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In the former setting, we prove that the upperbound and the lowerbund of $\\mathrm{D}^{Q}(\\rho||\\sigma) $ is $\\mathrm{D}^{R}(\\rho||\\sigma) :=\\mathrm{tr}% \\,\\rho\\ln\\sqrt{\\rho}\\sigma^{-1}\\sqrt{\\rho}$ and $\\mathrm{D}(\\rho||\\sigma) :=$ $\\mathrm{tr}\\,\\rho(\\ln\\rho-\\ln\\sigma) $, respectively. In the latter setting, we prove uniqueness of quantum relative entropy, that is, $\\mathrm{D}^{Q}(\\rho||\\sigma) $ sho"},"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":"1010.1030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-05T21:52:23Z","cross_cats_sorted":[],"title_canon_sha256":"ba83bc8143a24984591ad3f1cf3fdfb3c1759d1f8ac7d5a61c61d3171fd738df","abstract_canon_sha256":"3c8c9d676f67259afa35cd5e8e6e2dfb4df4842cdbc158488cf3ca3ce2dc6b9b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:49.949151Z","signature_b64":"cwAz6ZQ1UfxjcAvePXAV84cPeu84tUeJ5miwdqNr4YMivm1HcsOleqYV20eScC5rHLFh5Mk9fe/K5HIoqriaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"863f1bc8d3a61d84c6e800844678de3341be6b1b1559f55e003adfeccc6fce59","last_reissued_at":"2026-05-18T04:39:49.948620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:49.948620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reverse Test and Characterization of Quantum Relative Entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Keiji Matsumoto","submitted_at":"2010-10-05T21:52:23Z","abstract_excerpt":"The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the upperbound and the lowerbund of $\\mathrm{D}^{Q}(\\rho||\\sigma) $ is $\\mathrm{D}^{R}(\\rho||\\sigma) :=\\mathrm{tr}% \\,\\rho\\ln\\sqrt{\\rho}\\sigma^{-1}\\sqrt{\\rho}$ and $\\mathrm{D}(\\rho||\\sigma) :=$ $\\mathrm{tr}\\,\\rho(\\ln\\rho-\\ln\\sigma) $, respectively. In the latter setting, we prove uniqueness of quantum relative entropy, that is, $\\mathrm{D}^{Q}(\\rho||\\sigma) $ sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1030","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":"1010.1030","created_at":"2026-05-18T04:39:49.948727+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.1030v1","created_at":"2026-05-18T04:39:49.948727+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1030","created_at":"2026-05-18T04:39:49.948727+00:00"},{"alias_kind":"pith_short_12","alias_value":"QY7RXSGTUYOY","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"QY7RXSGTUYOYJRXI","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"QY7RXSGT","created_at":"2026-05-18T12:26:13.927090+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.01712","citing_title":"Quantum Noncommutativity Uniquely Determines Relative Entropy","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN","json":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN.json","graph_json":"https://pith.science/api/pith-number/QY7RXSGTUYOYJRXIACCEM6G6GN/graph.json","events_json":"https://pith.science/api/pith-number/QY7RXSGTUYOYJRXIACCEM6G6GN/events.json","paper":"https://pith.science/paper/QY7RXSGT"},"agent_actions":{"view_html":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN","download_json":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN.json","view_paper":"https://pith.science/paper/QY7RXSGT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.1030&json=true","fetch_graph":"https://pith.science/api/pith-number/QY7RXSGTUYOYJRXIACCEM6G6GN/graph.json","fetch_events":"https://pith.science/api/pith-number/QY7RXSGTUYOYJRXIACCEM6G6GN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN/action/storage_attestation","attest_author":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN/action/author_attestation","sign_citation":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN/action/citation_signature","submit_replication":"https://pith.science/pith/QY7RXSGTUYOYJRXIACCEM6G6GN/action/replication_record"}},"created_at":"2026-05-18T04:39:49.948727+00:00","updated_at":"2026-05-18T04:39:49.948727+00:00"}