{"paper":{"title":"Stabilizer-Code Channel Transforms Beyond Repetition Codes for Improved Hashing Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Any stabilizer code can improve hashing rates on asymmetric Pauli channels by acting as a channel transform.","cross_cats":["math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Matthieu R. Bloch, Ruediger Urbanke, Shrinivas Kudekar, Tyler Kann","submitted_at":"2026-01-21T22:24:46Z","abstract_excerpt":"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 "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The induced logical channel after inner decoding can be treated as memoryless for re-applying the hashing bound, with the joint error-syndrome distribution accurately capturing all relevant statistics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Arbitrary small stabilizer codes used as channel transforms improve hashing bounds for Pauli channels beyond repetition codes via induced logical noise distributions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Any stabilizer code can improve hashing rates on asymmetric Pauli channels by acting as a channel transform.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"46f19dddaa43a468ee059bcbb693055d677b8bd36f7c1fa8fe0979ccf0570c52"},"source":{"id":"2601.15505","kind":"arxiv","version":3},"verdict":{"id":"b24abcac-d4c4-4fcc-8ac4-e2136268c8ae","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T11:38:55.932829Z","strongest_claim":"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.","one_line_summary":"Arbitrary small stabilizer codes used as channel transforms improve hashing bounds for Pauli channels beyond repetition codes via induced logical noise distributions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The induced logical channel after inner decoding can be treated as memoryless for re-applying the hashing bound, with the joint error-syndrome distribution accurately capturing all relevant statistics.","pith_extraction_headline":"Any stabilizer code can improve hashing rates on asymmetric Pauli channels by acting as a channel transform."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}