The Relation Between Quantum Correlation And Critical Point Of XX Model,and The Construction Of Multipartite Joint-Measurement Bases

Quantum correlation,as a resource that can speed up the processing of information,plays an important role in quantum information science.At the beginning of the quantum information science,it is generally believed that quantum correlation can only take the form of quantum entanglement.However,with the development of quantum information,researchers have found that not only entanglement,other quantum correlation like quantum discord and quantum coherence,can also accelerate information processing.At present,the primary task of quantum information science is to study quantum correlation.Besides its application in information processing,quantum correlation can be applied in other fields,such as evolution of quantum states and quantum phase transition,and many research achievements have been gained.In this paper,we will discuss the relationship between quantum correlations and quantum phase transition of the XX model.And the construction of multipartite joint-measurement bases,which is generalized from Bell states,will also be mentioned.With the introduction of many kinds of quantum measurements,some plausible concepts can be quantified clearly and become clearer and more operable.Thus we can use quantum correlations as order parameter to study quantum phase transition.In this paper,we take the XX model as an example,calculate its density matrix of the nearest neighbor lattice,and use quantum correlation to research its critical phenomena.Through the analysis,we can find that these quantum correlations can be used to probe the critical point of quantum phase transition.Additionally,in the 2-qubit system,Bell states can be used as a set of joint-projectors.But there is no available joint-projector to measure arbitrary n-order d-dimension quantum system so far.Inspired by the Bell states,we extend them to any Hilbert space which formed as Hd(?)n,and get the joint-measurement bases in it,so we can take jointmeasurement in quantum multipartite systems.The thesis is organized as follows.In the first chapter,some basic theories and concepts of quantum information are briefly reviewed,and the XX model is then introduced.In the second chapter,we mainly calculate ground state wave functions of the XX model by using Jordan-Wigner transform.In addition,we analyze its ground state and energy level,and get the nearest neighbor lattice ground state density matrix of the XX model in free boundary condition.In the third chapter,we mainly discuss the hidden variable and Bell inequality,as well as the EPR quantum steering and Bell non-locality theory which are established on them.We analyze if there exist a classical structure to establishing a “quantum state” by using hidden variable model and semi-definite programming method.The fourth chapter introduces the measurement of quantum coherence and quantum entanglement,and analyzes phase transition of the XX model by quantum correlations.The Bell inequality and the mathematical programming in the third chapter are used to study the maximum violation of Bell inequality by the XX model adjacent lattice;the results are also consistent with previous theories,and the explanation is given from the level of quantum correlation.In the fifth chapter,we expend the Bell states to arbitrary higher dimension.We exclude many equivalent states by leveraging the group theory and find a method to construct a set of complete orthogonal genuine multipartite entanglement states.At the last,we also provide the joint-measurement bases of the 3-order 3-dimensional Hilbert space as an example and study the application of general results in the dense coding scheme as an application.