| φ $^{′}$〉 = P | φ 〉 = 1 3 ( ν + λ 2 )[ − √$_{2 + 2}$√$_{6}$ 3 α$_{3}$ | η 0 $^{′}$〉 + α$_{2}$ | π $^{0}$〉 − $_{(}$√$_{2}$$_{α}$$_{1}$ + α$_{3}$ ) | η $^{0}$〉 ] (9) 5 Another more simpler case is P = ¯ I 8 for which the final state reads As we can see, by changing the value of ν and λ , the entanglement degree C$_{φ}$ ′ can be tuned. This behavior is shown in Fig. 2 for the case of α$_{1}$ = α$_{2}$ = 1 $_{2}$. C$_{φ}$ ′ = − ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ + √$_{2}$ 2 α$_{2}$ − √$_{6}$ 6 α$_{3}$ ) $^{2}$Log$_{3}$ ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ + √$_{2}$ 2 α$_{2}$ − √$_{6}$ 6 α$_{3}$ ) 2 − ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ + √$_{6}$ 3 α$_{3}$ ) $^{2}$Log$_{3}$ ( ν + λ 2 ) 2 $_{(}$√$_{3}$ 3 α$_{1}$ + √$_{6}$ 3 α$_{3}$ ) $^{2}$. (8) The normalizing condition leads to µ = λ 2 and ( ν + λ $_{2}$)$^{2}$[1 − $_{(}$√$_{3}$ 3 α$_{1}$ − √$_{2}$ 2 α$_{2}$ − √$_{6}$ 6 α$_{3}$ ) $^{2}$] = 1. As discussed in the preceding section, the entanglement degree of the final state | φ $^{′}$〉 can be calculated by the use of Eq.(2) as As we discussed before, the entanglement degree of final state can be tuned by changing the parameters of the transition operator. As an example, let us act the transition operator of P = ¯ V + + ¯ V − on the initial state in Eq.(1), the corresponding final state is | φ $^{′}$〉 = P | φ 〉 = ( ν + λ 2 $_{)[(}$√$_{3}$ 3 α$_{1}$ + √$_{2}$ 2 α$_{2}$ − √$_{6}$ 6 α$_{3}$ ) | K $^{+}$〉 $_{+ (}$√$_{3}$ 3 α$_{1}$ + √$_{6}$ 3 α$_{3}$ ) | K $^{−}$〉 ] . (7) III. OBTAINING DIFFERENT ENTANGLEMENT DEGREES BY TUNING TRANSITION OPERATORS FIG. 2: (color online). The entanglement degree of the final state | φ $^{′}$〉 varies with ν and λ when α$_{1}$ = α$_{2}$ = 1 $_{2}$. -1 0 1 Ν -1 0 1 Λ 0 0.2 0.4 0.6 C$_{Φ}$$_{'}$