Antification Of Quantum Correlation And Its Applications In Quantum Infornation

Correlations are ubiquitous in nature, especially in quantum world. The origin of quantum correlation research, or more precisely, quantum entanglement can date back to the seminal EPR-paper in1935, and nowadays there is no doubt that quantum en-tanglement is one of the most significant concepts in quantum information processing (QIP). It has already been recognized as the fundamental feature of quantum mechanics and utilized as a crucial resource in quantum information science. However, entangle-ment should not be viewed as an unique measure of quantum correlations since there exist other types of nonclassical correlations which are not captured by entanglemen-t. In particular, the discovery that separable quantum states can exhibit some kind of quantum correlations other than entanglement has led to a new understanding of the quantum aspects of a physical system.Therefore, there is an urgent need to study correlations from a perspective differen-t than the entanglement-separability paradigm. To this end, quantum discord has been proposed to characterize quantum correlations within such a quantum-classical frame-work. Recently, it has been reported that quantum correlations also play a vital role in QIP. So far, the theoretical studies of quantum correlations fall into the following two categories:(1)Exploring the differences and connections between the theoretical frameworks of quantum entanglement and quantum correlations, which includes inves-tigating how to scientifically classify and quantify quantum correlations, and discussing the scope and properties of these measures;(2)Looking for quantum tasks or protocols in which quantum discord occupy a key position, and particularly, paying attention to those tasks in which quantum entanglement is useless or even there is no entanglement.Following the two lines of thought, this dissertation is devoted to the study of different notions of quantum correlations and their applications. The major scientific results are listed as below:(1) We have investigated the performance of various correlation measures in quan-tum phase transitions employing the quantum renormalization-group method. We have proved that all of these correlation measures can effectively detect the quantum criti-cal points after several iterations of the renormalization in one-dimensional anisotropic XXZ and XY model. Compared with previous literature using the spin-spin correla-tion functions, this method greatly simplifies the calculation and establishes a clear and intuitive physical picture.(2) We exploit quantum discord (and geometric discord) to detect quantum corre-lations present in quantum random access codes (QRACs). Analytical derivation shows that the quantum discord is nonzero and highlights that quantum discord might be re-garded as a figure of merit to characterize the quantum feature of QRACs. We also investigate the dynamical behavior of quantum discord under some specific state rota-tions and the connection between quantum discord and dimension witness.(3) We highlight the complementary relationship between quantum discord and the accessible information in the framework of ensemble of quantum states. These result demonstrate a close connection between quantum correlations and quantum communi-cation from a new perspective.(4) We have provided a pictorial interpretation of geometric discord for Bell-diagonal states and observed its nonanalytic behavior under decoherence employing this ap-proach. Besides, we have investigated the relationship between the violation of CHSH-Bell inequality and geometric discord for two-qubit systems. The dynamical behavior of these two quantities is also carefully analyzed under the action of several decoherence environments.(5) We analyze the decoherent properties of entangled coherent states due to chan-nel losses. Employing the concept of "entanglement of formation", degradation of fi-delity and degree of entanglement are calculated. We have obtained an explicit expres-sion of concurrence concerning the symmetric noise channel and demonstrated that en-tangled coherent states with sufficient small amplitudes are more robust against channel decoherence than Bell states.