We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms the receiver's share of a bipartite state that can be used for entanglement-assisted communications, both in the noiseless and noisy ebit error models. In the case of degenerate codes, we show that the receiver's share of the bipartite state can sometimes be compressed, at the cost of potentially reduced error-correction ability in the noisy ebit error model. We also give examples of permutation-invariant and XP-stabilizer entanglement-assisted codes, the first outside of the stabilizer and codeword-stabilized frameworks.

翻译：我们展示了如何通过将任意量子码与擦除信道量子码相关联来构建纠缠辅助码。若物理量子位的某个子集对于擦除错误是可纠正的，则该子集自然构成二分态的接收方份额，可用于纠缠辅助通信——无论对于无噪声还是有噪声的纠缠比特错误模型皆然。对于退化码，我们证明了二分态的接收方份额有时可被压缩，代价是在有噪声纠缠比特错误模型中可能降低纠错能力。我们还给出了置换不变码与XP稳定子纠缠辅助码的实例，这是首次在稳定子框架和码字稳定框架之外构建的纠缠辅助码。