{"paper":{"title":"Volume Fractions of the Kinematic \"Near-Critical\" Sets of the Quantum Ensemble Control Landscape","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Herschel Rabitz, Jason Dominy","submitted_at":"2011-02-25T15:19:49Z","abstract_excerpt":"An estimate is derived for the volume fraction of a subset $C_{\\epsilon}^{P} = \\{U : ||grad J(U)|\\leq {\\epsilon}\\}\\subset\\mathrm{U}(N)$ in the neighborhood of the critical set $C^{P}\\simeq\\mathrm{U}(\\mathbf{n})P\\mathrm{U}(\\mathbf{m})$ of the kinematic quantum ensemble control landscape J(U) = Tr(U\\rho U' O), where $U$ represents the unitary time evolution operator, {\\rho} is the initial density matrix of the ensemble, and O is an observable operator. This estimate is based on the Hilbert-Schmidt geometry for the unitary group and a first-order approximation of $||grad J(U)||^2$. An upper bound"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5269","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"}