A one-way stabilizer entanglement distillation protocol uses a stabilizer code for the distillation procedure. Suppose the stabilizer S for an [ n , k ] quantum error-correcting code has generators g 1 , … … , g n − − k . The distillation procedure begins with Alice measuring the n − − k generators in S . Let { P i } be the set of the 2 n − − k projectors that project onto the 2 n − − k orthogonal subspaces corresponding to the generators in S . The measurement projects | Φ Φ n + ⟩ randomly onto one of the i subspaces. Each P i commutes with the noisy operator A on Bob's side so that ( P i ⊗ ⊗ I ) ( I ⊗ ⊗ A ) | Φ Φ n + ⟩ = ( I ⊗ ⊗ A ) ( P i ⊗ ⊗ I ) | Φ Φ n + ⟩ .