{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2CHOEESJYSDZXVMGUF26ZNGMQ3","short_pith_number":"pith:2CHOEESJ","schema_version":"1.0","canonical_sha256":"d08ee21249c4879bd586a175ecb4cc86d9cfb50b7898a3095a043baaf82aa35e","source":{"kind":"arxiv","id":"1202.4810","version":3},"attestation_state":"computed","paper":{"title":"Probability density of quantum expectation values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lorenzo Campos Venuti, Paolo Zanardi","submitted_at":"2012-02-22T02:56:55Z","abstract_excerpt":"We consider the quantum expectation value \\mathcal{A}=\\<\\psi|A|\\psi\\> of an observable A over the state |\\psi\\> . We derive the exact probability distribution of \\mathcal{A} seen as a random variable when |\\psi\\> varies over the set of all pure states equipped with the Haar-induced measure. The probability density is obtained with elementary means by computing its characteristic function, both for non-degenerate and degenerate observables. To illustrate our results we compare the exact predictions for few concrete examples with the concentration bounds obtained using Levy's lemma. Finally we c"},"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":"1202.4810","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-22T02:56:55Z","cross_cats_sorted":[],"title_canon_sha256":"2a1d1d5af46dee2200521d38dc14bbcfb7720ed8c908e7dfe11b4c20ee816fe9","abstract_canon_sha256":"84492ac1a01265a7c2b2ef42be1c03629583ab0781c8a06fc253374dca3d6fca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:58:22.592073Z","signature_b64":"X5A6aY8E+65sDb+qe2Og58tRNZo/PhbkrNg2UOekYv9IyuZo4p4YlkbSto/kk2SKAi4m9THwr+mw0ePea8IUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d08ee21249c4879bd586a175ecb4cc86d9cfb50b7898a3095a043baaf82aa35e","last_reissued_at":"2026-05-18T01:58:22.591574Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:58:22.591574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probability density of quantum expectation values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lorenzo Campos Venuti, Paolo Zanardi","submitted_at":"2012-02-22T02:56:55Z","abstract_excerpt":"We consider the quantum expectation value \\mathcal{A}=\\<\\psi|A|\\psi\\> of an observable A over the state |\\psi\\> . We derive the exact probability distribution of \\mathcal{A} seen as a random variable when |\\psi\\> varies over the set of all pure states equipped with the Haar-induced measure. The probability density is obtained with elementary means by computing its characteristic function, both for non-degenerate and degenerate observables. To illustrate our results we compare the exact predictions for few concrete examples with the concentration bounds obtained using Levy's lemma. Finally we c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4810","kind":"arxiv","version":3},"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":"1202.4810","created_at":"2026-05-18T01:58:22.591662+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.4810v3","created_at":"2026-05-18T01:58:22.591662+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4810","created_at":"2026-05-18T01:58:22.591662+00:00"},{"alias_kind":"pith_short_12","alias_value":"2CHOEESJYSDZ","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2CHOEESJYSDZXVMG","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2CHOEESJ","created_at":"2026-05-18T12:26:50.516681+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/2CHOEESJYSDZXVMGUF26ZNGMQ3","json":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3.json","graph_json":"https://pith.science/api/pith-number/2CHOEESJYSDZXVMGUF26ZNGMQ3/graph.json","events_json":"https://pith.science/api/pith-number/2CHOEESJYSDZXVMGUF26ZNGMQ3/events.json","paper":"https://pith.science/paper/2CHOEESJ"},"agent_actions":{"view_html":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3","download_json":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3.json","view_paper":"https://pith.science/paper/2CHOEESJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.4810&json=true","fetch_graph":"https://pith.science/api/pith-number/2CHOEESJYSDZXVMGUF26ZNGMQ3/graph.json","fetch_events":"https://pith.science/api/pith-number/2CHOEESJYSDZXVMGUF26ZNGMQ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/action/storage_attestation","attest_author":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/action/author_attestation","sign_citation":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/action/citation_signature","submit_replication":"https://pith.science/pith/2CHOEESJYSDZXVMGUF26ZNGMQ3/action/replication_record"}},"created_at":"2026-05-18T01:58:22.591662+00:00","updated_at":"2026-05-18T01:58:22.591662+00:00"}