{"paper":{"title":"Entropy and Geometry of Quantum States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Anirudh Reddy, Joseph Samuel, Kumar Shivam, Supurna Sinha","submitted_at":"2016-09-23T09:06:26Z","abstract_excerpt":"We compare the roles of the Bures-Helstrom (BH) and Bogoliubov-Kubo-Mori (BKM) metrics in the subject of quantum information geometry. We note that there are two limits involved in state discrimination, which we call the \"thermodynamic\" limit (of $N$, the number of realizations going to infinity) and the infinitesimal limit (of the separation of states tending to zero). We show that these two limits do not commute in the quantum case. Taking the infinitesimal limit first leads to the BH metric and the corresponding Cram\\'er-Rao bound, which is widely accepted in this subject. Taking limits in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07279","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":""},"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"}