{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7HGMKGU7XANAVMBBOEET3GEJMT","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":"7a483fcb97446cf543c017577827fbb3c2bd0d6397571b140697ab8409e19552","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-07-24T08:58:02Z","title_canon_sha256":"14f1b40df7330313949289a2dba544b88f6e60247bbd079ab79024e7c3f80d34"},"schema_version":"1.0","source":{"id":"2407.17103","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.17103","created_at":"2026-07-05T10:35:34Z"},{"alias_kind":"arxiv_version","alias_value":"2407.17103v3","created_at":"2026-07-05T10:35:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.17103","created_at":"2026-07-05T10:35:34Z"},{"alias_kind":"pith_short_12","alias_value":"7HGMKGU7XANA","created_at":"2026-07-05T10:35:34Z"},{"alias_kind":"pith_short_16","alias_value":"7HGMKGU7XANAVMBB","created_at":"2026-07-05T10:35:34Z"},{"alias_kind":"pith_short_8","alias_value":"7HGMKGU7","created_at":"2026-07-05T10:35:34Z"}],"graph_snapshots":[{"event_id":"sha256:c6663b695797264ad921849fd325553998314d0940dbe033ca190b310523534d","target":"graph","created_at":"2026-07-05T10:35:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2407.17103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a simple, dimension-independent criterion which guarantees that some quantum channel $\\Phi$ is divisible, i.e. that there exists a non-trivial factorization $\\Phi=\\Phi_1\\Phi_2$. The idea is to first define an \"elementary\" channel $\\Phi_2$ and then to analyze when $\\Phi\\Phi_2^{-1}$ is completely positive. The sufficient criterion obtained this way -- which even yields an explicit factorization of $\\Phi$ -- is that one has to find orthogonal unit vectors $x,x^\\perp$ such that $\\langle x^\\perp|\\mathcal K_\\Phi\\mathcal K_\\Phi^\\perp|x\\rangle=\\langle x|\\mathcal K_\\Phi\\mathcal K_\\Phi^\\perp|","authors_text":"Frederik vom Ende","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-07-24T08:58:02Z","title":"A Sufficient Criterion for Divisibility of Quantum Channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17103","kind":"arxiv","version":3},"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":"sha256:0479feb3ca510c7bf7aa42c28bf73c426914bec727e9b47dafc252c8b680a470","target":"record","created_at":"2026-07-05T10:35:34Z","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":"7a483fcb97446cf543c017577827fbb3c2bd0d6397571b140697ab8409e19552","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-07-24T08:58:02Z","title_canon_sha256":"14f1b40df7330313949289a2dba544b88f6e60247bbd079ab79024e7c3f80d34"},"schema_version":"1.0","source":{"id":"2407.17103","kind":"arxiv","version":3}},"canonical_sha256":"f9ccc51a9fb81a0ab02171093d988964c24e873447a2bfc525392080690b80ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9ccc51a9fb81a0ab02171093d988964c24e873447a2bfc525392080690b80ec","first_computed_at":"2026-07-05T10:35:34.874813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:35:34.874813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fJvjOeAh3qwrLlgUVIz0SzggY8W6ccQd+bEhz9uc3vIZxsy7zpB+NWMGlDF9uU/WjS+WWKh7eBtl2UW4DLdwBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:35:34.875466Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.17103","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0479feb3ca510c7bf7aa42c28bf73c426914bec727e9b47dafc252c8b680a470","sha256:c6663b695797264ad921849fd325553998314d0940dbe033ca190b310523534d"],"state_sha256":"a6db5616ead781ede36d9d0d7a0330861da208d8d0d0e568cbdcd690ff05db22"}