We study the total quantum correlation, semiquantum correlation and joint quantum correlation induced by local von Neumann measurement in bipartite system. We analyze the properties of these quantum correlations and obtain analytical formula for pure states. The experiment witness for these quantum correlations is further provided and the significance of these quantum correlations is discussed in the context of local distinguishability of quantum states.

a b s t r a c tLet g be a Lie algebra over a field K . Endow the polynomial ring K [t] with a g-action by derivations and consider the resulting crossed product K [t] ⊙ θ g in the category of (K , K [t])-Lie algebras. We explore Lie-Rinehart bialgebra structures on (K [t], K [t] ⊙ θ g) that arise via compatible pairs and ε-dynamical r-matrices. We give a complete classification for g = sl(2, K ).

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