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We prove that there exists no pure state in $C(\\{1}{2}I_2, \\{1}{3}I_3)$. Further we generalize this result to an arbitrary $m \\times n$ bipartite systems. We prove that for $m < n$, no pure state exists in the convex set $C(\\rho_A,\\rho_B)$, for an arbitrary $\\rho_A$ and rank of $\\rho_B >m$."},"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":"1305.3672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-16T02:41:29Z","cross_cats_sorted":[],"title_canon_sha256":"3ae39a0eef900a5a8207b6bd327c3d09a191d920eabd438e16d0838701f2d13f","abstract_canon_sha256":"502bc42bb459a98d336e4895fecc37a562ed4db0d1fa3d0ca8aaf42845ddbb67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:34.217246Z","signature_b64":"uKxWFupB3ToYqE370EcRfyQXdfPmtwDWNJN5G4HDqbfaGrLewVxxSHHAw5vu2BOqHnMuLFGjnb6IDeTwaa5DDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7088c45b1d5cb96b3aae73f9e77fc133689a52e9cf4a3304a1938587d94b4915","last_reissued_at":"2026-05-18T03:25:34.216375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:34.216375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Restriction on the rank of marginals of bipartite pure states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"S.V.M. Satyanarayana","submitted_at":"2013-05-16T02:41:29Z","abstract_excerpt":"Consider a qubit-qutrit ($2 \\times 3$) composite state space. Let $C(\\{1}{2}I_2, \\{1}{3}I_3)$ be a convex set of all possible states of composite system whose marginals are given by $\\{1}{2}I_2$ and $\\{1}{3}I_3$ in two and three dimensional spaces respectively. We prove that there exists no pure state in $C(\\{1}{2}I_2, \\{1}{3}I_3)$. Further we generalize this result to an arbitrary $m \\times n$ bipartite systems. We prove that for $m < n$, no pure state exists in the convex set $C(\\rho_A,\\rho_B)$, for an arbitrary $\\rho_A$ and rank of $\\rho_B >m$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3672","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.3672","created_at":"2026-05-18T03:25:34.216491+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.3672v1","created_at":"2026-05-18T03:25:34.216491+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3672","created_at":"2026-05-18T03:25:34.216491+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCEMIWY5LS4W","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCEMIWY5LS4WWOVO","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCEMIWY5","created_at":"2026-05-18T12:27:54.935989+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/OCEMIWY5LS4WWOVOOP46O76BGN","json":"https://pith.science/pith/OCEMIWY5LS4WWOVOOP46O76BGN.json","graph_json":"https://pith.science/api/pith-number/OCEMIWY5LS4WWOVOOP46O76BGN/graph.json","events_json":"https://pith.science/api/pith-number/OCEMIWY5LS4WWOVOOP46O76BGN/events.json","paper":"https://pith.science/paper/OCEMIWY5"},"agent_actions":{"view_html":"https://pith.science/pith/OCEMIWY5LS4WWOVOOP46O76BGN","download_json":"https://pith.science/pith/OCEMIWY5LS4WWOVOOP46O76BGN.json","view_paper":"https://pith.science/paper/OCEMIWY5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.3672&json=true","fetch_graph":"https://pith.science/api/pith-number/OCEMIWY5LS4WWOVOOP46O76BGN/graph.json","fetch_events":"https://pith.science/api/pith-number/OCEMIWY5LS4WWOVOOP46O76BGN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCEMIWY5LS4WWOVOOP46O76BGN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCEMIWY5LS4WWOVOOP46O76BGN/action/storage_attestation","attest_author":"https://pith.science/pith/OCEMIWY5LS4WWOVOOP46O76BGN/action/author_attestation","sign_citation":"https://pith.science/pith/OCEMIWY5LS4WWOVOOP46O76BGN/action/citation_signature","submit_replication":"https://pith.science/pith/OCEMIWY5LS4WWOVOOP46O76BGN/action/replication_record"}},"created_at":"2026-05-18T03:25:34.216491+00:00","updated_at":"2026-05-18T03:25:34.216491+00:00"}