{"paper":{"title":"Constructing SU(2) x U(1) orbit space for qutrit mixed states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Arsen Khvedelidze, Vladimir Gerdt, Yuri Palii","submitted_at":"2014-08-28T12:15:33Z","abstract_excerpt":"The orbit space $\\mathfrak{P}(\\mathbb{R}^8)/\\mathrm{G}$, of the group $\\mathrm{G}:=\\mathrm{SU(2)\\times U(1)}\\subset\\mathrm{U(3)}$ acting adjointly on the state space $\\mathfrak{P}(\\mathbb{R}^8)$ of a 3-level quantum system is discussed. The semi-algebraic structure of $\\mathfrak{P}(\\mathbb{R}^8) /\\mathrm{G}$, is determined within the Procesi-Schwarz method. Using the integrity basis for the ring of G-invariant polynomials, $\\mathbb{R}[\\mathfrak{P}(\\mathbb{R}^8)]^{\\mathrm{G}}$, the set of constraints on the Casimir invariants of $\\mathrm{U}(3)$ group coming from the positivity requirement of Pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6697","kind":"arxiv","version":2},"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"}