on Bob’s c qubits. A set of generators of a stabilizer group S of the encoded state ( U$_{E}$ ⊗ I ) | ψ 〉 EA is { g$_{1}$, · · · , g$_{r}$, h$_{1}$, · · · , h$_{c}$ } , where and The logical operators on ( U$_{E}$ ⊗ I ) | ψ 〉 EA are and The 2 $^{k}$− dimensional subspace of the ( n + c ) − qubit state space fixed by the stabilizer group S with a set of generators { g$_{1}$, · · · , g$_{r}$, h$_{1}$, · · · , h$_{c}$ } is called an entanglement-assisted quantum error-correcting (EAQEC) code with parameters [[ n, k, d ; c ]] for some minimum distance d . With the help of c pairs of maximally-entangled states, the stabilizer group of an [[ n, k, d ; c ]] EAQEC code has c more generators than that of an [[ n, k, d ]] standard quantum stabilizer code. The operators on Bob’s side have no direct effect on the error- correcting ability of the EAQEC code if we assume that the c qubits of Bob suffer no error. These operators serve to make the stabilizer abelian, so that the generators can be measured simultaneously. For convenience, we denote 10 g ′ i = U$_{E}$Z$_{i}$U † $_{E}$, ¯ X$_{1}$ = U$_{E}$X$_{r}$$_{+1}$U † E ⊗ I, · · · , ¯ X$_{k}$ = U$_{E}$X$_{n}$U † E ⊗ I. ¯ Z$_{1}$ = U$_{E}$Z$_{r}$$_{+1}$U † E ⊗ I, · · · , ¯ Z$_{k}$ = U$_{E}$Z$_{n}$U † E ⊗ I, h$_{j}$ = U$_{E}$X$_{t}$$_{j}$U † E ⊗ X$_{j}$. g$_{i}$ =     U$_{E}$Z$_{i}$U † E ⊗ I, if i / ∈ T ; U$_{E}$Z$_{i}$U † E ⊗ Z$_{j}$, if i = t$_{j}$ ∈ T