At Table II M Γ 1 , M Γ 2 , Λ Γ ± and Δ Γ ± are defined as Then L r,s can be obtained from the positivity condition of ρ $^{Γ}$. Since, furthermore, L r,s should be a set of the edge states, the condition for the deformation of L reduces to As deformation of T Eq.(3.7) generates two surfaces, each of which corresponds to min ( µ Γ $_{−}$, ν Γ − ) = µ Γ − = 0 or min ( µ Γ $_{−}$, ν Γ − ) = ν Γ − = 0. Gluing these two surfaces one can make the deformation of L . In Fig. 4 we plot the deformation of L at r = s = 0 . 3 (Fig. 4a), r = − s = 0 . 3 (Fig. 4b), r = s = 0 . 5 (Fig. 4c) and r = − s = 0 . 5 (Fig. 4d). For comparison we plot L together. Like the deformation of T , Fig. 4 indicates that the effect of the non-zero Bloch vectors is to shrink L toward a particular direction. Fig. 4 also shows that the shrinking rate becomes larger and larger with increasing the norm of the Bloch vectors. Like T r,s again, the deformation of the octahedron L r,s also has smooth surfaces while L has sharp edges. In this section we show how to derive the CSS for the Vedral-Plenio (VP) states. The VP states are defined as mixture of one Bell state and separable states, which are not orthogonal to the Bell state. One but most general example of the VP state is where | β$_{1}$ 〉 = (1 $_{/}$√$_{2)(}$ | 00 〉 + | 11 〉 ) and λ$_{1}$ + λ$_{2}$ + λ$_{3}$ = 1. Let the arbitrary VP state be IV. CSS FOR THE GENERALIZED VEDRAL-PLENIO STATES M Γ 1 = M$_{1}$ ∣ q 2 →− q 2 = √ ( r − s ) 2 + ( q$_{1}$ − q$_{2}$ ) 2 (3.6) M Γ 2 = M$_{2}$ ∣ q 2 →− q 2 = ( r + s ) 2 + ( q$_{1}$ + q$_{2}$ ) 2 Λ Γ ± = √ { ( r − s ) ∓ M Γ 1 } 2 + ( q$_{1}$ − q$_{2}$ ) 2 Δ Γ ± = √ { ( r + s ) ∓ M Γ 2 } 2 + ( q$_{1}$ + q$_{2}$ ) $^{2}$. min ( µ Γ $_{−}$, ν Γ − ) = 0 . (3.7) ρ$_{vp}$ = λ$_{1}$ | β$_{1}$ 〉〈 β$_{1}$ | + λ$_{2}$ | 00 〉〈 00 | + λ$_{3}$ | 11 〉〈 11 | , (4.1) ρ$_{vp}$ = 1 4 ( I ⊗ I + r$_{vp}$ · σ ⊗ I + I ⊗ s$_{vp}$ · σ + 3 ∑ n =1 ( t$_{vp}$ )$_{n}$ σ$_{n}$ ⊗ σ$_{n}$ ) (4.2) 11