Entanglement of formation and quantum discord in multipartite j-spin coherent states.

We study the entanglement of formation and the quantum discord contained in even and odd multipartite j-spin coherent states. The key element of this investigation is the fact that a single j-spin coherent state is viewed as comprising 2j qubit states. We compute the quantum correlations present in the n even and odd j-spin coherent states by considering all possible bipartite splits of the multipartite system. We discuss the different bi-partition schemes of quantum systems and we examine in detail the conservation rules governing the distribution of quantum correlations between the different qubits of the multipartite system. Finally, we derive the explicit expressions of quantum correlations present in even and odd spin coherent states decomposed in four spin sub-systems. We also analyze the properties of monogamy and we show in particular that the entanglement of the formation and the quantum discord obey the relation of monogamy only for even multipartite j-spin coherent states.