The Research On Quantum Entanglement Measurement

In this thesis, the author will investigate and discuss two aspects of quantum entanglement.1 We study the 3-tangle changing rate of a 3-qubit pure state under the unitary evolution. The rate could be controlled by performing a local operation U on qubit C before the evolution. Our goal is to maximize this 3-tangle changing rate by adjusting the three parameters of U. In this work, we give an explicit definition of 3-tangle rate controlled by local operation and discuss GHZ and W states as examples. We find that, for GHZ state, the 3-tangle rate under XXZ model merely depends on the parameterθof UC , which corresponds to the rotation about the y-axis. For W state, all the three parameters of UC should be considered to maximize the 3-tangle rate.2 Based on the isomorphic relation between operator space and Hilbert space. Cirac et al. map the global superoperator to a mixed stateρwhich has the same separability of the initial superoperator. In this paper, we first give a new expression of Cirac's map. Then we use witness to detect the entanglement ofρto judge the separability of the initial superoperator. With the help of local orthogonal observables, we directly describe the separable criterion of superoperators by its each operator. Using the lower bound of the witness, we give an entanglement factor to describe the capability of entanglement generation for bipartite superoperator.