{"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. The results obtained indicate that the modified super-additivit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2023","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1305.2023/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}