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Local correlations of mixed two-qubit states

The quantum probability distribution arising from single-copy von Neumann measurements on an arbitrary two-qubit state is decomposed into the local and nonlocal parts, in the approach of Elitzur, Popescu and Rohrlich [A. Elitzur, S. Popescu, and D. Rohrlich, Phys. Lett. A 162, 25 (1992)]. A lower bound of the local weight is proved being connected with the concurrence of the state $p_L^{\max}= 1-\mathcal{C}(ρ)$. The local probability distributions for two families of mixed states are constructed independently, which accord with the lower bound.