Quantum Correlations And The Conversions Between Quantum Correlations And Coherence

Quantum resource theory is currently extensively concerned and essential theory,and can be strictly studied the mutual relations among kinds of quantum resources.Quantum correlations and coherence not only are very fundamental as quantum resources in the quantum information processing,but also of great importance in understanding the conceptual foundations of quantum theory and related physical phenomena.In this paper,we mainly studied two problems:first,how can we analytically quantify and characterize them?it is always one of the main problems in quantum information science;second,how can we find the necessary and sufficient conditions which determine whether quantum coherence can be converted to quantum correlations by the set of incoherent operations?It is also one of the substantial goals in the resource theory.Comparing with quantum entanglement and quantum nonlocality which are defined for bipartite or multipartite quantum systems,quantum coherence can be defined in the single systems.Quantum correlations and coherence play the critical roles in quantum information tasks.In the third chapter of the paper,based the resource theory,we study the relations between quantum coherence and quantum nonlocality,genuine quantum en-tanglement and genuine quantum nonlocality.And We prove that the nonzero coherence of a qubit state can be converted to the nonlocality of two-qubit states via incoherent operations;then the results are also generalized to the genuine quantum nonlocality in the three qubit case;Last,furthermore,rigorous relations between the quantum coher-ence of a single-partite state and genuine multipartite quantum entanglement,as well as the genuine three-qubit quantum nonlocality are established,giving the strict relations about the mutual conversions of two quantum resources,i.e.quantum correlations and coherence.Among the quantum correlations,quantum separability and nonlocality are the more preferred phenomena,enabling numerous applications in the quantum communication and computation.About quantum entanglement,for the given pure states in bipartite quantum systems,we can use the simple criterion,such as the Schmidt decomposition of quantum states,to decide whether they are separable or entangled;for the mixed states in the bipartite systems,there are also many mathematical criteria to characterise their intrinsic property.But for the states of multipartite quantum systems,because of the complexity of the definitions about separability,it becomes NP hard to estimate the states are separable or not.So in the fourth chapter of the paper,We study separability problem using general symmetric informationally complete measurements and propose separability criteria in Cd1(?)Cd2 and Cd1(?)Cd2(?)…(?)Cdn.Here our criteria give the just require less local measurements and provide experimental implementation in detecting entanglement of unknown quantum states.Bell inequalities and quantum nonlocality are the important project discussed in quantum information and computation.How to analytically express the Bell inequalities and the related nonlocality are always the very vital problems.So in the fifth chapter of the paper,by the related knowledge of quantum entanglement,the quantitative inequality relationships between the maximal expectation value of generalized CHSH operators and the entanglement measure,for example entanglement concurrence,are obtained for the pure and mixed states in the bipartite high dimensional quantum systems.