{"paper":{"title":"A gradient system on the quantum information space that realizes the Karmarkar flow for linear programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Hiromi Yuya, Yoshio Uwano","submitted_at":"2008-07-25T10:41:11Z","abstract_excerpt":"In the paper of Uwano [Czech. J. of Phys., vol.56, pp.1311-1316 (2006)], a gradient system is found on the space of density matrices endowed with the quantum SLD Fisher metric (to be referred to as the quantum information space) that realizes a generalization of a gradient system on the space of multinomial distributions studied by Nakamura [Japan J. Indust. Appl. Math., vol.10, pp.179-189 (1993)]. On motived by those papers, the present paper aims to construct a gradient system on the quantum information space that realizes the Karmarkar flow, the continuous limit of the Karmarkar projective "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4053","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"}