Entanglement-assisted codeword stabilized quantum codes

Entangled qubits can increase the capacity of quantum error-correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the dual-containing constraint. We show that it is possible to construct both additive and nonadditive quantum codes using the codeword stabilized quantum code framework. Nonadditive codes may offer improved performance over the more common stabilizer codes. Like other entanglement-assisted codes, the encoding procedure acts only on the qubits on Alice's side, and only these qubits are assumed to pass through the channel. However, errors in the codeword stabilized quantum code framework give rise to effective Z errors on Bob's side. We use this scheme to construct entanglement-assisted nonadditive quantum codes, in particular, ((5,16,2;1)) and ((7,4,5;4)) codes.