Research On Quantum Entanglement Measures And Coherence Measures

Quantum entanglement is the core concept of quantum information.How to characterize the measure of entanglement is an important problem in the study of quantum entanglement,moreover,the quantum entanglement measure and the coherence measure can reflect the quantum property of the physical system,so the quantification of the coherence is not only a quantum theory,in this paper,we mainly study the entanglement measure and the coherence measure based on different entropy systems.The first chapter mainly introduces the research significance of the monogamy and polygamy inequalities of quantum entanglement and the coherence measures based on the Tsallis relative operator entropy,the current research status of domestic and foreign scholars in this area.The second chapter is preliminary knowledge,which mainly introduces the basic knowledge and concepts used in the text.The third chapter mainly concerns on the tighter monogamy relations of the multipartite qubit system with respect to Rényi-? entanglement and the tighter polygamy relationship for multipartite entanglement based on the Rényi-? entanglement of assistance.First,by using a new inequality,the coefficients in Rényi-? entanglement and Rényi-? entanglement of assistance are changed,then,we obtain the monogamy relation about Rényi-? entanglement and the polygamy relation about Rényi-? entanglement of assistance.Subsequently,an example was used to show that for high-dimensional quantum systems,the inequalities of the monogamy and polygamy are more compact than previous conclusions.Finally,by changing the exponential power of the coefficients in the Rényi-? entanglement and the Rényi-? entanglement of assistance,we obtain the more compact single coordination relationship between the arbitrary entanglement and the Rényi-? entanglement and the Rényi-? entanglement of assistance for the multipartite qubit system.The fourth chapter mainly studies a family of coherence quantifiers based on the Tsallis relative operator entropy.Shannon inequality and its reverse one in Hilbert space operators derived by Furuta are extended in terms of the parameter of the Tsallis relative operator entropy.These quantifiers are shown to satisfy all the standard criteria for a well-defined measure of coherence,and include some existing coherence measures as special cases.Detailed examples are given to show the relations among the measures of quantum coherence.Some conclusions and future works are contained in the fifth chapter.