{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:V4R7JVH4GOU2X7EDNM4JN5WAI2","short_pith_number":"pith:V4R7JVH4","canonical_record":{"source":{"id":"1607.03364","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-12T14:17:29Z","cross_cats_sorted":[],"title_canon_sha256":"a9d27371cc6729659d396bd5c101df0066c5c0f783c3fec8aa51a7e4734b1654","abstract_canon_sha256":"be9935dfd48d0c91943ca45124eda4bbb751476c5b18893035afae98a65bf565"},"schema_version":"1.0"},"canonical_sha256":"af23f4d4fc33a9abfc836b3896f6c0469f9a4c7521ebf61b16947ae146b0335f","source":{"kind":"arxiv","id":"1607.03364","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03364","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03364v4","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03364","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"V4R7JVH4GOU2","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V4R7JVH4GOU2X7ED","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V4R7JVH4","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:V4R7JVH4GOU2X7EDNM4JN5WAI2","target":"record","payload":{"canonical_record":{"source":{"id":"1607.03364","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-12T14:17:29Z","cross_cats_sorted":[],"title_canon_sha256":"a9d27371cc6729659d396bd5c101df0066c5c0f783c3fec8aa51a7e4734b1654","abstract_canon_sha256":"be9935dfd48d0c91943ca45124eda4bbb751476c5b18893035afae98a65bf565"},"schema_version":"1.0"},"canonical_sha256":"af23f4d4fc33a9abfc836b3896f6c0469f9a4c7521ebf61b16947ae146b0335f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:23.500306Z","signature_b64":"ZuWHNU2upkUMx37grTxVN5MSchDSp9zzcYM9Mi1hfXVJCGPsqJ3oVXSEZDtKZiY9OD+QTC8RtQIa1QmCMKirDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af23f4d4fc33a9abfc836b3896f6c0469f9a4c7521ebf61b16947ae146b0335f","last_reissued_at":"2026-05-18T00:23:23.499498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:23.499498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.03364","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PsZeXv4+zP6mRbC1pfHZv/mB4cUDVn3eFzLSOdn8mZXlhDtqTKZz1S4vR6+92SrL8cWsPU07KRqsvbW0ZS/wBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:53:26.618703Z"},"content_sha256":"5b8a423781d694514dca52f4fec4ec260f8988c2a6ad31e412f1bfe5a1e7d923","schema_version":"1.0","event_id":"sha256:5b8a423781d694514dca52f4fec4ec260f8988c2a6ad31e412f1bfe5a1e7d923"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:V4R7JVH4GOU2X7EDNM4JN5WAI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Necessary and Sufficient Criterion for the Separability of Quantum State","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Cong-Feng Qiao, Jun-Li Li","submitted_at":"2016-07-12T14:17:29Z","abstract_excerpt":"Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn's problem. The work follows the work initiated by Horodecki {\\it et. al.} and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03364","kind":"arxiv","version":4},"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":"2026-05-18T00:23:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qoy2UNwSf3+p+R5NziC91DbDhbGQYt8FXfzwwXOlcl05VkKjz+4956UhY0aRgg/U891K42osTtKCBT/rt6OPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:53:26.619482Z"},"content_sha256":"7f06fcb5d92c1c5a7bbc5242d2c51a2efedba81bc8d5f4e816902d7c2ed0479b","schema_version":"1.0","event_id":"sha256:7f06fcb5d92c1c5a7bbc5242d2c51a2efedba81bc8d5f4e816902d7c2ed0479b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4R7JVH4GOU2X7EDNM4JN5WAI2/bundle.json","state_url":"https://pith.science/pith/V4R7JVH4GOU2X7EDNM4JN5WAI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4R7JVH4GOU2X7EDNM4JN5WAI2/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":"2026-06-10T07:53:26Z","links":{"resolver":"https://pith.science/pith/V4R7JVH4GOU2X7EDNM4JN5WAI2","bundle":"https://pith.science/pith/V4R7JVH4GOU2X7EDNM4JN5WAI2/bundle.json","state":"https://pith.science/pith/V4R7JVH4GOU2X7EDNM4JN5WAI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4R7JVH4GOU2X7EDNM4JN5WAI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:V4R7JVH4GOU2X7EDNM4JN5WAI2","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":"be9935dfd48d0c91943ca45124eda4bbb751476c5b18893035afae98a65bf565","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-12T14:17:29Z","title_canon_sha256":"a9d27371cc6729659d396bd5c101df0066c5c0f783c3fec8aa51a7e4734b1654"},"schema_version":"1.0","source":{"id":"1607.03364","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03364","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03364v4","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03364","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"V4R7JVH4GOU2","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"V4R7JVH4GOU2X7ED","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"V4R7JVH4","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:7f06fcb5d92c1c5a7bbc5242d2c51a2efedba81bc8d5f4e816902d7c2ed0479b","target":"graph","created_at":"2026-05-18T00:23:23Z","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":"Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn's problem. The work follows the work initiated by Horodecki {\\it et. al.} and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, ","authors_text":"Cong-Feng Qiao, Jun-Li Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-12T14:17:29Z","title":"A Necessary and Sufficient Criterion for the Separability of Quantum State"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03364","kind":"arxiv","version":4},"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":"sha256:5b8a423781d694514dca52f4fec4ec260f8988c2a6ad31e412f1bfe5a1e7d923","target":"record","created_at":"2026-05-18T00:23:23Z","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":"be9935dfd48d0c91943ca45124eda4bbb751476c5b18893035afae98a65bf565","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-12T14:17:29Z","title_canon_sha256":"a9d27371cc6729659d396bd5c101df0066c5c0f783c3fec8aa51a7e4734b1654"},"schema_version":"1.0","source":{"id":"1607.03364","kind":"arxiv","version":4}},"canonical_sha256":"af23f4d4fc33a9abfc836b3896f6c0469f9a4c7521ebf61b16947ae146b0335f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af23f4d4fc33a9abfc836b3896f6c0469f9a4c7521ebf61b16947ae146b0335f","first_computed_at":"2026-05-18T00:23:23.499498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:23.499498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZuWHNU2upkUMx37grTxVN5MSchDSp9zzcYM9Mi1hfXVJCGPsqJ3oVXSEZDtKZiY9OD+QTC8RtQIa1QmCMKirDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:23.500306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03364","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b8a423781d694514dca52f4fec4ec260f8988c2a6ad31e412f1bfe5a1e7d923","sha256:7f06fcb5d92c1c5a7bbc5242d2c51a2efedba81bc8d5f4e816902d7c2ed0479b"],"state_sha256":"0cb2ba982fe66c3a7bbdaa9692ae87fe93946987b3d5823874305515f0079132"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ysTGBaDq6nDmPvAglVQkONjZJccumg6RDMFPEvfVwjCJzWP7y93PMwVw07ae+rZAhpU+dNQPLjigaKa5jn5zAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T07:53:26.624175Z","bundle_sha256":"b62b7e7b1eaed237ccf85a4edd4512e0fef1e71942283894b4845d98fd947745"}}