diagonal States

Quantum information is an interdisciplinary subject between quantum physics and information science.It is a hot topic in international research in the recent 20 years.With the realization of 10 superconducting qubit computers,quantum information processing and quantum computing have attracted more and more attentions.Among them,the storage,representation and extraction of information cannot be separated from the quantum state and its changing process.Quantum entangled states play important roles in the field of quantum information because of their unique quantum correlation.They are important physical resources that distinguish quantum states from other classical physical states.In the quantum measurement shrinkage,they exhibit a non-local correlations,which means that entanglement is a correlation that cannot be found in classical physics.This property makes the research on quantum entanglement not only of important theoretical significance,but also of important technical application value in quantum communication and information processing.Because quantum entanglement mainly involves multipartite entanglement,and GHZ quantum state is the most common multipartite entangled quantum state in the experiment and theory of quantum information.It is susceptible to white noise,so in this thesis we will study the entanglement criteria of GHZ diagonal states.In this thesis,we introduce the basic definition of quantum entanglement and briefly describes the development of quantum entanglement theory.Some basic quantum computational knowledge,theoretical concepts,definitions of pure and entangled states,entanglement witnesses and the other entanglement criteria will be briefly introduced.We focuses on the properties of a special multipartite entangled five-qubit GHZ diagonal state.We use the method of optimal entanglement witness to study the necessary conditions of multipartite separability,and use the method of matched entangled witness to study the optimal conditions of separability.An entangled criterion for a certain kind five-qubit GHZ diagonal states is obtained.The entanglement criteria is applied to the highly symmetrical GHZ diagonal state to obtain entangled and separable regions.This thesis provides a new analysis method,which divides the entangled witness operator into diagonal and anti-diagonal parts,so the quantum state is also divided into diagonal and anti-diagonal parts when discussing the matched entangled witnesses.The knowledge of geometric space is also used to assist in the analysis of the entanglement and separability of the quantum state.This method enriches the study of quantum state entanglement criteria.