The Application Of Yang-Baxter Equation In Quantum Correlations Theory

Yang Baxter equation was originally derived from C N Yang and R J Baxter independently obtained two different relations, and later Lenin grad school in the former Soviet Union developed the quantum inverse scattering method, found two relations in essence is the same, collectively referred to as the Yang-Baxter equation. After years of development, has played an irreplaceable role it has in the quantum statistical model and quantum many body problems, in the field of integrable model.On the other hand, recent research has shown that quantum entanglement is a kind of special quantum correlations, using only quantum entanglement concept can not be completely different classical correlation and quantum correlation. In 2001, Ollivier and Zurek proposed the concept of quantum discord, which is currently the most widely accepted measure of quantum correlation method.In this thesis, Yang-Baxter equation and quantum correlation theory is combined, through Yang-Baxter to the braid group algebra, two--groups algebra, Yang-Baxter system has two- and three body different, were calculated for different Yang-Baxter system concurrence, the three body entanglement degree, the quantum discord, discusses the quantum correlation properties of Yang-Baxter system.Theoretical calculation shows that, the Yang-Baxter equation is applied to the quantum correlation theory, not only can get a series of potential value in quantum information science.Quantum state, but also can deepen the understanding of the quantum phenomena, and promote the development of quantum correlation theory.The paper is organized as follows:The first chapter reviews the related research background of this paper, mainly including the present and history of the development of quantum entanglement, quantum correlation. As a common metric, quantum entanglement, quantum discord definitions and calculation methods;The second chapter mainly explains the origin of Yang- Baxter equation, Temperley-Lieb algebra and two--groups algebra and its construction method, Yang-Baxter method, by the braid group algebra two and three body Yang-Baxter system method;In the third and four chapter, respectively by the Yang-Baxter system of braid group algebra,two--groups algebra structure of two and three body, to produce a series of quantum state by the Yang-Baxter system, the concurrent degree calculation of quantum states and quantum discord. After the discussion found series of quantum state produced by the Yang-Baxter system with the same degree of concurrency and the quantum discord, and its value is determined by one or several parameters of Yang-Baxter system.