FIG. 3: (color online). The entanglement degree of the final state | φ $^{′}$〉 varies with ν and λ when α$_{1}$ = α$_{2}$ = 1 $_{2}$. with normalization condition µ = λ 2 and ( ν + λ $_{2}$) 2 $_{[1 + 3(}$√$_{3}$ 3 α$_{1}$ + √$_{6}$ 3 α$_{3}$ ) $^{2}$] = 3. Similarly, which also depends on ν and λ , as shown in Fig. 3. These two examples clearly shows that by tuning the parameters ν and λ of transition operators, the entanglement degree of final state varies between 0 and 1. However, there are exceptional cases in which the entanglement degree of final state is found to be the same as the initial state or be zero, independent with ν and λ , as is shown in the next section. IV. TWO EXCEPTIONAL CASES Although generally, transition operators with different ν and λ provide final states with different entanglement degrees, there do exist special cases in which the final state possesses the same entanglement degree with the initial state or the final state are totally disentangled. Both cases are very important in quantum information and quantum computation. 6 C$_{φ}$ ′ = − 1 9 ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ + √$_{2}$ 2 α$_{2}$ − √$_{6}$ 6 α$_{3}$ ) $^{2}$Log$_{3}$ 1 9 ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ + √$_{2}$ 2 α$_{2}$ − √$_{6}$ 6 α$_{3}$ ) 2 − 1 9 ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ − √$_{2}$ 2 α$_{2}$ − √$_{6}$ 6 α$_{3}$ ) $^{2}$Log$_{3}$ 1 9 ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ − √$_{2}$ 2 α$_{2}$ − √$_{6}$ 6 α$_{3}$ ) 2 − 4 9 ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ + √$_{6}$ 3 α$_{3}$ ) $^{2}$Log$_{3}$ 4 9 ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ + √$_{6}$ 3 α$_{3}$ ) $^{2}$, (10) -2 0 2 Ν -4 -2 0 2 4 Λ 0 0.25 0.5 0.75 1 C$_{Φ}$$_{'}$