{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:P3H6DBTX7QOPSAEJV5KLQ7O3AR","short_pith_number":"pith:P3H6DBTX","schema_version":"1.0","canonical_sha256":"7ecfe18677fc1cf90089af54b87ddb046f9ab9a30707da07244925b9340bb8a5","source":{"kind":"arxiv","id":"1503.02471","version":1},"attestation_state":"computed","paper":{"title":"Geometry of Gaussian quantum states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Valentin Link, Walter T. Strunz","submitted_at":"2015-03-09T13:35:08Z","abstract_excerpt":"We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for a"},"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":"1503.02471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-03-09T13:35:08Z","cross_cats_sorted":[],"title_canon_sha256":"a02016bcebf839f4d37577793e71ea34681903a8cee550740eedb7a2579fe709","abstract_canon_sha256":"809408fc04b91d49981206273b2046e0526af5934ce2f0b1290379454525a1cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.539535Z","signature_b64":"Ww/z2EYrA3gtVPd/ajMVGQfrUcjtt7o3/9LLRVZiRh9QsRGAIS8FK6yQ7iGYEbW8HRfyvFq5kWC4pPFVEMHWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ecfe18677fc1cf90089af54b87ddb046f9ab9a30707da07244925b9340bb8a5","last_reissued_at":"2026-05-18T02:25:19.539150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.539150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometry of Gaussian quantum states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Valentin Link, Walter T. Strunz","submitted_at":"2015-03-09T13:35:08Z","abstract_excerpt":"We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02471","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":""},"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":"1503.02471","created_at":"2026-05-18T02:25:19.539205+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02471v1","created_at":"2026-05-18T02:25:19.539205+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02471","created_at":"2026-05-18T02:25:19.539205+00:00"},{"alias_kind":"pith_short_12","alias_value":"P3H6DBTX7QOP","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"P3H6DBTX7QOPSAEJ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"P3H6DBTX","created_at":"2026-05-18T12:29:34.919912+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/P3H6DBTX7QOPSAEJV5KLQ7O3AR","json":"https://pith.science/pith/P3H6DBTX7QOPSAEJV5KLQ7O3AR.json","graph_json":"https://pith.science/api/pith-number/P3H6DBTX7QOPSAEJV5KLQ7O3AR/graph.json","events_json":"https://pith.science/api/pith-number/P3H6DBTX7QOPSAEJV5KLQ7O3AR/events.json","paper":"https://pith.science/paper/P3H6DBTX"},"agent_actions":{"view_html":"https://pith.science/pith/P3H6DBTX7QOPSAEJV5KLQ7O3AR","download_json":"https://pith.science/pith/P3H6DBTX7QOPSAEJV5KLQ7O3AR.json","view_paper":"https://pith.science/paper/P3H6DBTX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02471&json=true","fetch_graph":"https://pith.science/api/pith-number/P3H6DBTX7QOPSAEJV5KLQ7O3AR/graph.json","fetch_events":"https://pith.science/api/pith-number/P3H6DBTX7QOPSAEJV5KLQ7O3AR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P3H6DBTX7QOPSAEJV5KLQ7O3AR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P3H6DBTX7QOPSAEJV5KLQ7O3AR/action/storage_attestation","attest_author":"https://pith.science/pith/P3H6DBTX7QOPSAEJV5KLQ7O3AR/action/author_attestation","sign_citation":"https://pith.science/pith/P3H6DBTX7QOPSAEJV5KLQ7O3AR/action/citation_signature","submit_replication":"https://pith.science/pith/P3H6DBTX7QOPSAEJV5KLQ7O3AR/action/replication_record"}},"created_at":"2026-05-18T02:25:19.539205+00:00","updated_at":"2026-05-18T02:25:19.539205+00:00"}