Quantum Entanglement And Decoherence

Quantum information science is a new field of science and technology, combining and drawing on the basic ideas of the disciplines of quantum mechanics, computer science, information science and encryption. Its speedy development also drive the further intersections between different disciplines of physics, chemistry, mathematics, electronics and control theory. The research on how to implement the coherent control of real quantum systems, has promoted the development of other fields, such as Cavity QED, Bose-Einstein condensate and nano-electronics. The mainstream in the development of quantum information theory is always accompanied with the intersections of different research areas. There is increasing interest in adopting the concepts and techniques in quantum information theory to solve problems in many-body physics and statistical physics. Quantum entanglement and decoherence are fundamental concepts in quantum information theory. Quantum entanglement is the indispensable physical resource in quantum information processing. How to characterize, quantify and manipulate quantum entanglement is the most central issue in quantum information theory. Compared to two-qubit entanglement, the understanding about the nature and structure of multipartite entanglement is far from clear. Quantum decoherence is introduced in the quantum measurement theory to give an explanation for the fundamental quantum-classical transition problem. It has close connections with quantum entanglement. To suppress the decoherence effects, people has proposed many quantum codes to encode quantum information into multipartite entangled states. Furthermore, the decoherence of many-body systems will emerge novel and interesting properties. Therefore, the research on quantum entanglement and decoherence is not only the fundamental problem in quantum mechanics and quantum information theory, but also the bridge of different disciplines. In addition, the theory of special relativity is another foundational part in modern physics. Its combination with quantum information theory will provide new insights into the connection between quantum mechanics and the theory of special relativity. It is interesting to investigate the effects of special relativity on quantum entanglement and decoherence. This dissertation can be divided into three parts. In the first part, we present a systematic study of quantum entanglement, in particular multipartite entanglement. In the second part, we investigate the decoherence of quantum entanglement and many-body systems. In the third part, we discuss the decoherence properties of a single Dirac electron, which is modulated by special relativity.1. The quantification of quantum entanglement is the most important problem in the theory of entanglement. People have proposed various kinds of local invariants for multipartite entanglement. However, the well defined measures of multipartite entanglement are still absent, except genuine three-qubit entanglement. How to quantify multipartite entanglement and understand its nature is a tough problem, however, it is the key step to apply the concept of quantum entanglement in many-body physics.We investigate the complementary relations between local and nonlocal information in multipartite quantum systems. From the viewpoint of different levels of entanglement, we propose a new kind of information-theoretic measure of multi-qubit entanglement. The properties of our measure naturally leads to a series of compatibility conditions and monogamy relations for multipartite pure states. We also investigate the properties of different levels of entanglement in graph states, which is a important kind of multipartite entangled states in quantum computation. Motivated by these results, we introduce the definition of maximally genuine multi-qubit entangled states. In addition, we propose a simple scheme based on two-particle interferometer for the determination of entanglement in a special kind of mixed states.2. In quantum information theory, quantum decoherence means the process in which quantum states depart from the ideal states. As a kind of valuable resource, quantum entanglement is fragile in a decoherent environment. Most recently, people become more interested in the decoherence properties of many-body quantum systems, which is of practical importance in large scale quantum information processing.We investigate the decay of two-qubit entanglement in various kinds of decoherence models, and find the most entanglement-stable states. We also consider the decoherence effects on the quantum state transfer through an open end spin chain, which is a many-body system, we demonstrate that the decoherence will become much more serious as the length of spin chain increases. Our results put forward new constraints on the quantum spin channels, and will help to understand and suppress the decoherence of many-body systems.3. The interrelationship between quantum mechanics and the theory of special relativity is an essential part of modern physics. The close connections between quantum information and special relativity theory attract more and more interest. The effects of special relativity on quantum measurement process, quantum von Neumann entropy, quantum entanglement and quantum teleportation has been widely investigated. In regular quantum information theory, people always assume that the central quantum system is at rest, therefore the combination of the theory of special relativity and open quantum systems is a very interesting topic.We investigate the decoherence properties of a moving spin-1/2 Dirac electron coupled with an external environment. The effects of special relativity will modify the decoherence properties significantly. We show that the decoherence process seems halting eventually. Our results will enlarge the research scope of relativistic quantum information theory, and establish interesting connections between special relativity and quantum mechanics.