Studies Of Quantum Correlations In High Dimensional Systems

Quantum information and comminication is the combination of information sci-ence and quantum mechanics.Quantum correlation is the significant to distinguishesquantum systems from classical system,and it is the major source of the phenomenonthat quantum computing is better than classical computing.Quantum discord is an important measure of quantum correlation.One of our workin this paper is a method to measure quantum discord of high-dimensional quantumstate.We also applied this method to the physical models and to calculate the quantumcorrelations in high-dimesioanl quantum states, and got some interesting results.In calculationg quantum discord, the important and difcult target is to find theoptimal measuring base for optimization. Here, it is needed to find a feasible methodof optimization. The usual practice is to rotate the measurement basis and find a set ofoptimal measurement basis set through operation of a computer program. In this paper,we adopted a method diferent from the one mentioned above, we fix the measuring basisand rotate the state density matrix basis in calculating the quantum discord in physicalmodel.Using this method, the optimization can be performed so as to find the minimumvalue, and hence the quantum discord.Local Quantum Uncertainty is a new measure of quantum correlation, it could onlydeal with two-dimensional quantum system in its original form. Another of our work inthis paper is that we introduce SU(N) generator to calculate local quantum uncertainty.We regroup the generator members and find the most optimal set of generator whichminimized the quantum measuring variance, and then find the local quantum uncertainty.Innovation of this paper:We introduce Hurwitz theory to calculate quantum discord,and then find a methodthat can realize the calculating any dimensional quantum state discord. We gavethe qauntum discord of Werner state, and find the maximum value is1.585. Wegave the quanutm discord of Horodecki state,XXZ thermal equilibrium state,andfind some new results.We present a method to get the entanglement of formation in arbitrary dimensionalstate using the relation of quantum discord and entangement of formation.We calculated the variation of the quantum local uncertainty for quantum states in the noise environment, found that there exist sudden change in some noisy models.We extended quantum local quantum uncertainty to high dimensional states,closed form was obtained for systems with arbitrary dimensions.