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Let $\\rho_1$ be random induced states $\\rho_1=Tr_{\\mathbb{C}^s}(|\\psi\\rangle\\langle \\psi |)$ whose distribution is $\\mu_{d^2,s}$; and let $\\rho_2$ be random induced states following the same distribution $\\mu_{d^2,s}$ independent from $\\rho_1$. Let $\\rho$ be a random state induced by the entanglement swapping of $\\rho_1$ and $\\rho_2$. We show that the empirical spectrum of $\\rho- {1\\"},"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":"1803.00143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-03-01T00:21:38Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"877d01e81df5b295b3ccb2655541fbb331d0fda531ed08d33cc907d9a23cce32","abstract_canon_sha256":"3dd51ef08182361303464bbca33226ae3e052c7c442859d6b9d381432a2f0546"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:44.228732Z","signature_b64":"k4Gs07dob60GZwFXsd+ucAtiOriQdBro0saFTwwdfrA441ACqU0sJtq6YdITgsMz0BKm4lg8IiUQnkLrPCeUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84b06404e98023c166cb104b4af6413f1eae9785daee4ec0842d36ab4c4ec4ee","last_reissued_at":"2026-05-17T23:52:44.228279Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:44.228279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The PPT square conjecture holds generically for some classes of independent states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Beno\\^it Collins, Ping Zhong, Zhi Yin","submitted_at":"2018-03-01T00:21:38Z","abstract_excerpt":"Let $|\\psi\\rangle\\langle \\psi|$ be a random pure state on $\\mathbb{C}^{d^2}\\otimes \\mathbb{C}^s$, where $\\psi$ is a random unit vector uniformly distributed on the sphere in $\\mathbb{C}^{d^2}\\otimes \\mathbb{C}^s$. Let $\\rho_1$ be random induced states $\\rho_1=Tr_{\\mathbb{C}^s}(|\\psi\\rangle\\langle \\psi |)$ whose distribution is $\\mu_{d^2,s}$; and let $\\rho_2$ be random induced states following the same distribution $\\mu_{d^2,s}$ independent from $\\rho_1$. Let $\\rho$ be a random state induced by the entanglement swapping of $\\rho_1$ and $\\rho_2$. We show that the empirical spectrum of $\\rho- {1\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00143","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":"1803.00143","created_at":"2026-05-17T23:52:44.228344+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.00143v1","created_at":"2026-05-17T23:52:44.228344+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00143","created_at":"2026-05-17T23:52:44.228344+00:00"},{"alias_kind":"pith_short_12","alias_value":"QSYGIBHJQAR4","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QSYGIBHJQAR4CZWL","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QSYGIBHJ","created_at":"2026-05-18T12:32:46.962924+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/QSYGIBHJQAR4CZWLCBFUV5SBH4","json":"https://pith.science/pith/QSYGIBHJQAR4CZWLCBFUV5SBH4.json","graph_json":"https://pith.science/api/pith-number/QSYGIBHJQAR4CZWLCBFUV5SBH4/graph.json","events_json":"https://pith.science/api/pith-number/QSYGIBHJQAR4CZWLCBFUV5SBH4/events.json","paper":"https://pith.science/paper/QSYGIBHJ"},"agent_actions":{"view_html":"https://pith.science/pith/QSYGIBHJQAR4CZWLCBFUV5SBH4","download_json":"https://pith.science/pith/QSYGIBHJQAR4CZWLCBFUV5SBH4.json","view_paper":"https://pith.science/paper/QSYGIBHJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.00143&json=true","fetch_graph":"https://pith.science/api/pith-number/QSYGIBHJQAR4CZWLCBFUV5SBH4/graph.json","fetch_events":"https://pith.science/api/pith-number/QSYGIBHJQAR4CZWLCBFUV5SBH4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QSYGIBHJQAR4CZWLCBFUV5SBH4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QSYGIBHJQAR4CZWLCBFUV5SBH4/action/storage_attestation","attest_author":"https://pith.science/pith/QSYGIBHJQAR4CZWLCBFUV5SBH4/action/author_attestation","sign_citation":"https://pith.science/pith/QSYGIBHJQAR4CZWLCBFUV5SBH4/action/citation_signature","submit_replication":"https://pith.science/pith/QSYGIBHJQAR4CZWLCBFUV5SBH4/action/replication_record"}},"created_at":"2026-05-17T23:52:44.228344+00:00","updated_at":"2026-05-17T23:52:44.228344+00:00"}