{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:W3BRBC6C7BMKUJ26ROW3GKSQ6V","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":"41bba149e72c7a9418f203da5e74ea33021cbd3047b746cd89431fb6988c68e8","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-09-29T11:35:07Z","title_canon_sha256":"fb77f1c8c80643438e9beb9761bc0159f14c1d964b1a5d3fb03dbe7d20df0f9e"},"schema_version":"1.0","source":{"id":"quant-ph/0609229","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0609229","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0609229v2","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0609229","created_at":"2026-05-18T00:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"W3BRBC6C7BMK","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"W3BRBC6C7BMKUJ26","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"W3BRBC6C","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:1b97844b66cc0b8a8111b3a0779d6ea58d5e84b568903535d914fc3052cd900c","target":"graph","created_at":"2026-05-18T00:57:44Z","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 consider ergodic causal classical-quantum channels (cq-channels) which additionally have a decaying input memory. In the first part we develop some structural properties of ergodic cq-channels and provide equivalent conditions for ergodicity. In the second part we prove the coding theorem with weak converse for causal ergodic cq-channels with decaying input memory. Our proof is based on the possibility to introduce joint input-output state for the cq-channels and an application of the Shannon-McMillan theorem for ergodic quantum states. In the last part of the paper it is shown how this res","authors_text":"Holger Boche, Igor Bjelakovic","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-09-29T11:35:07Z","title":"Ergodic Classical-Quantum Channels: Structure and Coding Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0609229","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:e08a3e19fe8d413153d936ed1cf37def80f8252d35458d79c323d550585a9f12","target":"record","created_at":"2026-05-18T00:57:44Z","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":"41bba149e72c7a9418f203da5e74ea33021cbd3047b746cd89431fb6988c68e8","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-09-29T11:35:07Z","title_canon_sha256":"fb77f1c8c80643438e9beb9761bc0159f14c1d964b1a5d3fb03dbe7d20df0f9e"},"schema_version":"1.0","source":{"id":"quant-ph/0609229","kind":"arxiv","version":2}},"canonical_sha256":"b6c3108bc2f858aa275e8badb32a50f575d5aec21114dba361d05c1e2d4a6a8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6c3108bc2f858aa275e8badb32a50f575d5aec21114dba361d05c1e2d4a6a8c","first_computed_at":"2026-05-18T00:57:44.659801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:44.659801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HxHVXqfTojtg4+TCdQ7prE/hbIYLQH9Jr1YjH6GfNF04+xFdoDazr+bUiCLPQf00zyOxsvx+oHaQ0Vwn82NnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:44.660420Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0609229","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e08a3e19fe8d413153d936ed1cf37def80f8252d35458d79c323d550585a9f12","sha256:1b97844b66cc0b8a8111b3a0779d6ea58d5e84b568903535d914fc3052cd900c"],"state_sha256":"8d45517e2f5fd40d864acc3683bdf61f524415d4fedc909ad336f1a3c9020c27"}