Quantum Correlations In A Heisenberg XYZ Model

The study of quantum correlations has recently become one of the central topics in quantum information science. As two typical correlations, quantum entanglement and quantum discord can be used to accomplish quantum computing, quantum cryptographic key distribution, quantum coding, quantum teleportation, and so on. However, previous works have mostly focused on discords in two-qubit systems, little is known about the possible connections between discord and entanglement beyond qubits. In this thesis, we analytically and numerically study quantum discord in a Heisenberg XYZ model and other states, and compare the discord and the generalized negativity.At first, we give the introduction of basic theory of quantum correlations, including the concepts of quantum entanglement and discord, and analytic expressions in a two-qubit state.We analytically and numerically investigate the thermal quantum correlations in a two-qubit Heisenberg XYZ model with different magnetic fields. It is demonstrated that the discord is more robust than the negativity against temperature. Moreover, a suitable magnetic field, interaction, and temperature is helpful to gain a nearly unchanged discord or negativity. The discord can display a sharp peak at a suitable coupling at finite temperature while the negativity cannot. Those supply adjustable quantum correlations with the varied magnetic field, coupling, and temperature, and may have an important application in the accomplishment of quantum tasks.We use two numerical methods to estimate quantum discord in high-dimensionally mixed states, and apply them to the discord in two qutrit states. It is shown that the discord displays the nonlinear function of state parameter while the negativity is a linear one with different turning points. However, both quantities have the similar behaviors in the ranges of large parameter in those states. Those are helpful in the understanding of quantum correlations in high-dimensional states.In summary, we have used two numerical methods to calculate quantum discord in bipartite quantum states, and studied quantum correlations in the two-qubit Heisenberg XYZ model and other two kinds of states. We believe that those can motive one to explore quantum discord in high-dimensional states, to characterize quantum discord in multipartite systems, and to investigate the influence of environment on the discord.