Theoretical Study On The Relationship Between Quantum Entanglement And Quantum Phase Transition And Quantum Control

Quantum information theory,a combination of quantum mechanics and information theory,is a brand-new subject,whose appearance brings about a bright future for the development of science and technology.And the development and improvement of quantum information is dependent on the profound research on quantum entanglement and quantum control.This dissertation mainly discusses some problems related to quantum entanglement and quantum control in theory,and obtains some important results.This dissertation consists of four parts.The first part includes Chapter 1 to Chapter 2.Chapter 1 introduces the significant meaning of quantum entanglement and quantum control systematically as well as their current studies.And the related theories to quantum information are presented in Chapter 2.Part two is composed of Chapter 3 and Chapter 4,which chiefly discusses the relationships between quantum entanglement and quantum phase transition in multi-particle system. Chapter 3 begins with brief introduction of the Dicke model,and then demonstrates the research on the entanglement properties between subsystems as well as quantum phase transition in the Dicke model with the dipole-dipole interactions.The results demonstrate that the entanglement properties between subsystems can well signal the occurrence of quantum phase transition,and the dipole-dipole interactions have a great impact on the entanglement between the subsystems.The XY spin chain is presented in Chapter 4,and the entanglement evolution of bipartite spin-1/2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied.The results indicate that the properties of entanglement between central particles are closed associated with the initial state of the system.When the temperature of the system is near absolute zero,the entanglement between central particles can reflect the quantum phase transition in spin chain.As the temperature increases,the quantum phase transition is washed out by thermodynamical fluctuations.In addition,the temperature can lead to disentanglement between central particles.Chapter 5 alone consists of the third part,in which quantum teleportation,an important application of quantum entanglement in quantum information,is studied.And emphasis is placed on the study of multi-qubit teleportation by employing quantum multi-particle entanglement. By introducing matrix operator,the judgment equation reflecting the relationships between quantum channel and measurement basis in quantum teleportation is described and some special solutions of the equation is given,which can help to seek and use multi-particles entanglement recourses in order to realize the quantum teleportation.Chapter 6 is the fourth part,which presents the concepts of quantum control,and reviews a previous incoherent quantum control scheme.Based on the former scheme,a new scheme is put forward,which can not only realize the controlling of two-level quantum system,but also can be extended to control the finite-dimensional quantum system.Finally,the results are summarized and suggestions are given for future research work.