{"paper":{"title":"A geometric characterization of invertible quantum measurement maps","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Chi-Kwong Li, Jin-Chuan Hou, Kan He","submitted_at":"2012-10-01T15:01:10Z","abstract_excerpt":"A geometric characterization is given for invertible quantum measurement maps. Denote by ${\\mathcal S}(H)$ the convex set of all states (i.e., trace-1 positive operators) on Hilbert space $H$ with dim$H\\leq \\infty$, and $[\\rho_1, \\rho_2]$ the line segment joining two elements $\\rho_1, \\rho_2$ in ${\\mathcal S}(H)$. It is shown that a bijective map $\\phi:{\\mathcal S}(H) \\rightarrow {\\mathcal S}(H)$ satisfies $\\phi([\\rho_1, \\rho_2]) \\subseteq [\\phi(\\rho_1),\\phi(\\rho_2)]$ for any $\\rho_1, \\rho_2 \\in {\\mathcal S}$ if and only if $\\phi$ has one of the following forms $$\\rho \\mapsto \\frac{M\\rho M^*}{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0433","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"}