{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WPEJJYX22U7KVINCE4OXYPQNE7","short_pith_number":"pith:WPEJJYX2","schema_version":"1.0","canonical_sha256":"b3c894e2fad53eaaa1a2271d7c3e0d27cc2859c0901ad5540de7233aa87a5a84","source":{"kind":"arxiv","id":"1203.3329","version":1},"attestation_state":"computed","paper":{"title":"On quantum information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.IT","math.MP"],"primary_cat":"cs.IT","authors_text":"Adam Paszkiewicz, Tomasz Sobieszek","submitted_at":"2012-03-15T11:41:04Z","abstract_excerpt":"We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator {\\rho}, tr {\\rho}=1. Let I(P)\\in R be defined for any partition P = (P_1,...,P_m), P_1+ ... +P_m=1_H, P_i \\in proj H$ and let I(P_i Qj, i \\leq m, j \\leq n) = I(P) + I(Q) for Q =(Q_1,..., Q_n), \\sum Q_j = 1_H and P_iQ_j = Q_j P_i, tr {\\rho} P_iQ_j = tr {\\rho} P_i tr {\\rho} Q_j (P, Q are physically independent). Assuming some continuity properties we give a general form of generalised information I."},"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":"1203.3329","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-15T11:41:04Z","cross_cats_sorted":["math-ph","math.IT","math.MP"],"title_canon_sha256":"c9adc686fe7ac4b089ed82eb615639e10394160081cd9455d250984aaf7f8c99","abstract_canon_sha256":"59c4c9054ab49bf329885dc0aba6f784668afa3e386f6b61214e290062a4a2cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:02.091236Z","signature_b64":"W/kFuVZGu8GZvaC+bhGsOdFAUqq0HB5EFhFUIDEVfSlwYlp8qGKPRWfxf7B4LeRaz3HNE9Lw7rn4iHSvdFa6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3c894e2fad53eaaa1a2271d7c3e0d27cc2859c0901ad5540de7233aa87a5a84","last_reissued_at":"2026-05-18T04:00:02.090536Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:02.090536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On quantum information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.IT","math.MP"],"primary_cat":"cs.IT","authors_text":"Adam Paszkiewicz, Tomasz Sobieszek","submitted_at":"2012-03-15T11:41:04Z","abstract_excerpt":"We investigate the following generalisation of the entropy of quantum measurement. Let H be an infinite-dimensional separable Hilbert space with a 'density' operator {\\rho}, tr {\\rho}=1. Let I(P)\\in R be defined for any partition P = (P_1,...,P_m), P_1+ ... +P_m=1_H, P_i \\in proj H$ and let I(P_i Qj, i \\leq m, j \\leq n) = I(P) + I(Q) for Q =(Q_1,..., Q_n), \\sum Q_j = 1_H and P_iQ_j = Q_j P_i, tr {\\rho} P_iQ_j = tr {\\rho} P_i tr {\\rho} Q_j (P, Q are physically independent). Assuming some continuity properties we give a general form of generalised information I."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3329","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":"1203.3329","created_at":"2026-05-18T04:00:02.090641+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.3329v1","created_at":"2026-05-18T04:00:02.090641+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3329","created_at":"2026-05-18T04:00:02.090641+00:00"},{"alias_kind":"pith_short_12","alias_value":"WPEJJYX22U7K","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WPEJJYX22U7KVINC","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WPEJJYX2","created_at":"2026-05-18T12:27:25.539911+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/WPEJJYX22U7KVINCE4OXYPQNE7","json":"https://pith.science/pith/WPEJJYX22U7KVINCE4OXYPQNE7.json","graph_json":"https://pith.science/api/pith-number/WPEJJYX22U7KVINCE4OXYPQNE7/graph.json","events_json":"https://pith.science/api/pith-number/WPEJJYX22U7KVINCE4OXYPQNE7/events.json","paper":"https://pith.science/paper/WPEJJYX2"},"agent_actions":{"view_html":"https://pith.science/pith/WPEJJYX22U7KVINCE4OXYPQNE7","download_json":"https://pith.science/pith/WPEJJYX22U7KVINCE4OXYPQNE7.json","view_paper":"https://pith.science/paper/WPEJJYX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.3329&json=true","fetch_graph":"https://pith.science/api/pith-number/WPEJJYX22U7KVINCE4OXYPQNE7/graph.json","fetch_events":"https://pith.science/api/pith-number/WPEJJYX22U7KVINCE4OXYPQNE7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WPEJJYX22U7KVINCE4OXYPQNE7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WPEJJYX22U7KVINCE4OXYPQNE7/action/storage_attestation","attest_author":"https://pith.science/pith/WPEJJYX22U7KVINCE4OXYPQNE7/action/author_attestation","sign_citation":"https://pith.science/pith/WPEJJYX22U7KVINCE4OXYPQNE7/action/citation_signature","submit_replication":"https://pith.science/pith/WPEJJYX22U7KVINCE4OXYPQNE7/action/replication_record"}},"created_at":"2026-05-18T04:00:02.090641+00:00","updated_at":"2026-05-18T04:00:02.090641+00:00"}