{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:6BKQ3K4VKWE424XEA7OUI5EIYG","short_pith_number":"pith:6BKQ3K4V","canonical_record":{"source":{"id":"2107.10521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-07-22T08:46:41Z","cross_cats_sorted":[],"title_canon_sha256":"d42b1838424e5763d709922c788f31c747895ee50c0d5a0d66098b6cf990b19d","abstract_canon_sha256":"d788c9f36fc7150d6e688026e44d034f2617eaad67c68fa76d607d4377ea32fc"},"schema_version":"1.0"},"canonical_sha256":"f0550dab955589cd72e407dd447488c193ca5a207d08c1fcdf6c50a759b3c3c1","source":{"kind":"arxiv","id":"2107.10521","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.10521","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"arxiv_version","alias_value":"2107.10521v1","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.10521","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"pith_short_12","alias_value":"6BKQ3K4VKWE4","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"pith_short_16","alias_value":"6BKQ3K4VKWE424XE","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"pith_short_8","alias_value":"6BKQ3K4V","created_at":"2026-07-05T04:16:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:6BKQ3K4VKWE424XEA7OUI5EIYG","target":"record","payload":{"canonical_record":{"source":{"id":"2107.10521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-07-22T08:46:41Z","cross_cats_sorted":[],"title_canon_sha256":"d42b1838424e5763d709922c788f31c747895ee50c0d5a0d66098b6cf990b19d","abstract_canon_sha256":"d788c9f36fc7150d6e688026e44d034f2617eaad67c68fa76d607d4377ea32fc"},"schema_version":"1.0"},"canonical_sha256":"f0550dab955589cd72e407dd447488c193ca5a207d08c1fcdf6c50a759b3c3c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:16:13.025755Z","signature_b64":"9WTiviQ8k0VGvlJCl+8oSMZ5t0mqU85dKbRdsDyyPmGb7IvKpEumoKwaoPxv6bUFLiPcAnpz97GEkBPGSV5XBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0550dab955589cd72e407dd447488c193ca5a207d08c1fcdf6c50a759b3c3c1","last_reissued_at":"2026-07-05T04:16:13.025299Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:16:13.025299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.10521","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:16:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rRZ6Vpa0J8+WclWExgAFFAM0nKX06+YIqGLRrKs1CYMRC176b/NVDmkPUGI4Zeuz0lPyc3gDEWM4AvCBpgapBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T14:55:03.713988Z"},"content_sha256":"24df61b39ca70542b6f69db98e32a6f3cfbd5948e06ad8b4a062266b21bb349d","schema_version":"1.0","event_id":"sha256:24df61b39ca70542b6f69db98e32a6f3cfbd5948e06ad8b4a062266b21bb349d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:6BKQ3K4VKWE424XEA7OUI5EIYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kramers-Kronig relations and precision limits in quantum phase estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Adriano Verna, Francesco Albarelli, Ilaria Gianani, Marco Barbieri, Rafal Demkowicz-Dobrzanski, Valeria Cimini","submitted_at":"2021-07-22T08:46:41Z","abstract_excerpt":"The ultimate precision in any measurement is dictated by the physical process implementing the observation. The methods of quantum metrology have now succeeded in establishing bounds on the achievable precision for phase measurements over noisy channels. In particular, they demonstrate how the Heisenberg scaling of the precision can not be attained in these conditions. Here we discuss how the ultimate bound in presence of loss has a physical motivation in the Kramers-Kronig relations and we show how they link the precision on the phase estimation to that on the loss parameter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.10521","kind":"arxiv","version":1},"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/2107.10521/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:16:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dJR4KwJ7DEw1b/A02auyZjb2jjqQfEDavPaNCU/Kp6+MfiM2FiR7eNL4Rs+uRd7As481EHq0+Nn+qCioUDm8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T14:55:03.714515Z"},"content_sha256":"08931a503214863176fbf671991bb934df87c4c4823ebaed2395b4e577e2fac6","schema_version":"1.0","event_id":"sha256:08931a503214863176fbf671991bb934df87c4c4823ebaed2395b4e577e2fac6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6BKQ3K4VKWE424XEA7OUI5EIYG/bundle.json","state_url":"https://pith.science