{"paper":{"title":"On Fixed Points of L\\\"{u}ders Operation","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Liu Weihua, Wu Junde","submitted_at":"2009-06-08T06:05:49Z","abstract_excerpt":"In this paper, we prove that if $\\mathcal{A}=\\{E_i\\}_{i=1}^{n}$ is a finite commutative quantum measurement, then the fixed points set of L\\\"{u}ders operation $L_{{\\cal A}}$ is the commutant ${\\cal A}'$ of ${\\cal A}$, the result answers an open problem partially. We also give a concrete example of a L\\\"{u}ders operation $L_{{\\cal A}}$ with $n=3$ such that $L_{{\\cal A}}(B)=B$ does not imply that the quantum effect $B$ commutes with all $E_1, E_2$ and $E_3$, this example answers another open problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.1412","kind":"arxiv","version":6},"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"}