We now substitute the above two equations above back into Eq. (4) and get | ⟨ ⟨ f ∣ ∣ g ⟩ ⟩ | 2 = ( 1 2 ⟨ ⟨ { A ^ ^ , B ^ ^ } ⟩ ⟩ − − ⟨ ⟨ A ^ ^ ⟩ ⟩ ⟨ ⟨ B ^ ^ ⟩ ⟩ ) 2 + ( 1 2 i ⟨ ⟨ [ A ^ ^ , B ^ ^ ] ⟩ ⟩ ) 2 .