Multipartite Quantum Entanglement Measure Construction Based On Coefficient Matrices

Quantum entanglement is one of the most remarkable phenomena in quantum mechanics,which clearly describes the difference between classical mechanics and quantum mechanics.As we all know,quantum entangled state,as an important physical resource,plays a key role in quantum information processing.Entanglement measure is a measure of the entanglement degree of quantum states.How to quantify entanglement reasonably is an important topic in quantum information theory.In this thesis,the construction of entanglement measures are studied based on coefficient matrices in quantum system.The main contents are as follows:1.The entanglement measures are constructed by using the coefficient matrices of pure states,respectively.Firstly,the primary and secondary mappings are constructed on the set of 2–order sub-matrices of the coefficient matrices,and the corresponding Euclidean nearness degree is given.Secondly,the Euclidean nearness degree is used to construct an entanglement measures of the quantum system.Finally,by calculating the entanglement measures of the Bell states and the common entangled states of the 4–partite quantum system,it is found to be consistent with the results of other entanglement measures calculations.2.The complete entanglement measures of multipartite quantum systems are studied.Firstly,we defines the unification entanglement measure,hierarchy entanglement measure and complete entanglement measure of the multipartite quantum systems,and discuss the completeness of the multipartite concurrence and 6)–ME concurrence.Next,the formation entanglement measure,concurrence and negativity are extended to multipartite quantum systems,and their completeness are discussed.Finally,the completeness of the entanglement measures constructed by the coefficient matrices are analyzed.