{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UVFCGJE7XUT45HUB3NJBL5XMKA","short_pith_number":"pith:UVFCGJE7","canonical_record":{"source":{"id":"1610.04634","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-14T20:48:05Z","cross_cats_sorted":[],"title_canon_sha256":"ada3a9dd6b1fb947242b407a2d84711e647e5c1d9688c0d60479c41ce7364d6d","abstract_canon_sha256":"bbe8153eceea181a15f48c5565ae39f1eb4fcd1a637f6336f6a847996370633f"},"schema_version":"1.0"},"canonical_sha256":"a54a23249fbd27ce9e81db5215f6ec503bea79436552f77376cc37602122a5da","source":{"kind":"arxiv","id":"1610.04634","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04634","created_at":"2026-05-18T00:52:38Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04634v1","created_at":"2026-05-18T00:52:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04634","created_at":"2026-05-18T00:52:38Z"},{"alias_kind":"pith_short_12","alias_value":"UVFCGJE7XUT4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UVFCGJE7XUT45HUB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UVFCGJE7","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UVFCGJE7XUT45HUB3NJBL5XMKA","target":"record","payload":{"canonical_record":{"source":{"id":"1610.04634","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-14T20:48:05Z","cross_cats_sorted":[],"title_canon_sha256":"ada3a9dd6b1fb947242b407a2d84711e647e5c1d9688c0d60479c41ce7364d6d","abstract_canon_sha256":"bbe8153eceea181a15f48c5565ae39f1eb4fcd1a637f6336f6a847996370633f"},"schema_version":"1.0"},"canonical_sha256":"a54a23249fbd27ce9e81db5215f6ec503bea79436552f77376cc37602122a5da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:38.358219Z","signature_b64":"opNYCTTa9No4P2KwfqDsirqqVtXH0g3oRZf4UxPwayhdvhe58WploaAIe78Kz9pZxdtozD0+Iwuiug5WAR08DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a54a23249fbd27ce9e81db5215f6ec503bea79436552f77376cc37602122a5da","last_reissued_at":"2026-05-18T00:52:38.357789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:38.357789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.04634","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LONRSz+SkvO08p1h52kIX1Em3kGNT0dVBvq7Dpu52TG464xD2VzS3Z0EmX3SICjDbpOxFCxWhYfdqE2ujzw/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:12:12.994999Z"},"content_sha256":"c559292ed428f5a8a4eb0546ba48dd51393763bc2c052448bf50f2a5b3e53f55","schema_version":"1.0","event_id":"sha256:c559292ed428f5a8a4eb0546ba48dd51393763bc2c052448bf50f2a5b3e53f55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UVFCGJE7XUT45HUB3NJBL5XMKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor power of dynamical maps and P- vs. CP-divisibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dariusz Chru\\'sci\\'nski, Fabio Benatti, Sergey Filippov","submitted_at":"2016-10-14T20:48:05Z","abstract_excerpt":"The are several non-equivalent notions of Markovian quantum evolution. In this paper we show that the one based on the so-called CP-divisibility of the corresponding dynamical map enjoys the following stability property: the dynamical map $\\Lambda_t$ is CP-divisible iff the second tensor power $\\Lambda_t\\otimes\\Lambda_t$ is CP-divisible as well. Moreover, the P-divisibility of the map $\\Lambda_t\\otimes\\Lambda_t$ is equivalent to the CP-divisibility of the map $\\Lambda_t$. Interestingly, the latter property is no longer true if we replace the P-divisibility of $\\Lambda_t\\otimes\\Lambda_t$ by sim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04634","kind":"arxiv","version":1},"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":"2026-05-18T00:52:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7tSfOtHtkTyjo27/ZfPx1dbF2zMtdYBsPKc68IbkqKKg+BM02M5VPzjuYKZhUAqBU6he6vveOPuLWC/7G2iAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T13:12:12.995467Z"},"content_sha256":"73a4ad16c4800ced73e0b2828376af25616ff591d97f886be65dfec3ba75bf6e","schema_version":"1.0","event_id":"sha256:73a4ad16c4800ced73e0b2828376af25616ff591d97f886be65dfec3ba75bf6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UVFCGJE7XUT45HUB3NJBL5XMKA/bundle.json","state_url":"https://pith.science/pith/UVFCGJE7XUT45HUB3NJBL5XMKