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The balance of quantum correlations for a class of feasible tripartite continuous variable states

We address the balance of quantum correlations for continuous variable (CV) states. In particular, we consider a class of feasible tripartite CV pure states and explicitly prove two Koashi-Winter-like conservation laws involving Gaussian entanglement of formation, Gaussian quantum discord and sub-system Von Neumann entropies. We also address the class of tripartite CV mixed states resulting from the propagation in a noisy environment, and discuss how the previous equalities evolve into inequalities.