Research On Quantum Entanglement And Quantum Correlation Dynamics Of The Open System

Quantum information is a new emerging discipline, which is the combination of quantum mechanics, information science and computer science, developed from 1980s. The naissance and development of quantum information has great significance in the realm of science and technology. Quantum entanglement is a key resource in realizing quantum information and quantum computing and also the ultimate factor for this field exhibiting great advantage and application foreground. By means of quantum entanglement one can achieve some tasks which can not be realized via classical methods, such as quantum teleportation, quantum dense coding and quantum cryptography and so on. However, in the process of system distribution as well as particle manipulation, each particle would unavoidably interact with external environment and this local decoherence would eventually destroy the necessary entanglement of the whole quantum system. So the breaking of entanglement limits the practical application in the quantum information and quantum computing. Therefore, the study of entanglement dynamics in various environmental models, particularly the issue of how to avoid or control entanglement decay in a realistic physical system is especially important, not only have great theoretical interests in understanding the concept of quantum entanglement but also have potential application values in quantum information processing and quantum computing. The main results of this thesis are as follows:1. We study the entanglement dynamics of strongly driven atoms off-resonantly coupled with cavity fields. We consider conditions characterized not only by the atom-field coupling but also by the atom-field detuning. By studying two different models within the framework of cavity QED, we show that the so-called atomic entanglement sudden death (ESD) always occurs if the atom-field coupling is larger than the atom-field detuning, and is independent of the type of initial atomic state.2. We mainly study entanglement transfer and entanglement dynamics about open quantum system and environments. Considering two entangled qubits interacting with independent environment, two entangled qubits can occur sudden death and entanglement sudden birth (ESB) appears between two environments. Through choosing Markovian environments and non-Markovian environments, we acquire different results:For the Markovian environments, we study the effect of purity of initial entangled state of two cavities on the entanglement evolution, and acquire that the purity of initial entangled state of two cavities can control the apparition time of the entanglement sudden death and the entanglement sudden birth. While in the case of non-Markovian environments, we mainly want to construct the entanglement transfer among qubits, and find that the two reservoirs have an intermediate effect in the transfer process.3. Firstly, we consider the non-markovian entanglement dynamics of two independent atoms, each off-resonantly coupling with a zero temperature reservoir. For two types of initial entanglement, corresponding to spin correlated and anti-correlated Bell-like states▕Φand|Ψ>, we study the dependence of the two-qubit entanglement transfer on both the off-resonant interactions and the cavity pseudomode decay. The speed of the entanglement transfer is related to the choice of the atom detuning from the cavity pseudomode, the cavity pseudomode decay and the relative coupling. Secondly, we consider the entanglement dynamics of N qubits interacting with independent structured reservoirs. The system is initially prepared in the multipartite Greenberger-Horne-Zeilinger (GHZ)-type state. Through dividing the overall system into two arbitrarily subsystems, the multipartite entanglement dynamics can be acquired by Negativity. We find the dependence of the entanglement dynamics on both the qubit number N and the purity of initial state. Also we choose the mixed W state to be the initial qubits' state, it is easy to find that N qubits' ESD can occur and the reservoirs undergo ESB correspondingly for a small N. While in the limit of large N, the phenomenon of qubits' ESD and reservoirs' ESB disappear.4. Using the pseudomode method, we evaluate exactly time-dependent entanglement for two independent qubits, each coupled to a non-Markovian structured environment. Our results suggest a possible way to retard entanglement sudden death by modifying the qubit-pseudomode detuning and the spectrum of the reservoirs. Particularly, in environments structured by a model of a density-of-states gap which has two poles, entanglement trapping and prevention of entanglement sudden death occur in the weak-coupling regime.5. We propose an exactly solvable model for the time evolution of two qubits interacting with a common structured reservoir. In this model the presence of system-environment correlations invalidates the initial state in which system and environment are independent, and both Markovian and non-Markovian effects are considered. Due to the non-Markovian effect, some oscillations are presenting, however oscillations would disappear in the Markovian regime. Firstly, we investigate the entanglement dynamics for two different initially correlated states of the qubits and the structured reservoir (the one contains both quantum correlation and classical correlation, the other only has classical correlation). These initial system-environment correlations play a crucial role in inhibiting ESD and ESB which appear in the case where the system and the environment are independent. And then, for the initially entangled states of the qubits, the initial system-environment quantum correlation can initially increase the two-qubit entanglement, while the initially decreased two-qubit entanglement can happen in the case where the system-environment state only contains the classical correlation. When the initial state of the two qubits is separable, the initial system-environment quantum correlation can lead to the initially larger created entanglement of the two qubits. Then we mainly study the role of initial system-environment correlation on quantum discord dynamics. Under a certain condition, the initial system-environment correlations not only can initially increase two-qubit quantum discord but also would lead to a larger long-time quantum discord asymptotic value. For another condition, correlations between two qubits and environment, can more effectively restrain the reduction of quantum discord than the case of the factorized state.