{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AMIV2YBEO22IPWNEECFRJMWOG5","short_pith_number":"pith:AMIV2YBE","schema_version":"1.0","canonical_sha256":"03115d602476b487d9a4208b14b2ce3751e48ee23be15e61004ec20f22b663ef","source":{"kind":"arxiv","id":"1509.00082","version":1},"attestation_state":"computed","paper":{"title":"Quantum information as a non-Kolmogorovian generalization of Shannon's theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"F. Holik, G. Bellomo, G.M. Bosyk","submitted_at":"2015-08-31T21:36:29Z","abstract_excerpt":"In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and 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":"1509.00082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-08-31T21:36:29Z","cross_cats_sorted":[],"title_canon_sha256":"3ba1bd5b05c210749a68f05915593299753b1ee967f70182857e89cdb1eb0749","abstract_canon_sha256":"2901cb4069cb53064bb6316892459cf52ed2d84f92fdd7a6b3a5f565e13618c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:48.137739Z","signature_b64":"OXJytVZXOglyyVNrIvjOLHAnUDDKNRSCvxhtKOSx2GrXiNZZMeGH5OHY0G8oqD5rRwIa8pazc1fb3pcMKBQ/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03115d602476b487d9a4208b14b2ce3751e48ee23be15e61004ec20f22b663ef","last_reissued_at":"2026-05-18T01:22:48.137017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:48.137017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum information as a non-Kolmogorovian generalization of Shannon's theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"F. Holik, G. Bellomo, G.M. Bosyk","submitted_at":"2015-08-31T21:36:29Z","abstract_excerpt":"In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00082","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":"1509.00082","created_at":"2026-05-18T01:22:48.137139+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.00082v1","created_at":"2026-05-18T01:22:48.137139+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00082","created_at":"2026-05-18T01:22:48.137139+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMIV2YBEO22I","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMIV2YBEO22IPWNE","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMIV2YBE","created_at":"2026-05-18T12:29:10.953037+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/AMIV2YBEO22IPWNEECFRJMWOG5","json":"https://pith.science/pith/AMIV2YBEO22IPWNEECFRJMWOG5.json","graph_json":"https://pith.science/api/pith-number/AMIV2YBEO22IPWNEECFRJMWOG5/graph.json","events_json":"https://pith.science/api/pith-number/AMIV2YBEO22IPWNEECFRJMWOG5/events.json","paper":"https://pith.science/paper/AMIV2YBE"},"agent_actions":{"view_html":"https://pith.science/pith/AMIV2YBEO22IPWNEECFRJMWOG5","download_json":"https://pith.science/pith/AMIV2YBEO22IPWNEECFRJMWOG5.json","view_paper":"https://pith.science/paper/AMIV2YBE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.00082&json=true","fetch_graph":"https://pith.science/api/pith-number/AMIV2YBEO22IPWNEECFRJMWOG5/graph.json","fetch_events":"https://pith.science/api/pith-number/AMIV2YBEO22IPWNEECFRJMWOG5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMIV2YBEO22IPWNEECFRJMWOG5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMIV2YBEO22IPWNEECFRJMWOG5/action/storage_attestation","attest_author":"https://pith.science/pith/AMIV2YBEO22IPWNEECFRJMWOG5/action/author_attestation","sign_citation":"https://pith.science/pith/AMIV2YBEO22IPWNEECFRJMWOG5/action/citation_signature","submit_replication":"https://pith.science/pith/AMIV2YBEO22IPWNEECFRJMWOG5/action/replication_record"}},"created_at":"2026-05-18T01:22:48.137139+00:00","updated_at":"2026-05-18T01:22:48.137139+00:00"}