{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XZ6U3OYNUWCCQCZSH6WCLCYCKQ","short_pith_number":"pith:XZ6U3OYN","canonical_record":{"source":{"id":"1608.04305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-15T15:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"6bf6dfd66737a4f2e8d4f565a47fd75a797d1be9b2a066e8c6839df8cb5011dc","abstract_canon_sha256":"88e8e106c660807aabb2402f22c7ca9150bc618f6be8bed6d8677906b1d7de9b"},"schema_version":"1.0"},"canonical_sha256":"be7d4dbb0da584280b323fac258b02543a2864d57fd06db755268483ea02e891","source":{"kind":"arxiv","id":"1608.04305","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04305","created_at":"2026-05-18T00:45:34Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04305v2","created_at":"2026-05-18T00:45:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04305","created_at":"2026-05-18T00:45:34Z"},{"alias_kind":"pith_short_12","alias_value":"XZ6U3OYNUWCC","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XZ6U3OYNUWCCQCZS","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XZ6U3OYN","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XZ6U3OYNUWCCQCZSH6WCLCYCKQ","target":"record","payload":{"canonical_record":{"source":{"id":"1608.04305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-15T15:29:17Z","cross_cats_sorted":[],"title_canon_sha256":"6bf6dfd66737a4f2e8d4f565a47fd75a797d1be9b2a066e8c6839df8cb5011dc","abstract_canon_sha256":"88e8e106c660807aabb2402f22c7ca9150bc618f6be8bed6d8677906b1d7de9b"},"schema_version":"1.0"},"canonical_sha256":"be7d4dbb0da584280b323fac258b02543a2864d57fd06db755268483ea02e891","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:34.684941Z","signature_b64":"2WQ1ACo+eprUXD5jARNE4j7xQPojDlujQsIltY8XlVvstzdDkkH+PFhIg4gDD5QTP+L36/omnPOQy7fzzW9ZDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be7d4dbb0da584280b323fac258b02543a2864d57fd06db755268483ea02e891","last_reissued_at":"2026-05-18T00:45:34.684075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:34.684075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.04305","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWqQ0SJDl8Z0rax4ndHb05ReAVkp6RZrEmg1i1jW5lrWlDSBGtrPNtFq/1ejwiZcHe/ZhziZXqvXypaF3DhjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:43:26.218958Z"},"content_sha256":"62dea8367a49d3a087ad2fd0579d2f0c609f3f8b78f642d0d0b85d15594a2274","schema_version":"1.0","event_id":"sha256:62dea8367a49d3a087ad2fd0579d2f0c609f3f8b78f642d0d0b85d15594a2274"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XZ6U3OYNUWCCQCZSH6WCLCYCKQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On quantum additive Gaussian noise channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Martin Idel, Robert Koenig","submitted_at":"2016-08-15T15:29:17Z","abstract_excerpt":"We give necessary and sufficient conditions for a Gaussian quantum channel to have a dilation involving a passive, i.e., number-preserving unitary. We then establish a normal form of such channels: any passively dilatable channel is the result of applying passive unitaries to the input and output of a Gaussian additive channel. The latter combine the state of the system with that of the environment by means of a multi-mode beamsplitter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04305","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eh0JS0OudUjbI3fLsQUe9BwCSING3mKaH7Av/aOzxS6VLPPAZ7QclKs0ycZuNPAOqfnS+RWAB0+zTzKJJpgYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:43:26.219332Z"},"content_sha256":"1f94b1d633db89a55baafee16dd2f4d75ff5dfd195c7d2c67d236154f4f0472e","schema_version":"1.0","event_id":"sha256:1f94b1d633db89a55baafee16dd2f4d75ff5dfd195c7d2c67d236154f4f0472e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZ6U3OYNUWCCQCZSH6WCLCYCKQ/bundle.json","state_url":"https://pith.science/pith/XZ6U3OYNUWCCQCZSH6WCLCYCKQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZ6U3OYNUWCCQCZSH6WCLCYCKQ/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":"2026-06-02T21:43:26Z","links":{"resolver":"https://pith.science/pith/XZ6U3OYNUWCCQCZSH6WCLCYCKQ","bundle":"https://pith.science/pith/XZ6U3OYNUWCCQCZSH6WCLCYCKQ/bundle.json","state":"https://pith.science/pith/XZ6U3OYNUWCCQCZSH6WCLCYCKQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZ6U3OYNUWCCQCZSH6WCLCYCKQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XZ6U3OYNUWCCQCZSH6WCLCYCKQ","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":"88e8e106c660807aabb2402f22c7ca9150bc618f6be8bed6d8677906b1d7de9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-15T15:29:17Z","title_canon_sha256":"6bf6dfd66737a4f2e8d4f565a47fd75a797d1be9b2a066e8c6839df8cb5011dc"},"schema_version":"1.0","source":{"id":"1608.04305","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04305","created_at":"2026-05-18T00:45:34Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04305v2","created_at":"2026-05-18T00:45:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04305","created_at":"2026-05-18T00:45:34Z"},{"alias_kind":"pith_short_12","alias_value":"XZ6U3OYNUWCC","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XZ6U3OYNUWCCQCZS","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XZ6U3OYN","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:1f94b1d633db89a55baafee16dd2f4d75ff5dfd195c7d2c67d236154f4f0472e","target":"graph","created_at":"2026-05-18T00:45:34Z","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 give necessary and sufficient conditions for a Gaussian quantum channel to have a dilation involving a passive, i.e., number-preserving unitary. We then establish a normal form of such channels: any passively dilatable channel is the result of applying passive unitaries to the input and output of a Gaussian additive channel. The latter combine the state of the system with that of the environment by means of a multi-mode beamsplitter.","authors_text":"Martin Idel, Robert Koenig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-15T15:29:17Z","title":"On quantum additive Gaussian noise channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04305","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":"sha256:62dea8367a49d3a087ad2fd0579d2f0c609f3f8b78f642d0d0b85d15594a2274","target":"record","created_at":"2026-05-18T00:45:34Z","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":"88e8e106c660807aabb2402f22c7ca9150bc618f6be8bed6d8677906b1d7de9b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-08-15T15:29:17Z","title_canon_sha256":"6bf6dfd66737a4f2e8d4f565a47fd75a797d1be9b2a066e8c6839df8cb5011dc"},"schema_version":"1.0","source":{"id":"1608.04305","kind":"arxiv","version":2}},"canonical_sha256":"be7d4dbb0da584280b323fac258b02543a2864d57fd06db755268483ea02e891","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be7d4dbb0da584280b323fac258b02543a2864d57fd06db755268483ea02e891","first_computed_at":"2026-05-18T00:45:34.684075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:34.684075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2WQ1ACo+eprUXD5jARNE4j7xQPojDlujQsIltY8XlVvstzdDkkH+PFhIg4gDD5QTP+L36/omnPOQy7fzzW9ZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:34.684941Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04305","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62dea8367a49d3a087ad2fd0579d2f0c609f3f8b78f642d0d0b85d15594a2274","sha256:1f94b1d633db89a55baafee16dd2f4d75ff5dfd195c7d2c67d236154f4f0472e"],"state_sha256":"e708b1ab98253456a12842fab017340010226fe154a6fd55d780d939a9b3acf9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/5nzIjRPzkoHRHC31odJNME6BWeLouPjTY54y7zKMqWMdNPrwNzgId911ehXG3QEzxJ8hJbnjwUxxvM6YQr/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:43:26.221335Z","bundle_sha256":"628128acc62b498f3b189b6bd89874ae22cc486ec94a9c1152d188ba682a7933"}}