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A numerical study on the conjectured inequality is conducted in this note. The results obtained indicate that the modified super-additivit"},"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":"1305.2023","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-05-09T07:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"58d3719d559b7bfbb87afecf6f9bb0075f90531bcfccfde83b31a6f6c5cc2382","abstract_canon_sha256":"a6bddd818c485e60b26af9ba8af3414b57cd7b55d066c5f488244b451d16c38d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T19:27:08.756263Z","signature_b64":"vDoKtAtf+3/9xGscgE87GQhx0JwpZ2jodI7a1N9h94dAItG3C5yp9QkUqZR2XhK8TSUpz7USBqW+AIt4h9AwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9dfbed65f9633f8dd9206df3655ec9436a137d702e32eb5a7b3fb78bbff5730","last_reissued_at":"2026-07-04T19:27:08.755639Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T19:27:08.755639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum marginal inequalities and the conjectured entropic inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Hongjin He, Lin Zhang, Yuan-hong Tao","submitted_at":"2013-05-09T07:26:09Z","abstract_excerpt":"A conjecture -- \\emph{the modified super-additivity inequality} of relative entropy -- was proposed in \\cite{Zhang2012}: There exist three unitary operators $U_A\\in \\unitary{\\cH_A},U_B\\in \\unitary{\\cH_B}$, and $U_{AB}\\in \\unitary{\\cH_A\\ot \\cH_B}$ such that $$ \\rS(U_{AB}\\rho_{AB}U^\\dagger_{AB}||\\sigma_{AB}) \\geqslant \\rS(U_A\\rho_AU^\\dagger_A||\\sigma_A) + \\rS(U_B\\rho_BU^\\dagger_B||\\sigma_B), $$ where the reference state $\\sigma$ is required to be full-ranked. A numerical study on the conjectured inequality is conducted in this note. 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