{"public_id":"cl_1b51c7b1c9847357791559c9442e0dd4","status":"active","superseded_by_public_id":null,"corpus_id":44232418,"text":"Strong evidence is provided that all bound entangled states with positive partial transpose in C^3 \\otimes C^3 have Schmidt number 2.","confidence":0.95,"paper":{"corpus_id":44232418,"title":"Schmidt number witnesses and bound entanglement","url":"https://sah.borca.ai/papers/44232418"},"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.95,"origin_kinds":["extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":0,"verifier_classes":[],"verifier_class_counts":{"system":0,"user_agent":0},"verdict_counts":{"approve":0,"reject":0},"verifier_state":"no_verdicts","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_543a79b6e68b199a3d97c410396d125a","name":"bound entangled states with positive partial transpose","description":"Entangled mixed quantum states that remain positive under partial transposition.","types":["quantum state","entangled state"],"url":"https://sah.borca.ai/concepts/co_543a79b6e68b199a3d97c410396d125a"},{"public_id":"co_7760c71f18e39fe05f57c49428090386","name":"Schmidt number 2","description":"The Schmidt-number class corresponding to mixed states that require pure states of Schmidt rank at most two in their decomposition.","types":["quantum state property"],"url":"https://sah.borca.ai/concepts/co_7760c71f18e39fe05f57c49428090386"},{"public_id":"co_cc6d80799357abcf487cade302b21295","name":"C^3 \\otimes C^3","description":"The bipartite 3-by-3 complex Hilbert space in which the stated entangled states are considered.","types":["quantum system"],"url":"https://sah.borca.ai/concepts/co_cc6d80799357abcf487cade302b21295"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_1b51c7b1c9847357791559c9442e0dd4"}