Genuine Correlations Of Tripartite System

It is well known that quantum correlation, such as entanglement and quantum discord, isone of the very important resources of quantum information processing. The quantumentanglement has been studied very well. As one kind of important resources, Entanglementshows a wide application prospect. It is found that theories of entanglement may be applied inquantum phase transitions and adiabatic quantum computation. In2001， one kind ofquantum correlations, the quantum discord has been proposed. Because it seems that quantumdiscord is more common than entanglement in quantum states, quantum discord has recentlydrawn much attention. Up to our knowledge, most of researches are limited in bipartitequantum states, such as the analytical evaluation of some special two-qubit states. There arenot many researches about quantum discord in multipartite states, therefore, our researchfocus on the genuine tripartite quantum discord in tripartite states.First, we introduce definitions of genuine tripartite total, classical and quantumcorrelations in tripartite systems, and found that both genuine tripartite classical correlationsand quantum discord are equal to half of the genuine tripartite total correlations in a pure state.For a symmetrical tripartite quantum state, the genuine tripartite total and classicalcorrelations is no less than the any pairwise counterpart, respectively. For quantumcorrelations, there is no fixed quantitative relation between genuine and pairwise quantumcorrelations.Second, we also showed that the genuine tripartite quantum discord can be regarded asa useful resource and can be interpreted as ‘quantum advantage’ in tripartite superdensecoding. The genuine tripartite quantum discord is greater than the bipartite counterpartsometimes, so that the genuine tripartite quantum discord has advantages than the bipartitequantum discord in quantum information as well. Analytical expressions for genuinetripartite correlations are obtained for pure states and rank-2states. The genuine correlationsin both entangled and separable states are calculated. We compared our results with which[PRL,107,190501] and the result showed that in our definition of genuine tripartite quantumcorrelation is no greater than the one defined in [PRL,107,190501], and the genuine classicalcorrelation is no less than the one defined in [PRL,107,190501]. The reason is that thebipartite system which be measured are treated as two systems in Ref [PRL,107,190501]whereas we regard them as a whole system. Besides, we have also given the definition of N-partite genuine correlations ofsymmetrical N-partite quantum states. In present dissertation, we do not discuss somephysical properties of N-partite genuine correlations in general states. In fact, there are stillmany problems about the multipartite correlations waiting to be solved.