Quantum Discord And Geometric Discord For Multiqubit Systems

Quantum correlation is a basic feature of quantum mechanics,which distinguishes the quantum world from the classical world and plays an important role in quantum information processing.Entanglement was considered to be equivalent to quantum correlation for a long time,until the introduction of quantum discord brought more advantages to quantum information processing and quantum computing than entanglement.However,the calculation of quantum discord is very heavy,so we only know the specific explanation formula of some special quantum states.In order to overcome this difficulty,some researchers proposed to replace the original quantum discord with the geometric measure of quantum discord.The computational workload is greatly reduced and concise expressions are easy to be given.In addition,at the beginning of the study,researchers only paid attention to the study of quantum discord in closed quantum systems.But in fact,any real quantum system will interact with the surrounding environment and exchange information and energy,leading to the system’s decoherence.The main research contents and results of this paper are as follows:The first chapter mainly introduces the research significance of quantum discord in multiqubit system and the research status at home and abroad,and summarizes the main content of this paper.The second chapter is the preliminary knowledge,mainly introduces the basic knowledge and concepts used in the article.The third chapter mainly calculates the multipartite quantum discord for a specific class of multiqubit states.More specifically,we generalize the well-known Bell-diagonal states to multiqubit systems,and determine the specific expressions for quantum discord of this family of multiqubit states by calculation.We also apply local dephasing noise to the multi-qubit systems and calculate quantum discord as a function of the decoherence probability,and thereafter demonstrate the well-known phenomenon of sudden change in the quantum discord,and the constancy of quantum discord with decoherence probability.We also mention the existence of an odd-even dichotomy in the constancy of quantum discord with the decoherence probability.The forth chapter mainly studies geometric discord for multipartite states.We showed explicit formulas for the geometric discord by employing a family of multiqubit states.The variation of geometric discord is to some extent a reflection of quantum discord.Furthermore,the dynamic behavior of the geometric discord was investigated for the family of two,three,and four qubit states under phase noise acting on a single qubit,resulting in the observation of sudden change behavior.The fifth chapter explores the monogamy of multipartite quantum discord,and proves that these preconditions are valid for a specific class of multiqubit states.Moreover,we investigate the dynamic behavior of these states under phase noise only acting on the first qubit.Some conclusions and future works are contained in the sixth chapter.