{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:TIOCE247OMHCDGJST7PFCBQVTY","short_pith_number":"pith:TIOCE247","schema_version":"1.0","canonical_sha256":"9a1c226b9f730e2199329fde5106159e0f632cac2038e1741db043cdad3b251b","source":{"kind":"arxiv","id":"1003.4575","version":3},"attestation_state":"computed","paper":{"title":"Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Masahito Hayashi","submitted_at":"2010-03-24T04:19:04Z","abstract_excerpt":"In a unified viewpoint in quantum channel estimation, we compare the Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound, whose maximum is shown to be equal to the asymptotic limit of the mini-max bound. It is shown that the local asymptotic mini-max bound is strictly larger than the Cramer-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O(1/n). We also derive a sufficient condition for that the min"},"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":"1003.4575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-03-24T04:19:04Z","cross_cats_sorted":[],"title_canon_sha256":"fd4991cae4a1df07c6fbc268b606c9011d45a8634d62878225cdb42474cff3d5","abstract_canon_sha256":"ba2e0b520ad927cfe8288564de42a15e88f0731f140ae8d219537e52cdac4e07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:32.695635Z","signature_b64":"VOWS6y9byU388H5bJTCCZyjxjYNgPBbkYIbSbmnvOm8IhBNmM3KwUewFnZK8ix/7mJd4AZERFUg2pRRkHFSfCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a1c226b9f730e2199329fde5106159e0f632cac2038e1741db043cdad3b251b","last_reissued_at":"2026-05-18T04:19:32.695179Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:32.695179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Masahito Hayashi","submitted_at":"2010-03-24T04:19:04Z","abstract_excerpt":"In a unified viewpoint in quantum channel estimation, we compare the Cramer-Rao and the mini-max approaches, which gives the Bayesian bound in the group covariant model. For this purpose, we introduce the local asymptotic mini-max bound, whose maximum is shown to be equal to the asymptotic limit of the mini-max bound. It is shown that the local asymptotic mini-max bound is strictly larger than the Cramer-Rao bound in the phase estimation case while the both bounds coincide when the minimum mean square error decreases with the order O(1/n). We also derive a sufficient condition for that the min"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4575","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1003.4575","created_at":"2026-05-18T04:19:32.695240+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.4575v3","created_at":"2026-05-18T04:19:32.695240+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4575","created_at":"2026-05-18T04:19:32.695240+00:00"},{"alias_kind":"pith_short_12","alias_value":"TIOCE247OMHC","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"TIOCE247OMHCDGJS","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"TIOCE247","created_at":"2026-05-18T12:26:13.927090+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/TIOCE247OMHCDGJST7PFCBQVTY","json":"https://pith.science/pith/TIOCE247OMHCDGJST7PFCBQVTY.json","graph_json":"https://pith.science/api/pith-number/TIOCE247OMHCDGJST7PFCBQVTY/graph.json","events_json":"https://pith.science/api/pith-number/TIOCE247OMHCDGJST7PFCBQVTY/events.json","paper":"https://pith.science/paper/TIOCE247"},"agent_actions":{"view_html":"https://pith.science/pith/TIOCE247OMHCDGJST7PFCBQVTY","download_json":"https://pith.science/pith/TIOCE247OMHCDGJST7PFCBQVTY.json","view_paper":"https://pith.science/paper/TIOCE247","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.4575&json=true","fetch_graph":"https://pith.science/api/pith-number/TIOCE247OMHCDGJST7PFCBQVTY/graph.json","fetch_events":"https://pith.science/api/pith-number/TIOCE247OMHCDGJST7PFCBQVTY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TIOCE247OMHCDGJST7PFCBQVTY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TIOCE247OMHCDGJST7PFCBQVTY/action/storage_attestation","attest_author":"https://pith.science/pith/TIOCE247OMHCDGJST7PFCBQVTY/action/author_attestation","sign_citation":"https://pith.science/pith/TIOCE247OMHCDGJST7PFCBQVTY/action/citation_signature","submit_replication":"https://pith.science/pith/TIOCE247OMHCDGJST7PFCBQVTY/action/replication_record"}},"created_at":"2026-05-18T04:19:32.695240+00:00","updated_at":"2026-05-18T04:19:32.695240+00:00"}