{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NRU75IJCYGUBR6EPLSGTD3BARL","short_pith_number":"pith:NRU75IJC","schema_version":"1.0","canonical_sha256":"6c69fea122c1a818f88f5c8d31ec208af43794312b6e533eb17157187a11d598","source":{"kind":"arxiv","id":"1111.0788","version":3},"attestation_state":"computed","paper":{"title":"Universality of the Heisenberg limit for estimates of random phase shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dominic W. Berry, Howard M. Wiseman, Marcin Zwierz, Michael J. W. Hall","submitted_at":"2011-11-03T10:55:50Z","abstract_excerpt":"The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/<N>, where <N> is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited, to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts. Our result gives the first completely general, constraint-free and non-asymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including mu"},"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":"1111.0788","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-03T10:55:50Z","cross_cats_sorted":[],"title_canon_sha256":"722122a58f652a53e788b843a871c8cd3c81306f425e4cd29e91c93f110041b3","abstract_canon_sha256":"9496762e65f1acf5894767a82d05b721a21e01efbaeec8e518e03cbc77a00ece"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:47.904857Z","signature_b64":"GVG+4pFy7PTGzHOhEhYpS8X7NH7gm4d8unJt/m/43RR8dgOEXntvFOuYA+0KAxk3NEHm17R/kylfwPf/ozJXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c69fea122c1a818f88f5c8d31ec208af43794312b6e533eb17157187a11d598","last_reissued_at":"2026-05-18T01:59:47.904168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:47.904168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universality of the Heisenberg limit for estimates of random phase shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dominic W. Berry, Howard M. Wiseman, Marcin Zwierz, Michael J. W. Hall","submitted_at":"2011-11-03T10:55:50Z","abstract_excerpt":"The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/<N>, where <N> is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited, to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts. Our result gives the first completely general, constraint-free and non-asymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0788","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":"1111.0788","created_at":"2026-05-18T01:59:47.904267+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.0788v3","created_at":"2026-05-18T01:59:47.904267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0788","created_at":"2026-05-18T01:59:47.904267+00:00"},{"alias_kind":"pith_short_12","alias_value":"NRU75IJCYGUB","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NRU75IJCYGUBR6EP","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NRU75IJC","created_at":"2026-05-18T12:26:37.096874+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/NRU75IJCYGUBR6EPLSGTD3BARL","json":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL.json","graph_json":"https://pith.science/api/pith-number/NRU75IJCYGUBR6EPLSGTD3BARL/graph.json","events_json":"https://pith.science/api/pith-number/NRU75IJCYGUBR6EPLSGTD3BARL/events.json","paper":"https://pith.science/paper/NRU75IJC"},"agent_actions":{"view_html":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL","download_json":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL.json","view_paper":"https://pith.science/paper/NRU75IJC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.0788&json=true","fetch_graph":"https://pith.science/api/pith-number/NRU75IJCYGUBR6EPLSGTD3BARL/graph.json","fetch_events":"https://pith.science/api/pith-number/NRU75IJCYGUBR6EPLSGTD3BARL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/action/storage_attestation","attest_author":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/action/author_attestation","sign_citation":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/action/citation_signature","submit_replication":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/action/replication_record"}},"created_at":"2026-05-18T01:59:47.904267+00:00","updated_at":"2026-05-18T01:59:47.904267+00:00"}