{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:K3CUIANVO27NKER2IUSVK4G6AE","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":"22d68b014ae215eda132062853696f598742c9cbd153903b2c6f96bafdc68d12","cross_cats_sorted":["cs.DS","cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-10-16T16:17:21Z","title_canon_sha256":"9e921cefcec81409ee6579e56ea8cf68b39d029211acd433135a37b04672948f"},"schema_version":"1.0","source":{"id":"2410.12712","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.12712","created_at":"2026-07-05T09:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"2410.12712v1","created_at":"2026-07-05T09:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.12712","created_at":"2026-07-05T09:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"K3CUIANVO27N","created_at":"2026-07-05T09:21:32Z"},{"alias_kind":"pith_short_16","alias_value":"K3CUIANVO27NKER2","created_at":"2026-07-05T09:21:32Z"},{"alias_kind":"pith_short_8","alias_value":"K3CUIANV","created_at":"2026-07-05T09:21:32Z"}],"graph_snapshots":[{"event_id":"sha256:cb229cee4686e8e9e5e7371c20fe7fb3f144f2d66223347534249bbaf2be23b8","target":"graph","created_at":"2026-07-05T09:21:32Z","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/2410.12712/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the sample complexity of the prototypical tasks quantum purity estimation and quantum inner product estimation. In purity estimation, we are to estimate $tr(\\rho^2)$ of an unknown quantum state $\\rho$ to additive error $\\epsilon$. Meanwhile, for quantum inner product estimation, Alice and Bob are to estimate $tr(\\rho\\sigma)$ to additive error $\\epsilon$ given copies of unknown quantum state $\\rho$ and $\\sigma$ using classical communication and restricted quantum communication.\n  In this paper, we show a strong connection between the sample complexity of purity estimation with bounded ","authors_text":"Jonas Haferkamp, Qi Ye, Weiyuan Gong, Zhihan Zhang","cross_cats":["cs.DS","cs.IT","cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-10-16T16:17:21Z","title":"On the sample complexity of purity and inner product estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.12712","kind":"arxiv","version":1},"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":"sha256:281b570031a4a86f10008f6c13b5353950c3946e489fee38155251c94ea0c396","target":"record","created_at":"2026-07-05T09:21:32Z","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":"22d68b014ae215eda132062853696f598742c9cbd153903b2c6f96bafdc68d12","cross_cats_sorted":["cs.DS","cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-10-16T16:17:21Z","title_canon_sha256":"9e921cefcec81409ee6579e56ea8cf68b39d029211acd433135a37b04672948f"},"schema_version":"1.0","source":{"id":"2410.12712","kind":"arxiv","version":1}},"canonical_sha256":"56c54401b576bed5123a45255570de0137fce0b1b106790e254fd43d2caac082","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56c54401b576bed5123a45255570de0137fce0b1b106790e254fd43d2caac082","first_computed_at":"2026-07-05T09:21:32.797072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:21:32.797072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1SWCtQ22yotaR8NWLHOMoSqmswpG3AQeVZl87taFhq6EIc+d4vzv89Qaj0D+ZAjx4oWe8S4D/pCqaaSE5D8RCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:21:32.797554Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.12712","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:281b570031a4a86f10008f6c13b5353950c3946e489fee38155251c94ea0c396","sha256:cb229cee4686e8e9e5e7371c20fe7fb3f144f2d66223347534249bbaf2be23b8"],"state_sha256":"d0ae7d93102b24a03bca13c445fecb8d23be5fa1794b08751daf1775683ed0d0"}