{"paper":{"title":"Local numerical range for a class of $2\\otimes d$ hermitian operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"A. Rutkowski, D. Chru\\'sci\\'nski, J. Jurkowski","submitted_at":"2014-10-10T10:36:05Z","abstract_excerpt":"A local numerical range is analyzed for a family of circulant observables and states of composite $2 \\otimes d$ systems. It is shown that for any $2\\otimes d$ circulant operator $\\cal O$ there exists a basis giving rise to the matrix representation with real non-negative off-diagonal elements. In this basis the problem of finding extremum of $\\cal O$ on product vectors $\\ket{x}\\otimes \\ket{y} \\in \\mathbb{C}^2\\otimes \\mathbb{C}^d$ reduces to the corresponding problem in $\\mathbb{R}^2\\otimes \\mathbb{R}^d$. The final analytical result for $d=2$ is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2732","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"}