Dynamics Of Quantum Entanglement And Quantum Discord In Photonic Crystals

In the last decades, quantum information has become a very hot research area. Quantum entanglement and quantum correlation, as one of the most intriguing characteristics of quantum mechanics, plays a key role in quantum information processing. Quantum entanglement is considered to be an important and irreplaceable resource for the manipulation, storage, transmission of quantum information. It is also an essential feature to distinguish quantum mechanics from classical mechanics. At present, many measures of entanglement have been proposed for bipartite and multipartite systems. It is found that the quantum system will be affected by the interaction of the environment inevitably, which may induce decoherence of the quantum system, and as well energy dissipation. As is well known, quantum entanglement can not describe all types of quantum correlations. In other words, there could be non-classical correlation in separable states. Quantum Discord is another measure of quantum correlation.In this thesis, by using a modified conjugate gradient method, we investigate the time evolution of residual entanglement in a three-qubit system embedded in a photonic crystal. In the isotropic photonic crystal the phenomena of entanglement "sudden death" and entanglement "sudden birth" are found due to the decoherence induced by the environment and its memory effect. Compared with the environment of an isotropic photonic crystal, entanglement has a longer lifetime in the anisotropic photonic crystal if the transition frequency is near the band edge. However, once the entanglement disappears, at a finite time in the anisotropic photonic crystal, it cannot revive, which means the phenomenon of entanglement sudden birth cannot happen in the anisotropic photonic crystal. The tripartite entanglement decays faster than bipartite entanglement in both types of photonic crystal, which indicates that multipartite entanglement is more fragile than bipartite entanglement in resisting quantum noise. At the same time, we analyzed the bipartite subsystem in the three-qubit system, and calculated the time evolution of concurrence and quantum discord in the subsystem. Compared with the concurrence, in both isotropic photonic crystal and anisotropic photonic crystal, quantum discord can only decay asymptotically. And zero entanglement does not guarantee zero quantum discord. The fact that quantum discord may be smaller than the entanglement is due to the different scale of quantum entanglement and quantum discord.