The Measure Of Entanglement For The Mixed States

Quantum information science is a field of science and technology, combining and drawing on the basic ideas of the disciplines of quantum mechanics, computer science, information science and encryption. How to quantify entanglement is the heart of quantum information. Although entanglement for the two-party pure state and the formation entanglement of two-qubit mixed state can be calculated, we know little about it as so far, especially for the case of general quantum states with high dimensions. In fact, it is impossible to quantify entanglement for a general state due to the difficulties above. However, we can give it an estimate, that is to say we can give the entanglement a upper bound or the lower one.In the thesis, we put an emphasis on the research of concurrence, concurrence has been an universal tool to quantify entanglement for bipartite system. For the relationship between concurrence and entanglement of formation is an analytical function, calculation of concurrence implies the result of entanglement for formation. Concurrence for mixed states can been constructed by convex roof, but it is not calculable. However in the research of bound on concurrence, it is widely used including our thesis.In the detection of entangled states, we often use assistant states such as the product states of its reduced density to detect entanglement for better results. Futhermore we apply this method to measure of entanglement, and we gain a new analytical lower bound on concurrence. Also we proved its tighter in theory. At the end of the thesis, we present three different examples to illustrate that our result can improve the bound on concurrence. Interestingly we found that for some cases our theory is consistent with the result in existence, while for others our theory is better.