Research On The Quantum Nonlocality Under The Environment

Quantum entanglement is a kind of very important resource in the process that realizing the quantum information processing and quantum computing. Quantum entanglement is a quantum property existing in more than the two-body quantum systems. By now this quantum property can be used for quantum key distribution, quantum dense coding, quantum teleportation, quantum error correcting code, quantum computing and many other aspects. It has been the source of strength that quantum information surpassing the classical information. As the quantum system and environment will interact with each other inevitably, the research of the entanglement evolution under the effect of environment becomes very meaningful. Since the phenomenon of the sudden death of entanglement was found, people have studied extensively on the entanglement evolution of the two-body quantum system both in experiment and theory.The multi-body quantum system also plays an important role in the quantum information processing, as it can present us more interesting features that can’t be found in two-body quantum systems. But the study of ESD is previously limited in two-body systems, because there are no proper entanglement measures for multipartite systems. When studying the multipartite system, people used to analyze the nonlocality by the extent of the quantum-mechanical violation of Bell-type inequalities. As tripartite system is the most basic multipartite system, the study on the Bell nonlocality of the tripartite system can not only help us understand features that can’t be found in two-body quantum systems but also contribute to realizing the quantum information processing. In recent years, the Bell-nonlocality sudden death (BNSD) of tripartite system has been demonstrated through analyzing the violation of the Mermin-Ardehali-Belinskii-Klyshko(MABK) inequality. The demonstration makes quantum information and calculation more challenging to us. Motivated by the research, we study on the Bell-nonlocality evolution of tripartite systems through analyzing the violation of different kinds of Bell inequalities. The study on the quantum nonlocality of entangled state can help us understand the quantum mechanics and the relation between the quantum entanglement and Bell-nonlocality deeply.The main content of our work is divided in three parts:1. We have investigated the nonlocality of the tripartite quantum system which consists of a T-C model and a J-C model. Assuming that three atoms are initially in the maximum entangled state— W state and GHZ state separately, we analyze the violation of WWZB and Svetlichny inequality. The results show that there exists sudden death and revival of the generic and genuine tripartite Bell nonlocalty.2. We have studied the quantum entanglement and nonlocality of the bipartite system under the amplitude damping noise. The quantum coherence would degrade under the amplitude damping noise. We studied the concurrence, Quantum Discord and Bell-nonlocality evolution of the bipartite systems versus the initial parameter under the one-side noise and the two-side noise. The results show that the evolution of the concurrence under the two-side noise and the Quantum Discord under the one-side, two-side noise are not proportional to that of no noise, while the evolution of the concurrence under the one-side noise and the Bell-nonlocalty under the one-side, two-side noise are proportional to that of no noise.3. We have discussed the effects of the amplitude damping noise on the nonlocality and the entanglement of the tripartite quantum system. The influences of the amplitude damping noise on the nonlocality and the entanglement are different. We studied the negativity and Bell-nonlocality evolution of the tripartite systems versus the initial parameter under the amplitude damping noise. It turns out that the evolution of the negativity versus the initial parameter under the amplitude damping noise are not proportional to that of no noise, while the evolution of the Bell-nonlocality versus the initial parameter under the amplitude damping noise are proportional to that of the initial state.