/pith/6BKQ3K4VKWE424XEA7OUI5EIYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6BKQ3K4VKWE424XEA7OUI5EIYG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-21T14:55:03Z","links":{"resolver":"https://pith.science/pith/6BKQ3K4VKWE424XEA7OUI5EIYG","bundle":"https://pith.science/pith/6BKQ3K4VKWE424XEA7OUI5EIYG/bundle.json","state":"https://pith.science/pith/6BKQ3K4VKWE424XEA7OUI5EIYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6BKQ3K4VKWE424XEA7OUI5EIYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:6BKQ3K4VKWE424XEA7OUI5EIYG","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":"d788c9f36fc7150d6e688026e44d034f2617eaad67c68fa76d607d4377ea32fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-07-22T08:46:41Z","title_canon_sha256":"d42b1838424e5763d709922c788f31c747895ee50c0d5a0d66098b6cf990b19d"},"schema_version":"1.0","source":{"id":"2107.10521","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.10521","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"arxiv_version","alias_value":"2107.10521v1","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.10521","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"pith_short_12","alias_value":"6BKQ3K4VKWE4","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"pith_short_16","alias_value":"6BKQ3K4VKWE424XE","created_at":"2026-07-05T04:16:13Z"},{"alias_kind":"pith_short_8","alias_value":"6BKQ3K4V","created_at":"2026-07-05T04:16:13Z"}],"graph_snapshots":[{"event_id":"sha256:08931a503214863176fbf671991bb934df87c4c4823ebaed2395b4e577e2fac6","target":"graph","created_at":"2026-07-05T04:16:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.10521/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The ultimate precision in any measurement is dictated by the physical process implementing the observation. The methods of quantum metrology have now succeeded in establishing bounds on the achievable precision for phase measurements over noisy channels. In particular, they demonstrate how the Heisenberg scaling of the precision can not be attained in these conditions. Here we discuss how the ultimate bound in presence of loss has a physical motivation in the Kramers-Kronig relations and we show how they link the precision on the phase estimation to that on the loss parameter.","authors_text":"Adriano Verna, Francesco Albarelli, Ilaria Gianani, Marco Barbieri, Rafal Demkowicz-Dobrzanski, Valeria Cimini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-07-22T08:46:41Z","title":"Kramers-Kronig relations and precision limits in quantum phase estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.10521","kind":"arxiv","version":1},"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":"sha256:24df61b39ca70542b6f69db98e32a6f3cfbd5948e06ad8b4a062266b21bb349d","target":"record","created_at":"2026-07-05T04:16:13Z","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":"d788c9f36fc7150d6e688026e44d034f2617eaad67c68fa76d607d4377ea32fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2021-07-22T08:46:41Z","title_canon_sha256":"d42b1838424e5763d709922c788f31c747895ee50c0d5a0d66098b6cf990b19d"},"schema_version":"1.0","source":{"id":"2107.10521","kind":"arxiv","version":1}},"canonical_sha256":"f0550dab955589cd72e407dd447488c193ca5a207d08c1fcdf6c50a759b3c3c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0550dab955589cd72e407dd447488c193ca5a207d08c1fcdf6c50a759b3c3c1","first_computed_at":"2026-07-05T04:16:13.025299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:16:13.025299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9WTiviQ8k0VGvlJCl+8oSMZ5t0mqU85dKbRdsDyyPmGb7IvKpEumoKwaoPxv6bUFLiPcAnpz97GEkBPGSV5XBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:16:13.025755Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.10521","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24df61b39ca70542b6f69db98e32a6f3cfbd5948e06ad8b4a062266b21bb349d","sha256:08931a503214863176fbf671991bb934df87c4c4823ebaed2395b4e577e2fac6"],"state_sha256":"8e1418a455dc3c6a73a9150060dd91272aac8c549edffee51ef377a04546a6c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9WE0rGbIYg5RhNH+rwsOmrEKC/c0bRyKwtNOo/lUyowS8kESNZXg+I+3txocyvUdyc7S3oDhhh45idAb1ksPCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T14:55:03.719443Z","bundle_sha256":"07ab887908c5ed6d98144c3b1b2ce956f15b790a8ba4fb68f6d57d88cb3f4a2e"}}