For a mixed state ρ, after obtaining an eigenvalue a n in a discrete, nondegenerate spectrum of the corresponding observable A , the updated state is given by ρ ρ ′ = P n ρ ρ P n † † tr ⁡ ⁡ ( P n ρ ρ P n † † ) . If the eigenvalue a n has degenerate, orthonormal eigenvectors { | a n 1 ⟩ ⟩ , | a n 2 ⟩ ⟩ , … … , | a n m ⟩ ⟩ } , then the projection operator onto the eigensubspace is P n = | a n 1 ⟩ ⟩ ⟨ ⟨ a n 1 | + | a n 2 ⟩ ⟩ ⟨ ⟨ a n 2 | + ⋯ ⋯ + | a n m ⟩ ⟩ ⟨ ⟨ a n m | .