{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:DOTBXTLNXONAA7IHQSM7CMMZ2S","short_pith_number":"pith:DOTBXTLN","schema_version":"1.0","canonical_sha256":"1ba61bcd6dbb9a007d078499f13199d4b110f8a405ab13c25cef40baa293f4e3","source":{"kind":"arxiv","id":"quant-ph/0310075","version":1},"attestation_state":"computed","paper":{"title":"Symmetric Informationally Complete Quantum Measurements","license":"","headline":"","cross_cats":["cs.IT","math.FA","math.IT"],"primary_cat":"quant-ph","authors_text":"A. J. Scott, Carlton M. Caves, Joseph M. Renes, Robin Blume-Kohout","submitted_at":"2003-10-13T19:40:15Z","abstract_excerpt":"We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d. SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical res"},"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":"quant-ph/0310075","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2003-10-13T19:40:15Z","cross_cats_sorted":["cs.IT","math.FA","math.IT"],"title_canon_sha256":"ed901841a25da4736163c0d8bbfce391b91ec759239099fa96f3a9a7b0418ff3","abstract_canon_sha256":"5bd8995f0797bb9a06a9cc196498d422c81a9fb50efade038a5efbe59e80b7d6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:03:03.455083Z","signature_b64":"k8WNO1yeCP1+iF2QSYIeouj0ypWwr/G7rCNzBsaHz28vlydoKo5WfXqY87jiuKs8COkori3aNen0PjpTfOr8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ba61bcd6dbb9a007d078499f13199d4b110f8a405ab13c25cef40baa293f4e3","last_reissued_at":"2026-07-04T15:03:03.454611Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:03:03.454611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric Informationally Complete Quantum Measurements","license":"","headline":"","cross_cats":["cs.IT","math.FA","math.IT"],"primary_cat":"quant-ph","authors_text":"A. J. Scott, Carlton M. Caves, Joseph M. Renes, Robin Blume-Kohout","submitted_at":"2003-10-13T19:40:15Z","abstract_excerpt":"We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d. SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0310075","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0310075/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"quant-ph/0310075","created_at":"2026-07-04T15:03:03.454684+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0310075v1","created_at":"2026-07-04T15:03:03.454684+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0310075","created_at":"2026-07-04T15:03:03.454684+00:00"},{"alias_kind":"pith_short_12","alias_value":"DOTBXTLNXONA","created_at":"2026-07-04T15:03:03.454684+00:00"},{"alias_kind":"pith_short_16","alias_value":"DOTBXTLNXONAA7IH","created_at":"2026-07-04T15:03:03.454684+00:00"},{"alias_kind":"pith_short_8","alias_value":"DOTBXTLN","created_at":"2026-07-04T15:03:03.454684+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.18291","citing_title":"Quantum randomness beyond projective measurements","ref_index":24,"is_internal_anchor":true},{"citing_arxiv_id":"2605.00626","citing_title":"Learning Lindblad Dynamics of a Superconducting Quantum Processor","ref_index":28,"is_internal_anchor":false},{"citing_arxiv_id":"2604.13172","citing_title":"Simple slow operators and quantum thermalization","ref_index":111,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S","json":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S.json","graph_json":"https://pith.science/api/pith-number/DOTBXTLNXONAA7IHQSM7CMMZ2S/graph.json","events_json":"https://pith.science/api/pith-number/DOTBXTLNXONAA7IHQSM7CMMZ2S/events.json","paper":"https://pith.science/paper/DOTBXTLN"},"agent_actions":{"view_html":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S","download_json":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S.json","view_paper":"https://pith.science/paper/DOTBXTLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0310075&json=true","fetch_graph":"https://pith.science/api/pith-number/DOTBXTLNXONAA7IHQSM7CMMZ2S/graph.json","fetch_events":"https://pith.science/api/pith-number/DOTBXTLNXONAA7IHQSM7CMMZ2S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S/action/storage_attestation","attest_author":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S/action/author_attestation","sign_citation":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S/action/citation_signature","submit_replication":"https://pith.science/pith/DOTBXTLNXONAA7IHQSM7CMMZ2S/action/replication_record"}},"created_at":"2026-07-04T15:03:03.454684+00:00","updated_at":"2026-07-04T15:03:03.454684+00:00"}