{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:B3QQCUJR5677677JJB4W6KKHOC","short_pith_number":"pith:B3QQCUJR","schema_version":"1.0","canonical_sha256":"0ee1015131efbfff7fe948796f294770922d5c46e025733cf8e4056a58d90df4","source":{"kind":"arxiv","id":"1203.1364","version":4},"attestation_state":"computed","paper":{"title":"Properties and construction of extreme bipartite states having positive partial transpose","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Dragomir Z. Djokovic, Lin Chen","submitted_at":"2012-03-07T01:47:24Z","abstract_excerpt":"We consider a bipartite quantum system H_A x H_B with M=dim H_A and N=dim H_B. We study the set E of extreme points of the compact convex set of all states having positive partial transpose (PPT) and its subsets E_r={rho in E: rank rho=r}. Our main results pertain to the subsets E_r^{M,N} of E_r consisting of states whose reduced density operators have ranks M and N, respectively. The set E_1 is just the set of pure product states. It is known that E_r^{M,N} is empty for 1< r <= min(M,N) and for r=MN. We prove that also E_{MN-1}^{M,N} is empty. Leinaas, Myrheim and Sollid have conjectured that"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.1364","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-07T01:47:24Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"efc05a9ae48fd7d681192342745021a48309b3a173cc5e7ea77fa1a68d10687e","abstract_canon_sha256":"8d17140f474c2502ed4ae8b22935f28e6c6708c8a8a11973ad5f7ee49e42617f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:02.286954Z","signature_b64":"NhBd0iQgreXdpwmNLSNJatA8YNAWD++cnH3XnSzuUL0/nW84xGiny0lRvNZt1At5ohKsJOUMX7c3iwyZPfeRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ee1015131efbfff7fe948796f294770922d5c46e025733cf8e4056a58d90df4","last_reissued_at":"2026-05-18T03:07:02.286510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:02.286510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Properties and construction of extreme bipartite states having positive partial transpose","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Dragomir Z. Djokovic, Lin Chen","submitted_at":"2012-03-07T01:47:24Z","abstract_excerpt":"We consider a bipartite quantum system H_A x H_B with M=dim H_A and N=dim H_B. We study the set E of extreme points of the compact convex set of all states having positive partial transpose (PPT) and its subsets E_r={rho in E: rank rho=r}. Our main results pertain to the subsets E_r^{M,N} of E_r consisting of states whose reduced density operators have ranks M and N, respectively. The set E_1 is just the set of pure product states. It is known that E_r^{M,N} is empty for 1< r <= min(M,N) and for r=MN. We prove that also E_{MN-1}^{M,N} is empty. Leinaas, Myrheim and Sollid have conjectured that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1364","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.1364","created_at":"2026-05-18T03:07:02.286583+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.1364v4","created_at":"2026-05-18T03:07:02.286583+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1364","created_at":"2026-05-18T03:07:02.286583+00:00"},{"alias_kind":"pith_short_12","alias_value":"B3QQCUJR5677","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"B3QQCUJR5677677J","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"B3QQCUJR","created_at":"2026-05-18T12:26:58.693483+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC","json":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC.json","graph_json":"https://pith.science/api/pith-number/B3QQCUJR5677677JJB4W6KKHOC/graph.json","events_json":"https://pith.science/api/pith-number/B3QQCUJR5677677JJB4W6KKHOC/events.json","paper":"https://pith.science/paper/B3QQCUJR"},"agent_actions":{"view_html":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC","download_json":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC.json","view_paper":"https://pith.science/paper/B3QQCUJR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.1364&json=true","fetch_graph":"https://pith.science/api/pith-number/B3QQCUJR5677677JJB4W6KKHOC/graph.json","fetch_events":"https://pith.science/api/pith-number/B3QQCUJR5677677JJB4W6KKHOC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC/action/storage_attestation","attest_author":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC/action/author_attestation","sign_citation":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC/action/citation_signature","submit_replication":"https://pith.science/pith/B3QQCUJR5677677JJB4W6KKHOC/action/replication_record"}},"created_at":"2026-05-18T03:07:02.286583+00:00","updated_at":"2026-05-18T03:07:02.286583+00:00"}