{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RNLSB2VSU53KSKOHVKTYXEWEH2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a7abb92644e1bcbeca52c108251ac8fd72a9fd081185298a4e062caeced29c48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-06-06T01:37:51Z","title_canon_sha256":"a6a97343c7dd630d57d3bf54165065ea7e308cbb23bb962df88e6e456620a9ba"},"schema_version":"1.0","source":{"id":"1306.1279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1279","created_at":"2026-05-18T03:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1279v2","created_at":"2026-05-18T03:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1279","created_at":"2026-05-18T03:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"RNLSB2VSU53K","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RNLSB2VSU53KSKOH","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RNLSB2VS","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:d640784452d275a8a65c38ea85a306c6e8a07285925ec40dd7c8aa2ce0bcce36","target":"graph","created_at":"2026-05-18T03:12:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramer-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as 1/omega^p with p>1, the minimum mean-square error in any (single-time) phase estimate scales as N^{-2(p-1)/(p+1)}, where N is the photon flux. This gives the usual Heisenberg limit for a constant phase (as the limit p--> infinity) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phas","authors_text":"Dominic W. Berry, Howard M. Wiseman, Michael J. W. Hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-06-06T01:37:51Z","title":"Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1279","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:91e6ebd5a1c865653bdb90ea425843443bede4d6e3dd10f05e607e595f73e238","target":"record","created_at":"2026-05-18T03:12:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a7abb92644e1bcbeca52c108251ac8fd72a9fd081185298a4e062caeced29c48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-06-06T01:37:51Z","title_canon_sha256":"a6a97343c7dd630d57d3bf54165065ea7e308cbb23bb962df88e6e456620a9ba"},"schema_version":"1.0","source":{"id":"1306.1279","kind":"arxiv","version":2}},"canonical_sha256":"8b5720eab2a776a929c7aaa78b92c43e9f6e8dbb73e85d5e9ae9a01f0967b723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b5720eab2a776a929c7aaa78b92c43e9f6e8dbb73e85d5e9ae9a01f0967b723","first_computed_at":"2026-05-18T03:12:48.122048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:48.122048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bmpD1HDddVGqlCGNRAwTrEAjtSPEV9p8gVonJ7MlMy4B5uyhxBPd0ApQUIjkO6H9W+bWkLh3JvbzV7+izxMAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:48.122778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91e6ebd5a1c865653bdb90ea425843443bede4d6e3dd10f05e607e595f73e238","sha256:d640784452d275a8a65c38ea85a306c6e8a07285925ec40dd7c8aa2ce0bcce36"],"state_sha256":"ea5e03da53ef043f2b857d524d7bb44cc4f8d0fffb171d23a68dca0fa954c823"}