{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PULXSSRUHYTLO3H2Z7DB43FJBR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"00dc9e0178d668238d8f66b5f6fcab34d75251da7bf981258afac697103a3b0d","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-31T00:22:40Z","title_canon_sha256":"cd00743699646357316aec0757b4000a786f018e77a3d6f9d6915a6899fca7b2"},"schema_version":"1.0","source":{"id":"1103.6067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.6067","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"arxiv_version","alias_value":"1103.6067v2","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.6067","created_at":"2026-05-18T04:04:44Z"},{"alias_kind":"pith_short_12","alias_value":"PULXSSRUHYTL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PULXSSRUHYTLO3H2","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PULXSSRU","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:dc258525af7b4b1c7375264303b687e9e948ca00b4e67e7af1ed43b53acab225","target":"graph","created_at":"2026-05-18T04:04:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The Quantum Substate Theorem due to Jain, Radhakrishnan, and Sen (2002) gives us a powerful operational interpretation of relative entropy, in fact, of the observational divergence of two quantum states, a quantity that is related to their relative entropy. Informally, the theorem states that if the observational divergence between two quantum states rho, sigma is small, then there is a quantum state rho' close to rho in trace distance, such that rho' when scaled down by a small factor becomes a substate of sigma. We present new proofs of this theorem. The resulting statement is optimal up to ","authors_text":"Ashwin Nayak, Rahul Jain","cross_cats":["cs.CC","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-31T00:22:40Z","title":"Short proofs of the Quantum Substate Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.6067","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e0ba2a2be9b457e73bb49ddcca0cbac912a01f1b9b77ff58158ec208bb1eaf00","target":"record","created_at":"2026-05-18T04:04:44Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"00dc9e0178d668238d8f66b5f6fcab34d75251da7bf981258afac697103a3b0d","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-03-31T00:22:40Z","title_canon_sha256":"cd00743699646357316aec0757b4000a786f018e77a3d6f9d6915a6899fca7b2"},"schema_version":"1.0","source":{"id":"1103.6067","kind":"arxiv","version":2}},"canonical_sha256":"7d17794a343e26b76cfacfc61e6ca90c7b8cd7b666514a58b33f983257645727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d17794a343e26b76cfacfc61e6ca90c7b8cd7b666514a58b33f983257645727","first_computed_at":"2026-05-18T04:04:44.800003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:44.800003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aA+GWBkPucCuUVWxn0bh6XTUEEpoSFbIYwe9W98fnFyS1hF/iaD/Rmo1x4AnFmKs4iH9ydiE1EGbxPNFykNkCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:44.800436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.6067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0ba2a2be9b457e73bb49ddcca0cbac912a01f1b9b77ff58158ec208bb1eaf00","sha256:dc258525af7b4b1c7375264303b687e9e948ca00b4e67e7af1ed43b53acab225"],"state_sha256":"43924b6de3447dd1e44bbf85ec7b73198bdc0d8ccb1d4e82ca3fe43877e7c100"}