{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:63SN6AA3J2PBFYJJUC46PJL6S2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2a58900bbdd10fed4d94bd9f4acbcc7282d65ecd5dd3a27dbae240e1fe992df5","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-04-19T11:50:25Z","title_canon_sha256":"6f72aacbdba5d3dfab5bb4a3ca4e703950a6aa38f98f8f988650d20464fee322"},"schema_version":"1.0","source":{"id":"1704.05703","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05703","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05703v2","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05703","created_at":"2026-05-17T23:47:12Z"},{"alias_kind":"pith_short_12","alias_value":"63SN6AA3J2PB","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"63SN6AA3J2PBFYJJ","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"63SN6AA3","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:7afaa37e94f5e20458524fdc41b17d8280b2edce1ba97ceb829a937d9c2caa10","target":"graph","created_at":"2026-05-17T23:47:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study lower bounds on the optimal error probability in classical coding over classical-quantum channels at rates below the capacity, commonly termed quantum sphere-packing bounds. Winter and Dalai have derived such bounds for classical-quantum channels; however, the exponents in their bounds only coincide when the channel is classical. In this paper, we show that these two exponents admit a variational representation and are related by the Golden-Thompson inequality, reaffirming that Dalai's expression is stronger in general classical-quantum channels. Second, we establish a sphere-packing ","authors_text":"Hao-Chung Cheng, Marco Tomamichel, Min-Hsiu Hsieh","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-04-19T11:50:25Z","title":"Quantum Sphere-Packing Bounds with Polynomial Prefactors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05703","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b0befd0b6e422d4c4f43343f5f2a67cd4ff907252bce077775b831d8756da754","target":"record","created_at":"2026-05-17T23:47:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2a58900bbdd10fed4d94bd9f4acbcc7282d65ecd5dd3a27dbae240e1fe992df5","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-04-19T11:50:25Z","title_canon_sha256":"6f72aacbdba5d3dfab5bb4a3ca4e703950a6aa38f98f8f988650d20464fee322"},"schema_version":"1.0","source":{"id":"1704.05703","kind":"arxiv","version":2}},"canonical_sha256":"f6e4df001b4e9e12e129a0b9e7a57e969077af894861a4a9800f62975824933f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e4df001b4e9e12e129a0b9e7a57e969077af894861a4a9800f62975824933f","first_computed_at":"2026-05-17T23:47:12.874696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:12.874696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lnrxLttEGh/SW+xETmgBha+A/ABzkZvrgFvDDC51NQuZ7r+eFJRZfMlm1MCijd0bYoeJLrT+u3WDMEvI63TECA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:12.875068Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05703","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0befd0b6e422d4c4f43343f5f2a67cd4ff907252bce077775b831d8756da754","sha256:7afaa37e94f5e20458524fdc41b17d8280b2edce1ba97ceb829a937d9c2caa10"],"state_sha256":"6096b49e392090b105a5b9f9f604e88de22e86fe42a37b2b029c8be8b80dd73b"}