Calculation And Application Of Quantum Entanglement Quantum Correlation

As an interdisciplinary science which combined with classical theory of information andquantum mechanics, Quantum information theorydevelops rapidly in the recent30years. Quantumentanglement, a kind of nonclassical correlationin quantum world, is a fundamental concept ofquantum mechanics. It is well accepted that entanglement plays acrucial role and is the invaluableresource in quantum computation and quantuminformation. Recently, it is realizedthatentanglement is not the only aspect of quantum correlations, and the nonclassical correlations otherthan entanglement may also play fundamental roles in quantum informationprocessing. Quantumdiscord, as an important supplementary to quantum entanglement, is found to be present in thedeterministicquantum computation with one qubitwhile the entanglement is vanishing. Quantumcorrelations have been widely received as important resources in some quantum informationprocessingprotocols, and they also show some special properties which are other than quantumentanglement. In this thesis, we introduce some common definitions of quantum entanglement andquantum correlations, and we also give a brief discussion of them. We study assisted optimal statediscrimination to find which kind of correlation is needed when we have the probability of success.We also investigate thedynamics of quantum discord of two qubit X shape state withonly oneparticle exposed to noise，it shows some special properties in the dynamics of quantum discord.This thesis focuses on the following two parts:1. Because of the no-cloning theorem, we cannot clone the two unknowing quantum statescompletely, unless they are orthogonal states or the same state, but in the final analysis, it is as aresult of the fundamental principle quantumsuperposition. This also means we cannot distinguishtwo unknowing nonorthogonal quantum states accurately and completely, but we still can do aunambiguous discrimination with probability. We study the assisted optimal state discriminationand calculate the quantum correlations between the principal system and assisted system, and wegive the least correlations needed in optimal discrimination. We point out that it may haveasuccessful discrimination in which does not need any quantum correlation between the principalsystem and assisted system when the two nonorthogonal states have an equal probability. 2. We study the quantum discord of the X class ofquantum states under threedifferent kinds ofnoise such asamplitude, dephasing and depolarizing in this article, and we give the analyticalexpression of quantum discord under the noise environment. Weshow that composite noise is notthe necessary condition forthe occurrence of sudden change of quantum discord and thesuddenchange can happen when the quantum noise act onlyon one qubit of the quantum system.On theother hand, we should note that the single noise acting on onlyone of the qubits of a two-qubitquantum state is not sufficient for the happening of sudden change of quantum discord,the suitablestate is also needed.