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UVFCGJE7XUT45HUB3NJBL5XMKA/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":"2026-05-26T13:12:12Z","links":{"resolver":"https://pith.science/pith/UVFCGJE7XUT45HUB3NJBL5XMKA","bundle":"https://pith.science/pith/UVFCGJE7XUT45HUB3NJBL5XMKA/bundle.json","state":"https://pith.science/pith/UVFCGJE7XUT45HUB3NJBL5XMKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UVFCGJE7XUT45HUB3NJBL5XMKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UVFCGJE7XUT45HUB3NJBL5XMKA","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":"bbe8153eceea181a15f48c5565ae39f1eb4fcd1a637f6336f6a847996370633f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-14T20:48:05Z","title_canon_sha256":"ada3a9dd6b1fb947242b407a2d84711e647e5c1d9688c0d60479c41ce7364d6d"},"schema_version":"1.0","source":{"id":"1610.04634","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.04634","created_at":"2026-05-18T00:52:38Z"},{"alias_kind":"arxiv_version","alias_value":"1610.04634v1","created_at":"2026-05-18T00:52:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.04634","created_at":"2026-05-18T00:52:38Z"},{"alias_kind":"pith_short_12","alias_value":"UVFCGJE7XUT4","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UVFCGJE7XUT45HUB","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UVFCGJE7","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:73a4ad16c4800ced73e0b2828376af25616ff591d97f886be65dfec3ba75bf6e","target":"graph","created_at":"2026-05-18T00:52:38Z","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":"The are several non-equivalent notions of Markovian quantum evolution. In this paper we show that the one based on the so-called CP-divisibility of the corresponding dynamical map enjoys the following stability property: the dynamical map $\\Lambda_t$ is CP-divisible iff the second tensor power $\\Lambda_t\\otimes\\Lambda_t$ is CP-divisible as well. Moreover, the P-divisibility of the map $\\Lambda_t\\otimes\\Lambda_t$ is equivalent to the CP-divisibility of the map $\\Lambda_t$. Interestingly, the latter property is no longer true if we replace the P-divisibility of $\\Lambda_t\\otimes\\Lambda_t$ by sim","authors_text":"Dariusz Chru\\'sci\\'nski, Fabio Benatti, Sergey Filippov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-14T20:48:05Z","title":"Tensor power of dynamical maps and P- vs. CP-divisibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.04634","kind":"arxiv","version":1},"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:c559292ed428f5a8a4eb0546ba48dd51393763bc2c052448bf50f2a5b3e53f55","target":"record","created_at":"2026-05-18T00:52:38Z","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":"bbe8153eceea181a15f48c5565ae39f1eb4fcd1a637f6336f6a847996370633f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-14T20:48:05Z","title_canon_sha256":"ada3a9dd6b1fb947242b407a2d84711e647e5c1d9688c0d60479c41ce7364d6d"},"schema_version":"1.0","source":{"id":"1610.04634","kind":"arxiv","version":1}},"canonical_sha256":"a54a23249fbd27ce9e81db5215f6ec503bea79436552f77376cc37602122a5da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a54a23249fbd27ce9e81db5215f6ec503bea79436552f77376cc37602122a5da","first_computed_at":"2026-05-18T00:52:38.357789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:38.357789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"opNYCTTa9No4P2KwfqDsirqqVtXH0g3oRZf4UxPwayhdvhe58WploaAIe78Kz9pZxdtozD0+Iwuiug5WAR08DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:38.358219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.04634","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c559292ed428f5a8a4eb0546ba48dd51393763bc2c052448bf50f2a5b3e53f55","sha256:73a4ad16c4800ced73e0b2828376af25616ff591d97f886be65dfec3ba75bf6e"],"state_sha256":"31ee52df5a530243b48a7964edbdfa9376387fb1229b9558bcc7ec51599f14a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2I0ZxKDVI0lA0Jw8deEpSgDuaQWWDEX8r4MLAHLU7ogyywNVKn8OeGtTkfXlyXKYqX7li+IsT/fj/+AD1CF+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T13:12:12.998230Z","bundle_sha256":"1dced0d6c3e3d44021c48903113c03c27f56543a6399607c4475e6b4f21b8b22"}}