Geometric Discord In Bipartite Quantum States

Quantum information theory is based on quantum mechanics and information theory. Information can be described via quantifying and characterizing the nonclassical correlation in a quantum system. Quantum entanglement and quantum discord, as the important quantities of nonclassical correlation, have played a key role in quantum coding and quantum key distribution. In this thesis we study quantum correlations in bipartite quantum states. The content and conclusion is given as follows.We investigate quantum correlation properties of generic bipartite states, and calculate entanglement and discord in two two-qutrit states through the Monte Carlo simulation and the downhill simplex method. It is shown that geometric discord is a nonlinear function for state parameter, while entanglement negative with different turning point is the linear, and both quantities are positively correlated in a larger parameter region. Hence, the hierarchy of entanglement negativity and geometric discord not only depend on the state under study, but also rely on the state parameter.We explore the properties of three geometric discords in a two-qubits Heisenberg XYZ model, and investigate concretely the effect of magnetic field, temperature, and interaction on those geometric discords. The studied results show that three geometric discords exhibit similar behavior in the most of parameter regions, implying that they are a good measure for the description of thermal quantum correlation in the model. However, three geometric discords behave differently in the following manner:(1) With the change of magnetic field, the original discord and the modified discord display a sudden change, while the revised geometric discord didn’t have such behavior. Interestingly, such behavior occurs in different magnetic field intensity with different angle. (2) With the increase of temperature, the maximum of three geometric discords is dependent on the magnetic field angle and the difference in the coupling parameter in X direction and Y direction. (3) The sudden change of geometric discords is highly sensitive to the magnetic field, the type of geometric discords, and the coupling parameters in the model. Those are helpful in deep studying and extensively utilizing quantum correlations.Our investigations can be regarded as a step forward to estimate geometric discords in high-dimensionally mixed states. We expect to explore the properties of geometric discords in other states and the dynamics of geometric discords in a model.