{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:AJJPYXEMKG5YLRJEN7EAEWQ73S","short_pith_number":"pith:AJJPYXEM","schema_version":"1.0","canonical_sha256":"0252fc5c8c51bb85c5246fc8025a1fdc9a3fcd06cc1fff771eef475744862ce0","source":{"kind":"arxiv","id":"quant-ph/0501177","version":3},"attestation_state":"computed","paper":{"title":"For Distinguishing Conjugate Hidden Subgroups, the Pretty Good Measurement is as Good as it Gets","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander Russell, Cristopher Moore","submitted_at":"2005-01-31T09:30:35Z","abstract_excerpt":"Recently Bacon, Childs and van Dam showed that the ``pretty good measurement'' (PGM) is optimal for the Hidden Subgroup Problem on the dihedral group D_n in the case where the hidden subgroup is chosen uniformly from the n involutions. We show that, for any group and any subgroup H, the PGM is the optimal one-register experiment in the case where the hidden subgroup is a uniformly random conjugate of H. We go on to show that when H forms a Gel'fand pair with its parent group, the PGM is the optimal measurement for any number of registers. In both cases we bound the probability that the optimal"},"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":"quant-ph/0501177","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-31T09:30:35Z","cross_cats_sorted":[],"title_canon_sha256":"d4c84ca5b6778777c59bfc71ab56eb490d0320089bfe039eaa76ac188290d1df","abstract_canon_sha256":"57b3a422009bbce82572b229f75bb7100c094e55563e7377ae3341566217a108"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:46:54.841732Z","signature_b64":"GyN50DwVduaFOaU9ePwqOAddPX3cRSxbRUHYT1HpLmz2hgUJ/02ul5W4Ci+bOk5XBbkNNxQATelK8p79u63LDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0252fc5c8c51bb85c5246fc8025a1fdc9a3fcd06cc1fff771eef475744862ce0","last_reissued_at":"2026-07-04T14:46:54.841399Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:46:54.841399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"For Distinguishing Conjugate Hidden Subgroups, the Pretty Good Measurement is as Good as it Gets","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander Russell, Cristopher Moore","submitted_at":"2005-01-31T09:30:35Z","abstract_excerpt":"Recently Bacon, Childs and van Dam showed that the ``pretty good measurement'' (PGM) is optimal for the Hidden Subgroup Problem on the dihedral group D_n in the case where the hidden subgroup is chosen uniformly from the n involutions. We show that, for any group and any subgroup H, the PGM is the optimal one-register experiment in the case where the hidden subgroup is a uniformly random conjugate of H. We go on to show that when H forms a Gel'fand pair with its parent group, the PGM is the optimal measurement for any number of registers. In both cases we bound the probability that the optimal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0501177","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0501177/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":"quant-ph/0501177","created_at":"2026-07-04T14:46:54.841454+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0501177v3","created_at":"2026-07-04T14:46:54.841454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0501177","created_at":"2026-07-04T14:46:54.841454+00:00"},{"alias_kind":"pith_short_12","alias_value":"AJJPYXEMKG5Y","created_at":"2026-07-04T14:46:54.841454+00:00"},{"alias_kind":"pith_short_16","alias_value":"AJJPYXEMKG5YLRJE","created_at":"2026-07-04T14:46:54.841454+00:00"},{"alias_kind":"pith_short_8","alias_value":"AJJPYXEM","created_at":"2026-07-04T14:46:54.841454+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/AJJPYXEMKG5YLRJEN7EAEWQ73S","json":"https://pith.science/pith/AJJPYXEMKG5YLRJEN7EAEWQ73S.json","graph_json":"https://pith.science/api/pith-number/AJJPYXEMKG5YLRJEN7EAEWQ73S/graph.json","events_json":"https://pith.science/api/pith-number/AJJPYXEMKG5YLRJEN7EAEWQ73S/events.json","paper":"https://pith.science/paper/AJJPYXEM"},"agent_actions":{"view_html":"https://pith.science/pith/AJJPYXEMKG5YLRJEN7EAEWQ73S","download_json":"https://pith.science/pith/AJJPYXEMKG5YLRJEN7EAEWQ73S.json","view_paper":"https://pith.science/paper/AJJPYXEM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0501177&json=true","fetch_graph":"https://pith.science/api/pith-number/AJJPYXEMKG5YLRJEN7EAEWQ73S/graph.json","fetch_events":"https://pith.science/api/pith-number/AJJPYXEMKG5YLRJEN7EAEWQ73S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AJJPYXEMKG5YLRJEN7EAEWQ73S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AJJPYXEMKG5YLRJEN7EAEWQ73S/action/storage_attestation","attest_author":"https://pith.science/pith/AJJPYXEMKG5YLRJEN7EAEWQ73S/action/author_attestation","sign_citation":"https://pith.science/pith/AJJPYXEMKG5YLRJEN7EAEWQ73S/action/citation_signature","submit_replication":"https://pith.science/pith/AJJPYXEMKG5YLRJEN7EAEWQ73S/action/replication_record"}},"created_at":"2026-07-04T14:46:54.841454+00:00","updated_at":"2026-07-04T14:46:54.841454+00:00"}