The K-me Concurrence For Special Quantum Pure States And K Nonseparability For Quantum Mixed States

Quantum entanglement as a special physical resource is not only the important com-ponent of quantum computation but also the key of quantum communication. One ofthe critical problems is how to detect and quantify the entanglement. Although peoplehave proposed many methods, yet they are not perfect. This paper list some as follow:in the bipartite quantum systems, there are PPT criterion、reduction criterion、matrixrealignment criterion、covariance matrix criterion、concurrence and so on. Concurrenceis a nice measure of bipartite quantum systems, and it has been extended to multipartitequantum systems. Such as Ma ???? ????. have put forward GME concurrence to measuregenuine multipartite entanglement, and calculated its lower bounds; Hong、 Gao、 Yanhave given the k-ME concurrence(when k=2, 2-ME concurrence is GME concurrence)to measure k-partite entanglement, and calculated its lower bounds. Since k-ME concur-rence well satisfies some significant properties of entanglement measure, it leads a newway for the problem of entanglement in high dimensional and multipartite systems.This thesis mainly applys k-ME concurrence as multipartite entanglement measuregiven by Hong、 Gao and Yan to calculate the entanglement of some special classes ofquantum states. It is divided into three chapters: in the first chapter, we give the basicknowledge needed for this article, including background knowledge and concepts; in thesecond chapter, we calculate the multipartite quantum entanglement of a special class ofpure quantum states(the k??-photon concatenated Greenberger-Horne-Zeilinger states),using k-ME concurrence defined by Hong、Gao and Yan; in the third chapter, we use thecondition of the k nonseparability to calculate some quantum states mixed with whitenoise, As an example, one of maximally entangled states of four qubits which mixed withwhite noise.