{"paper":{"title":"Geometry of quantum systems: density states and entanglement","license":"","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Giuseppe Marmo, Janusz Grabowski, Marek Ku\\'s","submitted_at":"2005-07-18T22:45:42Z","abstract_excerpt":"Various problems concerning the geometry of the space $u^*(\\cH)$ of Hermitian operators on a Hilbert space $\\cH$ are addressed. In particular, we study the canonical Poisson and Riemann-Jordan tensors and the corresponding foliations into K\\\"ahler submanifolds. It is also shown that the space $\\cD(\\cH)$ of density states on an $n$-dimensional Hilbert space $\\cH$ is naturally a manifold stratified space with the stratification induced by the the rank of the state. Thus the space $\\cD^k(\\cH)$ of rank-$k$ states, $k=1,...,n$, is a smooth manifold of (real) dimension $2nk-k^2-1$ and this stratific"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0507045","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0507045/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}