The quantum hashing bound guarantees that rates up to $1-H(p_I, p_X, p_Y, p_Z)$ are achievable for memoryless Pauli channels, but it is not generally tight. A known way to improve achievable rates for certain asymmetric Pauli channels is to apply a small inner stabilizer code to a few channel uses, decode, and treat the resulting logical noise as an induced Pauli channel; reapplying the hashing argument to this induced channel can beat the baseline hashing bound. We generalize this induced-channel viewpoint to arbitrary stabilizer codes used purely as channel transforms. Given any $ [\![ n, k ]\!] $ stabilizer generator set, we construct a full symplectic tableau, compute the induced joint distribution of logical Pauli errors and syndromes under the physical Pauli channel, and obtain an achievable rate via a hashing bound with decoder side information. We perform a structured search over small transforms and report instances that improve the baseline hashing bound for a family of Pauli channels with skewed and independent errors studied in prior work.

翻译：量子哈希界保证了对于无记忆泡利信道，可达速率可达 $1-H(p_I, p_X, p_Y, p_Z)$，但该界通常并非紧界。对于某些非对称泡利信道，一种已知的提高可达速率的方法是：对少量信道使用应用一个小的内部稳定子码，进行解码，并将产生的逻辑噪声视为一个诱导泡利信道；将哈希论证重新应用于此诱导信道，可以超越基准哈希界。我们将这种诱导信道的观点推广到任意仅用作信道变换的稳定子码。给定任意 $ [\![ n, k ]\!] $ 稳定子生成元集，我们构造一个完整的辛表，计算在物理泡利信道下逻辑泡利错误与伴随式的联合诱导分布，并通过一个带有解码器边信息的哈希界获得一个可达速率。我们对小型变换进行了结构化搜索，并报告了针对先前工作中研究的具有偏斜且独立错误的泡利信道族，能够改进基准哈希界的实例。