state ρ defined in Eq.(2.3) with g = ( q$_{1}$, q$_{2}$, q$_{3}$ ) reduces to ρ = 1 4    1 + r + s + q$_{3}$ 0 0 q$_{1}$ − q$_{2}$ 0 1 + r − s − q$_{3}$ q$_{1}$ + q$_{2}$ 0 0 q$_{1}$ + q$_{2}$ 1 − r + s − q$_{3}$ 0 q$_{1}$ − q$_{2}$ 0 0 1 − r − s + q$_{3}$   $^{.}$ (3.1) FIG. 3: The deformation of T is plotted when r = s = 0 . 3 (Fig. 3a), r = − s = 0 . 3 (Fig. 3b), r = s = 0 . 5 (Fig. 3c) and r = − s = 0 . 5 (Fig. 3d). For comparison we plot T together. The appearance of non-zero Bloch vectors generally shrink the tetrahedron. The shrinking rate becomes larger with increasing the norm of the Bloch vectors. The eigenvalues and eigenvectors of ρ are summarized at Table I. eigenvalues of ρ eigenvectors of ρ µ$_{±}$ = 1 4 { (1 − q$_{3}$ ) ± M$_{1}$ } | µ$_{±}$ 〉 = 1 Λ ± [( q$_{1}$ + q$_{2}$ ) | 01 〉 − { ( r − s ) ∓ M$_{1}$ } | 10 〉 ] ν$_{±}$ = 1 4 { (1 + q$_{3}$ ) ± M$_{2}$ } | ν$_{±}$ 〉 = 1 Δ ± [( q$_{1}$ − q$_{2}$ ) | 00 〉 − { ( r + s ) ∓ M$_{2}$ } | 11 〉 ] Table I: Eigenvalues and Eigenvectors of ρ in Eq.(3.1) At Table I M$_{1}$ , M$_{2}$ , Λ$_{±}$ and Δ$_{±}$ are given by M$_{1}$ = √ ( r − s ) 2 + ( q$_{1}$ + q$_{2}$ ) 2 M$_{2}$ = √ ( r + s ) 2 + ( q$_{1}$ − q$_{2}$ ) 2 (3.2) Λ$_{±}$ = { ( r − s ) ∓ M$_{1}$ } 2 + ( q$_{1}$ + q$_{2}$ ) 2 Δ$_{±}$ = √ { ( r + s ) ∓ M$_{2}$ } 2 + ( q$_{1}$ − q$_{2}$ ) $^{2}$. min( µ$_{−}$, ν$_{−}$ ) = 0 . (3.3) Then, the deformation of T can be obtained from the positivity condition of ρ . Since deformation should be a set of the boundary states, the condition of the deformation becomes One can make two surfaces by making use of Eq.(3.3). Each surface corresponds to min( µ$_{−}$, ν$_{−}$ ) = µ$_{−}$ = 0 or min( µ$_{−}$, ν$_{−}$ ) = ν$_{−}$ = 0. Gluing these surfaces together yields the deformation of T . In Fig. 3 we plot the deformation of T when r = s = 0 . 3 (Fig. 3a), r = − s = 0 . 3 (Fig. 3b), r = s = 0 . 5 (Fig. 3c) and r = − s = 0 . 5 (Fig. 3d). For comparison we plot T together. 9