{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:5KEMEIXQ67SCJMES2YMV4YBVPS","short_pith_number":"pith:5KEMEIXQ","schema_version":"1.0","canonical_sha256":"ea88c222f0f7e424b092d6195e60357c899505dd99375d9fbbf208e979bcebac","source":{"kind":"arxiv","id":"1701.02957","version":2},"attestation_state":"computed","paper":{"title":"Sphere-Packing Bound for Symmetric Classical-Quantum Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Hao-Chung Cheng, Marco Tomamichel, Min-Hsiu Hsieh","submitted_at":"2017-01-11T12:59:53Z","abstract_excerpt":"We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of the subexponential to the polynomial. The established pre-factor is essentially optimal because it matches the best known random coding upper bound in the classical case. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.02957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-01-11T12:59:53Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"b88d8008201edd9e270c174ae79d69d17b5173f17228bd5996ae5b4a6d1b1c9a","abstract_canon_sha256":"e5d22fa53b882f572b37f2e82632f5d794675a0b15e5cf978d38dc929ff5885d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:48.995999Z","signature_b64":"G1Oa7B5iUpJnI+2LWVLPot/ZuoBtiGN6JW2gFQdu6DtmErOBDZ45iYIdSIiT/9pInOFbQLYIpQP72UohuuHnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea88c222f0f7e424b092d6195e60357c899505dd99375d9fbbf208e979bcebac","last_reissued_at":"2026-05-18T00:52:48.995359Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:48.995359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sphere-Packing Bound for Symmetric Classical-Quantum Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Hao-Chung Cheng, Marco Tomamichel, Min-Hsiu Hsieh","submitted_at":"2017-01-11T12:59:53Z","abstract_excerpt":"We provide a sphere-packing lower bound for the optimal error probability in finite blocklengths when coding over a symmetric classical-quantum channel. Our result shows that the pre-factor can be significantly improved from the order of the subexponential to the polynomial. The established pre-factor is essentially optimal because it matches the best known random coding upper bound in the classical case. Our approaches rely on a sharp concentration inequality in strong large deviation theory and crucial properties of the error-exponent function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02957","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.02957","created_at":"2026-05-18T00:52:48.995446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.02957v2","created_at":"2026-05-18T00:52:48.995446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02957","created_at":"2026-05-18T00:52:48.995446+00:00"},{"alias_kind":"pith_short_12","alias_value":"5KEMEIXQ67SC","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5KEMEIXQ67SCJMES","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5KEMEIXQ","created_at":"2026-05-18T12:31:00.734936+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS","json":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS.json","graph_json":"https://pith.science/api/pith-number/5KEMEIXQ67SCJMES2YMV4YBVPS/graph.json","events_json":"https://pith.science/api/pith-number/5KEMEIXQ67SCJMES2YMV4YBVPS/events.json","paper":"https://pith.science/paper/5KEMEIXQ"},"agent_actions":{"view_html":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS","download_json":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS.json","view_paper":"https://pith.science/paper/5KEMEIXQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.02957&json=true","fetch_graph":"https://pith.science/api/pith-number/5KEMEIXQ67SCJMES2YMV4YBVPS/graph.json","fetch_events":"https://pith.science/api/pith-number/5KEMEIXQ67SCJMES2YMV4YBVPS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS/action/storage_attestation","attest_author":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS/action/author_attestation","sign_citation":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS/action/citation_signature","submit_replication":"https://pith.science/pith/5KEMEIXQ67SCJMES2YMV4YBVPS/action/replication_record"}},"created_at":"2026-05-18T00:52:48.995446+00:00","updated_at":"2026-05-18T00:52:48.995446+00:00"}