Then the above expression is equal to the following: ( I ⊗ ⊗ A ) ( P i ⊗ ⊗ I ) | Φ Φ n + ⟩ = ( I ⊗ ⊗ A ) ( P i 2 ⊗ ⊗ I ) | Φ Φ n + ⟩ = ( I ⊗ ⊗ A ) ( P i ⊗ ⊗ P i T ) | Φ Φ n + ⟩ . Therefore, each of Alice's projectors P i projects Bob's qubits onto a subspace P i T corresponding to Alice's projected subspace P i . Alice restores her qubits to the simultaneous +1- eigenspace of the generators in S . She sends her measurement results to Bob. Bob measures the generators in S . Bob combines his measurements with Alice's to determine a syndrome for the error. He performs a recovery operation on his qubits to reverse the error. He restores his qubits S . Alice and Bob both perform the decoding unitary corresponding to stabilizer S to convert their k logical ebits to k physical ebits.