{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:DILLPQKACK4VM3RQZUH2AGOHZ7","short_pith_number":"pith:DILLPQKA","canonical_record":{"source":{"id":"quant-ph/0608223","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-08-29T06:43:27Z","cross_cats_sorted":[],"title_canon_sha256":"5e8b63d550590f83a933a748ec3f35c8ef672252014ebf3afe574aa47d1c46e1","abstract_canon_sha256":"6efffdaafbbb1ae5dd51910f687a74dfc9f4bb2b7e3221eba60f02c1486cce9b"},"schema_version":"1.0"},"canonical_sha256":"1a16b7c14012b9566e30cd0fa019c7cfd8a9ec379450222b1117ca6ed3d10410","source":{"kind":"arxiv","id":"quant-ph/0608223","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0608223","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0608223v5","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0608223","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"DILLPQKACK4V","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DILLPQKACK4VM3RQ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DILLPQKA","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:DILLPQKACK4VM3RQZUH2AGOHZ7","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0608223","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-08-29T06:43:27Z","cross_cats_sorted":[],"title_canon_sha256":"5e8b63d550590f83a933a748ec3f35c8ef672252014ebf3afe574aa47d1c46e1","abstract_canon_sha256":"6efffdaafbbb1ae5dd51910f687a74dfc9f4bb2b7e3221eba60f02c1486cce9b"},"schema_version":"1.0"},"canonical_sha256":"1a16b7c14012b9566e30cd0fa019c7cfd8a9ec379450222b1117ca6ed3d10410","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:55.848003Z","signature_b64":"VV8nknT2D1bTj/jeB+3GjCv10vJfmfzCPNMEytEKNJN62wHl5FxRcclcsAeEQvCvPT4mB5Hc5bSLg1//uRKfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a16b7c14012b9566e30cd0fa019c7cfd8a9ec379450222b1117ca6ed3d10410","last_reissued_at":"2026-05-18T00:58:55.847265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:55.847265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0608223","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sk0N8Y7m0VVTQ88IXPmvJpeEzFi4gSIAspEmtMUg1ggP7zz9X6NNBWec5nafftNz1fCQlNdkhPGeura8n67SAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:57:12.701223Z"},"content_sha256":"efad62d97188e0bab9be48ab3a9b3601edd67a107e769396bf9fec089841ccc6","schema_version":"1.0","event_id":"sha256:efad62d97188e0bab9be48ab3a9b3601edd67a107e769396bf9fec089841ccc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:DILLPQKACK4VM3RQZUH2AGOHZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum network communication -- the butterfly and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andreas Winter, Debbie Leung, Jonathan Oppenheim","submitted_at":"2006-08-29T06:43:27Z","abstract_excerpt":"We study the k-pair communication problem for quantum information in networks of quantum channels. We consider the asymptotic rates of high fidelity quantum communication between specific sender-receiver pairs. Four scenarios of classical communication assistance (none, forward, backward, and two-way) are considered. (i) We obtain outer and inner bounds of the achievable rate regions in the most general directed networks. (ii) For two particular networks (including the butterfly network) routing is proved optimal, and the free assisting classical communication can at best be used to modify the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0608223","kind":"arxiv","version":5},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nro3dXa4FT7FKvJVu55xiJNtHt4umpTqXr3CtqMga3Ac/IKGUAYMrb04gpg0nUh7NXMuC6MpJ9q/5vrJZRZZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:57:12.701878Z"},"content_sha256":"f70837444881e5494268c12e437f6b9638761250793d2db28043ab535fe80152","schema_version":"1.0","event_id":"sha256:f70837444881e5494268c12e437f6b9638761250793d2db28043ab535fe80152"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DILLPQKACK4VM3RQZUH2AGOHZ7/bundle.json","state_url":"https://pith.science/pith/DILLPQKACK4VM3RQZUH2AGOHZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DILLPQKACK4VM3RQZUH2AGOHZ7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T13:57:12Z","links":{"resolver":"https://pith.science/pith/DILLPQKACK4VM3RQZUH2AGOHZ7","bundle":"https://pith.science/pith/DILLPQKACK4VM3RQZUH2AGOHZ7/bundle.json","state":"https://pith.science/pith/DILLPQKACK4VM3RQZUH2AGOHZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DILLPQKACK4VM3RQZUH2AGOHZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:DILLPQKACK4VM3RQZUH2AGOHZ7","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":"6efffdaafbbb1ae5dd51910f687a74dfc9f4bb2b7e3221eba60f02c1486cce9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-08-29T06:43:27Z","title_canon_sha256":"5e8b63d550590f83a933a748ec3f35c8ef672252014ebf3afe574aa47d1c46e1"},"schema_version":"1.0","source":{"id":"quant-ph/0608223","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0608223","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0608223v5","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0608223","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"DILLPQKACK4V","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"DILLPQKACK4VM3RQ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"DILLPQKA","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f70837444881e5494268c12e437f6b9638761250793d2db28043ab535fe80152","target":"graph","created_at":"2026-05-18T00:58:55Z","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 the k-pair communication problem for quantum information in networks of quantum channels. We consider the asymptotic rates of high fidelity quantum communication between specific sender-receiver pairs. Four scenarios of classical communication assistance (none, forward, backward, and two-way) are considered. (i) We obtain outer and inner bounds of the achievable rate regions in the most general directed networks. (ii) For two particular networks (including the butterfly network) routing is proved optimal, and the free assisting classical communication can at best be used to modify the","authors_text":"Andreas Winter, Debbie Leung, Jonathan Oppenheim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-08-29T06:43:27Z","title":"Quantum network communication -- the butterfly and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0608223","kind":"arxiv","version":5},"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:efad62d97188e0bab9be48ab3a9b3601edd67a107e769396bf9fec089841ccc6","target":"record","created_at":"2026-05-18T00:58:55Z","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":"6efffdaafbbb1ae5dd51910f687a74dfc9f4bb2b7e3221eba60f02c1486cce9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2006-08-29T06:43:27Z","title_canon_sha256":"5e8b63d550590f83a933a748ec3f35c8ef672252014ebf3afe574aa47d1c46e1"},"schema_version":"1.0","source":{"id":"quant-ph/0608223","kind":"arxiv","version":5}},"canonical_sha256":"1a16b7c14012b9566e30cd0fa019c7cfd8a9ec379450222b1117ca6ed3d10410","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a16b7c14012b9566e30cd0fa019c7cfd8a9ec379450222b1117ca6ed3d10410","first_computed_at":"2026-05-18T00:58:55.847265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:55.847265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VV8nknT2D1bTj/jeB+3GjCv10vJfmfzCPNMEytEKNJN62wHl5FxRcclcsAeEQvCvPT4mB5Hc5bSLg1//uRKfCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:55.848003Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0608223","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efad62d97188e0bab9be48ab3a9b3601edd67a107e769396bf9fec089841ccc6","sha256:f70837444881e5494268c12e437f6b9638761250793d2db28043ab535fe80152"],"state_sha256":"cabfb43cc77a7f2cc222ca0d648d72e9344ee012e69a12363aefefc9d320c26d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Rs/XLpYaUrg4Q/Y4qmVvsUP80IgiIcLJ/EJg8mGLWUD0ryHmfP46VCYIuMvxDHjDCx0ZhwrS6jWWwAcmP3EBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:57:12.705565Z","bundle_sha256":"e67d49409a7e8c24930bbf2667fffb8ee3b4cbfe5aadfcd45e85cfc6ec703c0d"}}