{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:53ZKYJGSRR6VK3TYYCFSM76SW2","short_pith_number":"pith:53ZKYJGS","schema_version":"1.0","canonical_sha256":"eef2ac24d28c7d556e78c08b267fd2b693c3c12675b0bf94da85788d637f1ec8","source":{"kind":"arxiv","id":"2509.01571","version":1},"attestation_state":"computed","paper":{"title":"Measuring Less to Learn More: Quadratic Speedup in learning Nonlinear Properties of Quantum Density Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Xiao Yuan, You Zhou, Yukun Zhang, Yusen Wu","submitted_at":"2025-09-01T15:56:49Z","abstract_excerpt":"A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\\mathrm{Tr}(\\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of the state $\\rho$, and we rigorously establish this lower bound under sample access to $\\rho$. Surprisingly, this limitation can be overcome when one has purified access via a unitary that prepares a purification of $\\rho$, a scenario naturally arising in quantum simulation and computation. In this setting, we find a different lower bound of $\\Theta(\\sqrt{k})$,"},"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":"2509.01571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-09-01T15:56:49Z","cross_cats_sorted":[],"title_canon_sha256":"32a29069a4c7da432d3113eb4862e95c198b5efe1ee6407a981fce79f6f8a76d","abstract_canon_sha256":"7713b1560dbf2b5566131b875b211e5f97b901349c3e53e852c40dd6e75ee371"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:03.458227Z","signature_b64":"May2H7eDcbx8INkCcItFR7Gs0A6vCu5fKgjMU6hYG7eBN+0q9TIjCCeka+peBWa2mqlhHX5ljgBa8BHWbNDjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eef2ac24d28c7d556e78c08b267fd2b693c3c12675b0bf94da85788d637f1ec8","last_reissued_at":"2026-07-05T12:03:03.457552Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:03.457552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Measuring Less to Learn More: Quadratic Speedup in learning Nonlinear Properties of Quantum Density Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Xiao Yuan, You Zhou, Yukun Zhang, Yusen Wu","submitted_at":"2025-09-01T15:56:49Z","abstract_excerpt":"A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\\mathrm{Tr}(\\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of the state $\\rho$, and we rigorously establish this lower bound under sample access to $\\rho$. Surprisingly, this limitation can be overcome when one has purified access via a unitary that prepares a purification of $\\rho$, a scenario naturally arising in quantum simulation and computation. In this setting, we find a different lower bound of $\\Theta(\\sqrt{k})$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01571","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/2509.01571/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":"2509.01571","created_at":"2026-07-05T12:03:03.457617+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.01571v1","created_at":"2026-07-05T12:03:03.457617+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01571","created_at":"2026-07-05T12:03:03.457617+00:00"},{"alias_kind":"pith_short_12","alias_value":"53ZKYJGSRR6V","created_at":"2026-07-05T12:03:03.457617+00:00"},{"alias_kind":"pith_short_16","alias_value":"53ZKYJGSRR6VK3TY","created_at":"2026-07-05T12:03:03.457617+00:00"},{"alias_kind":"pith_short_8","alias_value":"53ZKYJGS","created_at":"2026-07-05T12:03:03.457617+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.03496","citing_title":"Information-Theoretic Lower Bounds for Approximating Monomials via Optimal Quantum Tsallis Entropy Estimation","ref_index":134,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2","json":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2.json","graph_json":"https://pith.science/api/pith-number/53ZKYJGSRR6VK3TYYCFSM76SW2/graph.json","events_json":"https://pith.science/api/pith-number/53ZKYJGSRR6VK3TYYCFSM76SW2/events.json","paper":"https://pith.science/paper/53ZKYJGS"},"agent_actions":{"view_html":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2","download_json":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2.json","view_paper":"https://pith.science/paper/53ZKYJGS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.01571&json=true","fetch_graph":"https://pith.science/api/pith-number/53ZKYJGSRR6VK3TYYCFSM76SW2/graph.json","fetch_events":"https://pith.science/api/pith-number/53ZKYJGSRR6VK3TYYCFSM76SW2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2/action/storage_attestation","attest_author":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2/action/author_attestation","sign_citation":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2/action/citation_signature","submit_replication":"https://pith.science/pith/53ZKYJGSRR6VK3TYYCFSM76SW2/action/replication_record"}},"created_at":"2026-07-05T12:03:03.457617+00:00","updated_at":"2026-07-05T12:03:03.457617+00:00"}