Entanglement-assisted operator codeword stabilized quantum codes

Abstract

In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes (QECCs), including additive and nonadditive codes, based on the codeword stabilized (CWS) framework on subsystems. The CWS framework is a scheme to construct QECCs, including both additive and nonadditive codes, and gives a method to construct a QECC from a classical error-correcting code in standard form. Entangled pairs of qubits (ebits) can be used to improve capacity of quantum error correction. In addition, it gives a method to overcome the dual-containing constraint. Operator quantum error correction (OQEC) gives a general framework to construct QECCs. We construct OQEC codes with ebits based on the CWS framework. This new scheme, entanglement-assisted operator codeword stabilized (EAOCWS) quantum codes, is the most general framework we know of to construct both additive and nonadditive codes from classical error-correcting codes. We describe the formalism of our scheme, demonstrate the construction with examples, and give several EAOCWS codes.