Researches On Monogamy Of Quantum Correlations

Different from classical information, measured in bits, quantum information which is measured in qubits is nonlocal. In quantum theory,quantum systems can have correlations different from classical correlation. Quantum correlation is one of the most important physical resources in quantum cryptography, quantum coding and quantum computing. So far, quantum correlation measures in two-qubit systems have been well studied, but the distribution of quantum correlation in multi-qubit systems and the quantification of quantum correlation in many-body systems are both difficult problems. Monogamy of quantum correlation is an important property in multipartite quantum systems,which reflects that quantum correlation cannot be freely shared and can be used to characterize the correlation structure in multipartite systems.In recent years, quantification and characterization of quantum entanglement sharing and correlation distribution have attracted great attention.We study entropic measures of quantum correlation sharing. The contributions of this dissertation mainly include monogamy of quantum entanglement, linear monogamy of quantum entanglement and the distribution of quantum correlation. The details are as follows:With respect to the monogamy of quantum entanglement,multipartite entanglement indicators, which are constructed from Bai-Xu-Wang-class monogamy relations, can detect the entanglement not stored in pairs of the focus particle and the other subset of particles.We provide some criterion for the maximal multipartite entanglement indicators. In the second lecture, we provide two counterexamples of monogamy inequalities for the squared entanglement negativity: one three-qutrit pure state which violates of the He-Vidal monogamy conjecture, and one four-qubit pure state which disproves the Regula-Martino-Lee-Adesso-class strong monogamy conjecture. We also investigate the sharing of the entanglement negativity in a composite cavity-reservoir system using the corresponding multipartite entanglement indicators. We then show that the entanglement of two cavity photons is a decreasing function of the evolution time, and the entanglement will suddenly disappear interacting with independent reservoirs. Furthermore, we find that there is no simple dominating relation between multipartite entanglement indicators and the entanglement negativity in composite cavity-reservoir systems.With respect to the linear monogamy of quantum entanglement, we analytically prove that both the concurrence and EoF obey linear monogamy relations in an arbitrary three-qubit state ABC. Furthermore,we verify that all three-qubit pure states are maximally entangled in the bipartition A|BC when they saturate the linear monogamy relations. We also study the distribution of the concurrence and EoF. More specifically,when the amount of entanglement between A and B equals to that of A and C, we show that the sum of EoF itself saturates the linear monogamy relation, while the sum of the squared EoF is minimum.Different from EoF, both the concurrence and the squared concurrence saturate the linear monogamy relations when the entanglement between A and B equals to that of A and C.With respect to the distribution of quantum correlation, we define the discord distance as the difference between the left discord and the right discord. When the Lindblad conjecture is true, we show that the joint entropy is a tight upper bound for the discord distance. We also prove that the subadditive relation holds for quantum discord in any tripartite systems,so it does not obey the monogamy-class relation.