{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SAN2QGTMI2KMGCFJYLLBM46JTF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"74195da17fbd754f1e0d06312c8fc12df152966c1358412db7003a222abe497f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-10-23T09:47:43Z","title_canon_sha256":"c57c6574bafc03b253f6faecd18d4f657274c47d3dfd2b4def94073716e1785c"},"schema_version":"1.0","source":{"id":"2410.17718","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.17718","created_at":"2026-07-05T10:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"2410.17718v2","created_at":"2026-07-05T10:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.17718","created_at":"2026-07-05T10:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"SAN2QGTMI2KM","created_at":"2026-07-05T10:53:12Z"},{"alias_kind":"pith_short_16","alias_value":"SAN2QGTMI2KMGCFJ","created_at":"2026-07-05T10:53:12Z"},{"alias_kind":"pith_short_8","alias_value":"SAN2QGTM","created_at":"2026-07-05T10:53:12Z"}],"graph_snapshots":[{"event_id":"sha256:486f464ebb4530fcf749ca9a38e6b7d2731e75ed20f42b3d5862b658bdc08a92","target":"graph","created_at":"2026-07-05T10:53:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.17718/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In quantum learning tasks, quantum memory can offer exponential reductions in statistical complexity compared to any single-copy strategies, but this typically necessitates at least doubling the system size. We show that such exponential reductions can also be achieved by having access to the purification of the target mixed state. Specifically, for a low-rank mixed state, only a constant number of ancilla qubits is needed for estimating properties related to its purity, cooled form, principal component and quantum Fisher information with constant sample complexity, which utilizes single-copy ","authors_text":"Weiyuan Gong, Zhenhuan Liu, Zhenyu Cai, Zhenyu Du","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-10-23T09:47:43Z","title":"Exponential Separations between Quantum Learning with and without Purification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.17718","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:08aa5a7cd0de81202be0128215a5409419ed9e503c4bb04f5bb68eaddf32065a","target":"record","created_at":"2026-07-05T10:53:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"74195da17fbd754f1e0d06312c8fc12df152966c1358412db7003a222abe497f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-10-23T09:47:43Z","title_canon_sha256":"c57c6574bafc03b253f6faecd18d4f657274c47d3dfd2b4def94073716e1785c"},"schema_version":"1.0","source":{"id":"2410.17718","kind":"arxiv","version":2}},"canonical_sha256":"901ba81a6c4694c308a9c2d61673c9996e3616c605821890c0d67f720f8bd483","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"901ba81a6c4694c308a9c2d61673c9996e3616c605821890c0d67f720f8bd483","first_computed_at":"2026-07-05T10:53:12.783176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:53:12.783176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mFHGEd85Miz2x7NIFbQyeWAn6fe6ShJGsdZrnw5bB5PtZjZ1em6RNswc25E+VU6xRZf76MtGrKa82/LTCBChBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:53:12.783699Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.17718","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08aa5a7cd0de81202be0128215a5409419ed9e503c4bb04f5bb68eaddf32065a","sha256:486f464ebb4530fcf749ca9a38e6b7d2731e75ed20f42b3d5862b658bdc08a92"],"state_sha256":"0b3af1f3e230a9a56e1cf54b35fda28b903f29abd768c974a444c1ca572b0770"}