{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:PZHH7RMSKAMYILGLADAZJ67SQJ","short_pith_number":"pith:PZHH7RMS","schema_version":"1.0","canonical_sha256":"7e4e7fc5925019842ccb00c194fbf282749a69488757be957d6ff1d37e728952","source":{"kind":"arxiv","id":"2404.19105","version":2},"attestation_state":"computed","paper":{"title":"Optimal tradeoffs for estimating Pauli observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Qi Ye, Sitan Chen, Weiyuan Gong","submitted_at":"2024-04-29T20:57:05Z","abstract_excerpt":"We revisit the problem of Pauli shadow tomography: given copies of an unknown $n$-qubit quantum state $\\rho$, estimate $\\text{tr}(P\\rho)$ for some set of Pauli operators $P$ to within additive error $\\epsilon$. This has been a popular testbed for exploring the advantage of protocols with quantum memory over those without: with enough memory to measure two copies at a time, one can use Bell sampling to estimate $|\\text{tr}(P\\rho)|$ for all $P$ using $O(n/\\epsilon^4)$ copies, but with $k\\le n$ qubits of memory, $\\Omega(2^{(n-k)/3})$ copies are needed.\n  These results leave open several natural q"},"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":"2404.19105","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2024-04-29T20:57:05Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"d716cc54cd98c07fc5b003e18335f9e77d5b9c9bc19cde8904558bcd1b7cc54f","abstract_canon_sha256":"bd3ee797ef796a18870cec27e7f71d7741d503f946e6aa6ce70d764d13904143"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:35:48.779920Z","signature_b64":"bCspDVNmHW1qQWYL1SSniUEjW6oKt9jDpDV3qnrDMdpjpKDRq1cjIBIQXtqkshFZLgD03QVUxIYBq2x7ewAaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e4e7fc5925019842ccb00c194fbf282749a69488757be957d6ff1d37e728952","last_reissued_at":"2026-07-05T09:35:48.779392Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:35:48.779392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal tradeoffs for estimating Pauli observables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Qi Ye, Sitan Chen, Weiyuan Gong","submitted_at":"2024-04-29T20:57:05Z","abstract_excerpt":"We revisit the problem of Pauli shadow tomography: given copies of an unknown $n$-qubit quantum state $\\rho$, estimate $\\text{tr}(P\\rho)$ for some set of Pauli operators $P$ to within additive error $\\epsilon$. This has been a popular testbed for exploring the advantage of protocols with quantum memory over those without: with enough memory to measure two copies at a time, one can use Bell sampling to estimate $|\\text{tr}(P\\rho)|$ for all $P$ using $O(n/\\epsilon^4)$ copies, but with $k\\le n$ qubits of memory, $\\Omega(2^{(n-k)/3})$ copies are needed.\n  These results leave open several natural q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.19105","kind":"arxiv","version":2},"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/2404.19105/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":"2404.19105","created_at":"2026-07-05T09:35:48.779446+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.19105v2","created_at":"2026-07-05T09:35:48.779446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.19105","created_at":"2026-07-05T09:35:48.779446+00:00"},{"alias_kind":"pith_short_12","alias_value":"PZHH7RMSKAMY","created_at":"2026-07-05T09:35:48.779446+00:00"},{"alias_kind":"pith_short_16","alias_value":"PZHH7RMSKAMYILGL","created_at":"2026-07-05T09:35:48.779446+00:00"},{"alias_kind":"pith_short_8","alias_value":"PZHH7RMS","created_at":"2026-07-05T09:35:48.779446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2505.00087","citing_title":"Quantum Glassiness From Efficient Learning","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2604.26043","citing_title":"An Exponential Advantage for Adaptive Tomography of Structured States under Pauli Basis Measurements","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02057","citing_title":"Exponential speedups in fault-tolerant processing of quantum experiments","ref_index":29,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ","json":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ.json","graph_json":"https://pith.science/api/pith-number/PZHH7RMSKAMYILGLADAZJ67SQJ/graph.json","events_json":"https://pith.science/api/pith-number/PZHH7RMSKAMYILGLADAZJ67SQJ/events.json","paper":"https://pith.science/paper/PZHH7RMS"},"agent_actions":{"view_html":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ","download_json":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ.json","view_paper":"https://pith.science/paper/PZHH7RMS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.19105&json=true","fetch_graph":"https://pith.science/api/pith-number/PZHH7RMSKAMYILGLADAZJ67SQJ/graph.json","fetch_events":"https://pith.science/api/pith-number/PZHH7RMSKAMYILGLADAZJ67SQJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ/action/storage_attestation","attest_author":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ/action/author_attestation","sign_citation":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ/action/citation_signature","submit_replication":"https://pith.science/pith/PZHH7RMSKAMYILGLADAZJ67SQJ/action/replication_record"}},"created_at":"2026-07-05T09:35:48.779446+00:00","updated_at":"2026-07-05T09:35:48.779446+00:00"}