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

General quantum error-correcting code with entanglement based on codeword stabilized quantum code