{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:XPILLQLDTFTDGWND5RTWHFRFGV","short_pith_number":"pith:XPILLQLD","schema_version":"1.0","canonical_sha256":"bbd0b5c16399663359a3ec6763962535754c72c8bc1d242f771a302523d654fc","source":{"kind":"arxiv","id":"2404.04136","version":1},"attestation_state":"computed","paper":{"title":"Geodesics for mixed quantum states via their geometric mean operator","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Carlo Cafaro, Paul M. Alsing, Shannon Ray","submitted_at":"2024-04-05T14:36:11Z","abstract_excerpt":"We examine the geodesic between two mixed states of arbitrary dimension by means of their geometric mean operator. We utilize the fiber bundle approach by which the distance between two mixed state density operators $\\rho_1$ and $\\rho_2$ in the base space $M$ is given by the shortest distance in the (Hilbert Schmidt) bundle space $E$ of their purifications. The latter is well-known to be given by the Bures distance along the horizontal lift in $E$ of the geodesic between the $\\rho_1$ and $\\rho_2$ in $M$. The horizontal lift is that unique curve in $E$ that orthogonally traverses the fibers $F\\"},"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":"2404.04136","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"quant-ph","submitted_at":"2024-04-05T14:36:11Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2300f4b66814a8abf0e89ac123aebe77297d2d15636579bdf59b4826ce651ba8","abstract_canon_sha256":"d3d3224714edd14c1079f59e146756cfe4e860c238df98681fcb5aa79ee31ed7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:46.106861Z","signature_b64":"qu9vFJxm0rnhh/HlyVlqwTwjGz/ufsBaWLR6gUrZykbfjzDLGRYwhK7TSOoI164tZS5LzFaIygF9rlBhHpSzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbd0b5c16399663359a3ec6763962535754c72c8bc1d242f771a302523d654fc","last_reissued_at":"2026-07-05T08:04:46.106399Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:46.106399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geodesics for mixed quantum states via their geometric mean operator","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Carlo Cafaro, Paul M. Alsing, Shannon Ray","submitted_at":"2024-04-05T14:36:11Z","abstract_excerpt":"We examine the geodesic between two mixed states of arbitrary dimension by means of their geometric mean operator. We utilize the fiber bundle approach by which the distance between two mixed state density operators $\\rho_1$ and $\\rho_2$ in the base space $M$ is given by the shortest distance in the (Hilbert Schmidt) bundle space $E$ of their purifications. The latter is well-known to be given by the Bures distance along the horizontal lift in $E$ of the geodesic between the $\\rho_1$ and $\\rho_2$ in $M$. The horizontal lift is that unique curve in $E$ that orthogonally traverses the fibers $F\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.04136","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/2404.04136/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":"2404.04136","created_at":"2026-07-05T08:04:46.106452+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.04136v1","created_at":"2026-07-05T08:04:46.106452+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.04136","created_at":"2026-07-05T08:04:46.106452+00:00"},{"alias_kind":"pith_short_12","alias_value":"XPILLQLDTFTD","created_at":"2026-07-05T08:04:46.106452+00:00"},{"alias_kind":"pith_short_16","alias_value":"XPILLQLDTFTDGWND","created_at":"2026-07-05T08:04:46.106452+00:00"},{"alias_kind":"pith_short_8","alias_value":"XPILLQLD","created_at":"2026-07-05T08:04:46.106452+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.12071","citing_title":"A thermofield-double model of Uhlmann anholonomy","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV","json":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV.json","graph_json":"https://pith.science/api/pith-number/XPILLQLDTFTDGWND5RTWHFRFGV/graph.json","events_json":"https://pith.science/api/pith-number/XPILLQLDTFTDGWND5RTWHFRFGV/events.json","paper":"https://pith.science/paper/XPILLQLD"},"agent_actions":{"view_html":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV","download_json":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV.json","view_paper":"https://pith.science/paper/XPILLQLD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.04136&json=true","fetch_graph":"https://pith.science/api/pith-number/XPILLQLDTFTDGWND5RTWHFRFGV/graph.json","fetch_events":"https://pith.science/api/pith-number/XPILLQLDTFTDGWND5RTWHFRFGV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV/action/storage_attestation","attest_author":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV/action/author_attestation","sign_citation":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV/action/citation_signature","submit_replication":"https://pith.science/pith/XPILLQLDTFTDGWND5RTWHFRFGV/action/replication_record"}},"created_at":"2026-07-05T08:04:46.106452+00:00","updated_at":"2026-07-05T08:04:46.106452+00:00"}