{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:PRZJZ2NKVYUFLSFFCEGRCJIXIK","short_pith_number":"pith:PRZJZ2NK","schema_version":"1.0","canonical_sha256":"7c729ce9aaae2855c8a5110d11251742947f1011e3a0d894b76023b240fbc73f","source":{"kind":"arxiv","id":"1003.4982","version":2},"attestation_state":"computed","paper":{"title":"Concentration of measure for quantum states with a fixed expectation value","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"David Gross, Jens Eisert, Markus Mueller","submitted_at":"2010-03-25T19:54:28Z","abstract_excerpt":"Given some observable H of a finite-dimensional quantum system, we investigate the typical properties of random quantum state vectors that have a fixed expectation value with respect to H. Under some some conditions on the spectrum, we prove that this manifold of quantum states shows a concentration of measure phenomenon: any continuous function on this set is almost everywhere close to its mean. We also give a method to estimate the corresponding expectation values analytically, and we prove a formula for the typical reduced density matrix in the case that H is a sum of local observables. We "},"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":"1003.4982","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-03-25T19:54:28Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"3115b301104b6a0c8f5280ed3ab87838a3d67e800e86747d8a36619008e4e68a","abstract_canon_sha256":"cf9f406b5bb8632b5e0d8e173c310826105cd57d08d5931d09222b4dda4df86e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:13.311740Z","signature_b64":"bnO6Gt59KD4bXLXQnsFD3Ig5HnN2jrsYc6A5Xi+2hxDHNjMujRrDyxLlwRL9hqtEfqWOxcQ7RbQOJsKQijTODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c729ce9aaae2855c8a5110d11251742947f1011e3a0d894b76023b240fbc73f","last_reissued_at":"2026-05-18T04:23:13.311146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:13.311146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration of measure for quantum states with a fixed expectation value","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"David Gross, Jens Eisert, Markus Mueller","submitted_at":"2010-03-25T19:54:28Z","abstract_excerpt":"Given some observable H of a finite-dimensional quantum system, we investigate the typical properties of random quantum state vectors that have a fixed expectation value with respect to H. Under some some conditions on the spectrum, we prove that this manifold of quantum states shows a concentration of measure phenomenon: any continuous function on this set is almost everywhere close to its mean. We also give a method to estimate the corresponding expectation values analytically, and we prove a formula for the typical reduced density matrix in the case that H is a sum of local observables. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4982","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":""},"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":"1003.4982","created_at":"2026-05-18T04:23:13.311236+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.4982v2","created_at":"2026-05-18T04:23:13.311236+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4982","created_at":"2026-05-18T04:23:13.311236+00:00"},{"alias_kind":"pith_short_12","alias_value":"PRZJZ2NKVYUF","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"PRZJZ2NKVYUFLSFF","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"PRZJZ2NK","created_at":"2026-05-18T12:26:12.377268+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/PRZJZ2NKVYUFLSFFCEGRCJIXIK","json":"https://pith.science/pith/PRZJZ2NKVYUFLSFFCEGRCJIXIK.json","graph_json":"https://pith.science/api/pith-number/PRZJZ2NKVYUFLSFFCEGRCJIXIK/graph.json","events_json":"https://pith.science/api/pith-number/PRZJZ2NKVYUFLSFFCEGRCJIXIK/events.json","paper":"https://pith.science/paper/PRZJZ2NK"},"agent_actions":{"view_html":"https://pith.science/pith/PRZJZ2NKVYUFLSFFCEGRCJIXIK","download_json":"https://pith.science/pith/PRZJZ2NKVYUFLSFFCEGRCJIXIK.json","view_paper":"https://pith.science/paper/PRZJZ2NK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.4982&json=true","fetch_graph":"https://pith.science/api/pith-number/PRZJZ2NKVYUFLSFFCEGRCJIXIK/graph.json","fetch_events":"https://pith.science/api/pith-number/PRZJZ2NKVYUFLSFFCEGRCJIXIK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PRZJZ2NKVYUFLSFFCEGRCJIXIK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PRZJZ2NKVYUFLSFFCEGRCJIXIK/action/storage_attestation","attest_author":"https://pith.science/pith/PRZJZ2NKVYUFLSFFCEGRCJIXIK/action/author_attestation","sign_citation":"https://pith.science/pith/PRZJZ2NKVYUFLSFFCEGRCJIXIK/action/citation_signature","submit_replication":"https://pith.science/pith/PRZJZ2NKVYUFLSFFCEGRCJIXIK/action/replication_record"}},"created_at":"2026-05-18T04:23:13.311236+00:00","updated_at":"2026-05-18T04:23:13.311236+00:00"}