Applications Of Quantum Information Theory On Quantum Information Technology And Quantum Dynamics

Quantum information science and technology has been developing very fast since decades ago.In this thesis,I demonstrate my research on the theory of quantum infor-mation during the past five years.The contents of the research fall into two parts.One is about the quantum information processing without dynamical details.To be more specific,it is about the generalization of graph states to qudit hypergraph states.We study the properties of these quantum states and put forward their possible applications.The other part is about the quantum stochastic dynamics with memory effects.In quan-tum information processing,the systems we are interested in usually cannot be seen as being isolated.Therefore,the particles or fields they interact with bring in stochasticity to their dynamics.As the condition of Born-Markov approximation cannot be satisfied sometimes,especially in the contemporary experimental systems,memory effects in quantum dynamics has to be taken into account.My research about the memory effects in open quantum systems covers two works I did in the past five years.The first one is about a boson-boson pure-dephasing model.We propose it in our work and study the memory effects in it.During the research,we propose a new witness of quantum non-Markovianity based on the time-evolution of the quantumness of the system.We analytically proved its effectiveness for the pure-dephasing of two level systems,and numerically demonstrated that it works for the boson-boson pure-dephasing proposed by us.In studying the divisibility of our model,which is an infinite level system,we notice that for a large class of quantum dynamics,one can construct a hierarchy of divis,ibility conditions.A systematic research of this divisibility hierarchy forms my second work about non-Markovian open quantum systems.