It is known that relative entropy of entanglement for an entangled state p is defined via its closest separable(or positive partial transpose) state a. Recently, it has been shown how to find p provided that a is given in atwo-qubit system. In this article we study the reverse process, that is, how to find a provided that p is given. It isshown that if p is of a Bell-diagonal, generalized Vedral-Plenio, or generalized Horodecki state, one can find afrom a geometrical point of view. This is possible due to the following two facts: (i) the Bloch vectors of p anda are identical to each other; (ii) the correlation vector of a can be computed from a crossing point between aminimal geometrical object, in which all separable states reside in the presence of Bloch vectors, and a straightline, which connects the point corresponding to the correlation vector of p and the nearest vertex of the maximaltetrahedron, where all two-qubit states reside. It is shown, however, that these properties are not maintained forthe arbitrary two-qubit states.
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