An Easy Measure Of Quantum Correlation And Its Comparison With Quantum Entanglement

Quantum mechanics,created and developed in the twentieth century,is one of the greatest achievements in science.After a hundred years of development,it is attracting more and more attention,and its applications have extended to other fields,such as chemistry,biology,material science,and so on.Modern quantum mechanics has leaded to the generation of quantum information science,which information science is an interdisciplinary subject of quantum mechanics and information science.In the recent years,the concerns in quantum information science has gradually turned from theory to experiment,which is an unavoidable step towards its potential applications.It is well accepted that quantum entanglement is not the only useful resource in quantum information science,and quantum correlation may also play its own role in this area.In this thesis,we proposed a simple measure of quantum correlation and compared the results with the quantum entanglement.In order to measure the quantum correlation of a bipartite state,a test matrix is constructed through the commutations among the blocks of its density matrix,which turns out to be a zero matrix for a classical state with zero quantum correlation,and a nonzero one for a quantum state with positive quantum correlation.The Frobenius norm of the test matrix is used to measure the quantum correlation,which satisfies the basic requirements for a good measure.By using this method,we studies the quantum correlation of two-qubit pure states and Werner states.More importantly,the present measurement can be used to calculate the quantum correlation of high-dimensional bipartite states.Through the comparison with the quantum entanglement it is shown that the quantum correlation of a two-qubit entangled stateis equal to its quantum entanglement,quantified by the Wootters concurrence.In another example,the quantum correlation and quantum entanglement of the Werner state is discussed.As a function of the parameter p,its concurrence shows a sudden change at one point,but no sudden change is found in the quantum correlation of the Werner state.In addition,another important statement is verified in our current work,i.e.,a separable state might have nonzero quantum correlation.Finally,we studied the quantum correlation of a 32? and a 3?3 bipartite states,and compared the results with the their quantum entanglement,quantified by Negativity.It is found that the calculation of quantumentanglement of a high dimensional bipartite state is much harder than the calculation of its quantum correlation,if the simple measure of quantum correlation proposed here is chosen.In this thesis,we propose a new measure of quantum correlation,where no optimization is involved in the definition.This measure can compute bipartite state of quantum correlation efficiently and satisfy all the required conditions.So it is a good measure.