{"paper":{"title":"Stratified Manifold of Quantum States, actions of the complex special linear group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alberto Ibort, Dariusz Chruscinski, Florio M. Ciaglia, Franco Ventriglia, Giuseppe Marmo","submitted_at":"2018-11-18T21:21:41Z","abstract_excerpt":"We review the geometry of the space of quantum states $\\mathscr{S}(\\mathcal{H})$ of a finite-level quantum system with Hilbert space $\\mathcal{H}$ from a group-theoretical point of view. This space carries two stratifications generated by the action of two different Lie groups: the special unitary group $\\mathcal{SU}(\\mathcal{H})$ and its complexification $\\mathcal{SL}(\\mathcal{H})$, the complex special linear group. A stratum of the stratification generated by $\\mathcal{SU}(\\mathcal{H})$ is composed of isospectral states, that is, density operators with the same spectrum, A stratum of the str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07406","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"}