Quantum Entanglement And Quantum Correlation

The quantum correlation is of particular importance in quantum-information pro-cessing and is responsible for many quantum tasks. In recent years, quantification ofquantum entanglement and correlation has attracted great attention. Quantum statescan be classified either separable or entangled, or classically correlated or quantum cor-related. Separable states may also have non-classical correlations.Quantum entanglement is a kind of nonlocal quantum correlation that has beenwidely used in quantum information processing. It is just one kind of quantum correla-tions. Characterization and quantification of quantum entanglement have become a veryimportant issue. This thesis includes five sections and our main results are given in theseconder, third, and forth sections. In Chapter2and3, we discuss the quantum corre-lation of quantum state which depend on whether it is separable state or not. Throughthe analysis and study of quantum entanglement measure, we get the upper and lowerbounds of the entanglement measure. In Chapter4, we discuss the quantum correlationof quantum state which depend on whether it is classical state or not. The structure ofthis thesis is as follows.In Chapter1, we give a survey of the backgrounds and recent developments of thequantum correlation theory. We introduce some elementary concepts and results aboutquantum correlation that will be used in this thesis.In Chapters2,3and4, we present our main results of this thesis. There are threesections in Chapter2. First, we study the lower bound of concurrence for tripartite quan-tum states, in terms of the concurrence of sub-quantum states. The lower bound mayimprove all of the existing lower bounds of concurrence. The approach is generalized toarbitrary dimensional multipartite systems. Seconder in Chapter2, we study the concur-rence of four-qubit quantum states and provide analytical lower bounds of concurrencein terms of the monogamy inequality of concurrence for qubit systems. The approach isgeneralized to arbitrary qubit systems. Finally in Chapter2, we study the concurrenceof multipartite quantum states. Some lower bounds of the multipartite concurrence arereviewed. We further present more efective lower bounds for detecting and qualifying en-tanglement, by establishing functional relations between the concurrence of multipartitequantum states and concurrence of the multipartite systems as bipartite quantum states.Specifically, we studied the N-qubit mixed state with decomposition on the generalizedW states. In Chapter3, we provide analytical lower and upper bounds for entanglement offormation for bipartite systems, which give a direct relation between the bounds of en-tanglement of formation and concurrence, and improve the previous results. Detailedexamples are presented.In Chapter4, we introduce one-way unlocalizable information deficit with respect tothe one-way information deficit, similar to the definition of one-way unlocalizable quan-tum discord with respect to one-way quantum discord. The properties of the one-wayunlocalizable information deficit and the relations among one-way unlocalizable informa-tion deficit, one-way unlocalizable quantum discord, one-way quantum discord, one-wayinformation deficit and other quantum correlations are investigated. Analytical formulasof the one-way unlocalizable quantum discord are given to detailed examples.We finally give a summary of the content in this thesis, together with some openproblems in this field.