{"paper":{"title":"Higher rank numerical ranges and low rank perturbations of quantum channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.FA","authors_text":"Chi-Kwong Li, Nung-sing Sze, Yiu-Tung Poon","submitted_at":"2007-10-15T19:49:33Z","abstract_excerpt":"For a positive integer $k$, the rank-$k$ numerical range $\\Lambda_k(A)$ of an operator $A$ acting on a Hilbert space $\\cH$ of dimension at least $k$ is the set of scalars $\\lambda$ such that $PAP = \\lambda P$ for some rank $k$ orthogonal projection $P$. In this paper, a close connection between low rank perturbation of an operator $A$ and $\\Lambda_k(A)$ is established. In particular, for $1 \\le r < k$ it is shown that $\\Lambda_k(A) \\subseteq \\Lambda_{k-r}(A+F)$ for any operator $F$ with $\\rank (F) \\le r$. In quantum computing, this result implies that a quantum channel with a $k$-dimensional e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2898","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"}