v$_{1}$ v$_{2}$ v$_{3}$ v$_{4}$ o$_{1}$ GLYPH<LParen1>$_{GLYPH<Plus>}$GLYPH<RParen1> o$_{1}$ GLYPH<LParen1>$_{GLYPH<Minus>}$GLYPH<RParen1> o$_{2}$ GLYPH<LParen1>$_{GLYPH<Plus>}$GLYPH<RParen1> o$_{2}$ GLYPH<LParen1>$_{GLYPH<Minus>}$GLYPH<RParen1> o$_{3}$ GLYPH<LParen1>$_{GLYPH<Plus>}$GLYPH<RParen1> o$_{3}$ GLYPH<LParen1>$_{GLYPH<Minus>}$GLYPH<RParen1> Ρ Σ FIG. 2: This figure shows how to find the CSS for the Bell-diagonal state. First, extend the line segment between ρ and the point corresponding to the nearest vertex of T . Second, compute the coordinate of the crossing point between the line and the nearest surface of the octahedron L . Finally, find the CSS of ρ which corresponds to the crossing point. has z -directional Bloch vectors and its correlation vector changes from ( g$_{1}$, g$_{2}$, g$_{3}$ ) to ( − g$_{3}$, g$_{2}$, g$_{1}$ ). Similarly, one can change the state with y -directional Bloch vectors into the state with z -directional Bloch vectors without altering the diagonal property of the correla- tion term. In this reason it is reasonable to assume that the directions of the Bloch vectors are z -direction by writing r = (0 , 0 , r ) and s = (0 , 0 , s ) $^{4}$. In this case the arbitrary two-qubit 4 Even if r and s are not parallel with each other, one can make them to be z -directional via an appropriate local-unitary transformation. In this case, however, the correlation term loses its diagonal property. 8