{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:PEUXG75UGYXLZVZ3L2TOOIFEHX","short_pith_number":"pith:PEUXG75U","schema_version":"1.0","canonical_sha256":"7929737fb4362ebcd73b5ea6e720a43df559c8107a9849a8506f36b3aaf5823d","source":{"kind":"arxiv","id":"2608.11151","version":1},"attestation_state":"computed","paper":{"title":"Breaking the Quadratic Barrier for von Neumann Entropy Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Minbo Gao, Qisheng Wang","submitted_at":"2026-08-11T17:10:34Z","abstract_excerpt":"We study the sample complexity of estimating the von Neumann entropy of an unknown $d$-dimensional quantum state. All previously known estimators require $\\Omega(d^2)$ samples, and plug-in estimators are known to face a quadratic barrier. We give the first subquadratic-sample estimator: for additive error $\\varepsilon$, our estimator uses\n  \\[\n  O\\!\\left(\\frac{d^2 \\log^2(\\log(d)) \\log(1/\\varepsilon)}{\\varepsilon^2 \\log^2(d)} + \\frac{\\log^2(d/\\varepsilon)}{\\varepsilon^2}\\right)\n  \\] samples. In particular, for constant $\\varepsilon$, the complexity is $O_\\varepsilon(d^2\\log^2(\\log(d))/\\log^2(d)"},"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":"2608.11151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-08-11T17:10:34Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"c52a23631bf73aa5527e5f01428d62d4858201162e8197396088e76316d60c96","abstract_canon_sha256":"69d5ef0cf3fdaeb9f38c63c737e810b5f2246c52bf5bfdd508b1c45b81820d35"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:24:42.412824Z","signature_b64":"Sp/c0BcD8y1nPFEe//A8vRguHjSOb7s0THBkgDRbid/PgNxu8nEHD1ruJ9WndMFXE7Di7Kj9Xsq0kdpKmR6MAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7929737fb4362ebcd73b5ea6e720a43df559c8107a9849a8506f36b3aaf5823d","last_reissued_at":"2026-08-12T01:24:42.411123Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:24:42.411123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Breaking the Quadratic Barrier for von Neumann Entropy Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Minbo Gao, Qisheng Wang","submitted_at":"2026-08-11T17:10:34Z","abstract_excerpt":"We study the sample complexity of estimating the von Neumann entropy of an unknown $d$-dimensional quantum state. All previously known estimators require $\\Omega(d^2)$ samples, and plug-in estimators are known to face a quadratic barrier. We give the first subquadratic-sample estimator: for additive error $\\varepsilon$, our estimator uses\n  \\[\n  O\\!\\left(\\frac{d^2 \\log^2(\\log(d)) \\log(1/\\varepsilon)}{\\varepsilon^2 \\log^2(d)} + \\frac{\\log^2(d/\\varepsilon)}{\\varepsilon^2}\\right)\n  \\] samples. In particular, for constant $\\varepsilon$, the complexity is $O_\\varepsilon(d^2\\log^2(\\log(d))/\\log^2(d)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11151","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/2608.11151/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":"2608.11151","created_at":"2026-08-12T01:24:42.414943+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.11151v1","created_at":"2026-08-12T01:24:42.414943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11151","created_at":"2026-08-12T01:24:42.414943+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEUXG75UGYXL","created_at":"2026-08-12T01:24:42.414943+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEUXG75UGYXLZVZ3","created_at":"2026-08-12T01:24:42.414943+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEUXG75U","created_at":"2026-08-12T01:24:42.414943+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/PEUXG75UGYXLZVZ3L2TOOIFEHX","json":"https://pith.science/pith/PEUXG75UGYXLZVZ3L2TOOIFEHX.json","graph_json":"https://pith.science/api/pith-number/PEUXG75UGYXLZVZ3L2TOOIFEHX/graph.json","events_json":"https://pith.science/api/pith-number/PEUXG75UGYXLZVZ3L2TOOIFEHX/events.json","paper":"https://pith.science/paper/PEUXG75U"},"agent_actions":{"view_html":"https://pith.science/pith/PEUXG75UGYXLZVZ3L2TOOIFEHX","download_json":"https://pith.science/pith/PEUXG75UGYXLZVZ3L2TOOIFEHX.json","view_paper":"https://pith.science/paper/PEUXG75U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.11151&json=true","fetch_graph":"https://pith.science/api/pith-number/PEUXG75UGYXLZVZ3L2TOOIFEHX/graph.json","fetch_events":"https://pith.science/api/pith-number/PEUXG75UGYXLZVZ3L2TOOIFEHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEUXG75UGYXLZVZ3L2TOOIFEHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEUXG75UGYXLZVZ3L2TOOIFEHX/action/storage_attestation","attest_author":"https://pith.science/pith/PEUXG75UGYXLZVZ3L2TOOIFEHX/action/author_attestation","sign_citation":"https://pith.science/pith/PEUXG75UGYXLZVZ3L2TOOIFEHX/action/citation_signature","submit_replication":"https://pith.science/pith/PEUXG75UGYXLZVZ3L2TOOIFEHX/action/replication_record"}},"created_at":"2026-08-12T01:24:42.414943+00:00","updated_at":"2026-08-12T01:24:42.414943+00:00"}