Quantum Non-locality And Nonlocality Dynamics

Since the two striking phenomena-'quantum entanglement' and 'nonlocality'- were introduced into quantum mechanics by the EPR Argument, quantum entanglement, quantum nonlocality and their relationship have become an reseach hot-spot to many physicists. Especially after the Bell Inequality and its generalized formula-the CHSH Inequality-was put forward, the argument between Einstein and Bohr have become a problem which can be tested quantitatively. The related experiments have been developed since then. In quantum information process, because of the inevitable couple between the quantum system and environment, the quantum system loses its quantum characteristics such as nonlocality and entanglement if it is open to the environment. It is important to study how the quantum property such as entanglement, coherence, and nonlocality evolve with time. In this dissertation, by making use of the superoperator methods for solving the master equations-an effective theoretical tool, we obtain the explicit analytic expression of the density operator, we study several problems on the Bell nonlocality and dynamics of nonlocality of quantum states. The main contents are as follows:We review the fundamental theory of EPR argument, the Bell Inequality as well as CHSH Inequality which is a famous generalized formula of Bell Inequality. Several fundamental conceptions about Bell nonlocality, such as locality description, nonlocality description, and the nonlocality quality of wave function collapse are introduced. Bell nonlocality of successive variables are studied. We mainly introduce the method of the 'pseudospin operator' which we will use in our later analyses.We study the solution methods to the master equation, especially the superoperator method. We solve several typical master equations by using thismethod. The maximum advantage of this method lies in that it can conveniently derive the analytic expression of the density operator from an arbitrary initial state. It provides us an effective theoretical tool for studying how the quantum characteristics such as decoherence, nonlocality and entanglement of quantum states evolve with time.We analysis carefully the dynamics of quantum nonlocality and entanglement for a two-mode squeezed vacuum state in a phase damping channel. We obtained the explicit expression of the density evolution operator of the system by using the superoperator methods for master equations. The nonlocality of the state is well uncovered by introducing appropriate Bell operator based on the 'pseudospin operator'. Moreover, we calculate directly the relative entropy of entanglement of the state. Based on these calculation and analysis, we drawn an exact conclusion that the state is always be entangled throughout the evolution time. And also, we give a wonderful example of analyzing the dynamics of nonlocality for the hybrid entangled state in thermal reservoir by the same method and obtain some interesting results.