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We show that the Hermitian matrix $W_{\\Phi_{t,\\pi}}$ induced by $\\Phi_{t,\\pi}$ is an optimal entanglement witness if and only if $t=1$ and $\\pi$ is cyclic."},"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":"1301.7558","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"quant-ph","submitted_at":"2013-01-31T09:22:35Z","cross_cats_sorted":[],"title_canon_sha256":"6edad9d1d726448dfca87cc8d5e3db7a397ede16203f56b8e0aaf60c2313f7bc","abstract_canon_sha256":"44022f8bc3e43bec8b9ac576280a72f373d78a8f442aaea77396d419bc562eea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:51:56.688849Z","signature_b64":"PZdcSIESRLBihOXaak0lU9vh/rytdwBjxOErxQhyT8QWOFiRhdcLqMrgybLEJ6I8NplVOeT8oQuXGwYQFz6vAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beb3325fd662660ab8e17c3fc68c99fd70e41ef9ec0818492309859914dc61d8","last_reissued_at":"2026-05-18T01:51:56.688420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:51:56.688420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimality of a class of entanglement witnesses for $3\\otimes 3$ systems","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jinchuan Hou, Xiaofei Qi","submitted_at":"2013-01-31T09:22:35Z","abstract_excerpt":"Let $\\Phi_{t,\\pi}: M_3({\\mathbb C}) \\rightarrow M_3({\\mathbb C})$ be a linear map defined by $\\Phi_{t,\\pi}(A)=(3-t)\\sum_{i=1}^3E_{ii}AE_{ii}+t\\sum_{i=1}^3E_{i,\\pi(i)}AE_{i,\\pi(i)}^\\dag-A$, where $0\\leq t\\leq 3$ and $\\pi$ is a permutation of $(1,2,3)$. We show that the Hermitian matrix $W_{\\Phi_{t,\\pi}}$ induced by $\\Phi_{t,\\pi}$ is an optimal entanglement witness if and only if $t=1$ and $\\pi$ is cyclic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7558","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":"1301.7558","created_at":"2026-05-18T01:51:56.688492+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.7558v1","created_at":"2026-05-18T01:51:56.688492+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7558","created_at":"2026-05-18T01:51:56.688492+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2ZTEX6WMJTA","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2ZTEX6WMJTAVOHB","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2ZTEX6W","created_at":"2026-05-18T12:28:06.772260+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/X2ZTEX6WMJTAVOHBPQ74NDEZ7V","json":"https://pith.science/pith/X2ZTEX6WMJTAVOHBPQ74NDEZ7V.json","graph_json":"https://pith.science/api/pith-number/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/graph.json","events_json":"https://pith.science/api/pith-number/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/events.json","paper":"https://pith.science/paper/X2ZTEX6W"},"agent_actions":{"view_html":"https://pith.science/pith/X2ZTEX6WMJTAVOHBPQ74NDEZ7V","download_json":"https://pith.science/pith/X2ZTEX6WMJTAVOHBPQ74NDEZ7V.json","view_paper":"https://pith.science/paper/X2ZTEX6W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.7558&json=true","fetch_graph":"https://pith.science/api/pith-number/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/graph.json","fetch_events":"https://pith.science/api/pith-number/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/action/storage_attestation","attest_author":"https://pith.science/pith/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/action/author_attestation","sign_citation":"https://pith.science/pith/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/action/citation_signature","submit_replication":"https://pith.science/pith/X2ZTEX6WMJTAVOHBPQ74NDEZ7V/action/replication_record"}},"created_at":"2026-05-18T01:51:56.688492+00:00","updated_at":"2026-05-18T01:51:56.688492+00:00"}