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，高达 $1-H(p_I, p_X, p_Y, p_Z)$ 的速率是可实现的，但该界通常并不紧致。对于某些非对称泡利信道，一种已知的提高可实现速率的方法是：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，计算物理泡利信道下逻辑泡利错误与校验子的联合诱导分布，并通过带有解码器边信息的哈希界获得一个可实现速率。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一类泡利信道，能够改进基准哈希界的实例。