{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:J3FL777AE3ZRDDMXKXBKWWHWHJ","short_pith_number":"pith:J3FL777A","schema_version":"1.0","canonical_sha256":"4ecabfffe026f3118d9755c2ab58f63a4f887e12188ab8611fb349c4794dacbe","source":{"kind":"arxiv","id":"2101.03256","version":2},"attestation_state":"computed","paper":{"title":"Towards Optimal Transport for Quantum Densities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.OC"],"primary_cat":"math-ph","authors_text":"Emanuele Caglioti, Fran\\c{c}ois Golse, Thierry Paul","submitted_at":"2021-01-08T23:34:26Z","abstract_excerpt":"An analogue of the quadratic Wasserstein (or Monge-Kantorovich) distance between Borel probability measures on $\\mathbf{R}^d$ has been defined in [F. Golse, C. Mouhot, T. Paul: Commun. Math. Phys. 343 (2015), 165-205] for density operators on $L^2(\\mathbf{R}^d)$, and used to estimate the convergence rate of various asymptotic theories in the context of quantum mechanics. The present work proves a Kantorovich type duality theorem for this quantum variant of the Monge-Kantorovich or Wasserstein distance, and discusses the structure of optimal quantum couplings. Specifically, we prove that optima"},"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":"2101.03256","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2021-01-08T23:34:26Z","cross_cats_sorted":["math.MP","math.OC"],"title_canon_sha256":"21ebe6f070a1dcbb3554b73c4b08d26d965209754469e9885326cef83638f5de","abstract_canon_sha256":"86aa7964f10c44d59f8b937778206a2f73ce8564b0d712ed12f2677295a02da3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:13:34.147983Z","signature_b64":"KFEHCOcsWwdDqL7Ox9XiGBEhNotr+bgzsr+3srLWyDz80Lc91vIIN67+W1ivTvYGU/Dr80hO8fTVfNTQnkOvDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ecabfffe026f3118d9755c2ab58f63a4f887e12188ab8611fb349c4794dacbe","last_reissued_at":"2026-07-05T02:13:34.147518Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:13:34.147518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards Optimal Transport for Quantum Densities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.OC"],"primary_cat":"math-ph","authors_text":"Emanuele Caglioti, Fran\\c{c}ois Golse, Thierry Paul","submitted_at":"2021-01-08T23:34:26Z","abstract_excerpt":"An analogue of the quadratic Wasserstein (or Monge-Kantorovich) distance between Borel probability measures on $\\mathbf{R}^d$ has been defined in [F. Golse, C. Mouhot, T. Paul: Commun. Math. Phys. 343 (2015), 165-205] for density operators on $L^2(\\mathbf{R}^d)$, and used to estimate the convergence rate of various asymptotic theories in the context of quantum mechanics. The present work proves a Kantorovich type duality theorem for this quantum variant of the Monge-Kantorovich or Wasserstein distance, and discusses the structure of optimal quantum couplings. Specifically, we prove that optima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.03256","kind":"arxiv","version":2},"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/2101.03256/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":"2101.03256","created_at":"2026-07-05T02:13:34.147573+00:00"},{"alias_kind":"arxiv_version","alias_value":"2101.03256v2","created_at":"2026-07-05T02:13:34.147573+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.03256","created_at":"2026-07-05T02:13:34.147573+00:00"},{"alias_kind":"pith_short_12","alias_value":"J3FL777AE3ZR","created_at":"2026-07-05T02:13:34.147573+00:00"},{"alias_kind":"pith_short_16","alias_value":"J3FL777AE3ZRDDMX","created_at":"2026-07-05T02:13:34.147573+00:00"},{"alias_kind":"pith_short_8","alias_value":"J3FL777A","created_at":"2026-07-05T02:13:34.147573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.10075","citing_title":"An algorithm for dynamical quantum optimal transport with applications to quantum chemistry","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2501.08066","citing_title":"Wasserstein distances and divergences of order $p$ by quantum channels","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2506.09794","citing_title":"Wasserstein Distances on Quantum Structures: an Overview","ref_index":27,"is_internal_anchor":false},{"citing_arxiv_id":"2506.14523","citing_title":"Quantum Wasserstein distance and its relation to several types of fidelities","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03027","citing_title":"Relations between different definitions of the quantum Wasserstein distance for qubits","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03022","citing_title":"General method for obtaining the energy minimum of spin Hamiltonians for separable states","ref_index":48,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ","json":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ.json","graph_json":"https://pith.science/api/pith-number/J3FL777AE3ZRDDMXKXBKWWHWHJ/graph.json","events_json":"https://pith.science/api/pith-number/J3FL777AE3ZRDDMXKXBKWWHWHJ/events.json","paper":"https://pith.science/paper/J3FL777A"},"agent_actions":{"view_html":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ","download_json":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ.json","view_paper":"https://pith.science/paper/J3FL777A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2101.03256&json=true","fetch_graph":"https://pith.science/api/pith-number/J3FL777AE3ZRDDMXKXBKWWHWHJ/graph.json","fetch_events":"https://pith.science/api/pith-number/J3FL777AE3ZRDDMXKXBKWWHWHJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ/action/storage_attestation","attest_author":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ/action/author_attestation","sign_citation":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ/action/citation_signature","submit_replication":"https://pith.science/pith/J3FL777AE3ZRDDMXKXBKWWHWHJ/action/replication_record"}},"created_at":"2026-07-05T02:13:34.147573+00:00","updated_at":"2026-07-05T02:13:34.147573+00:00"}