{"paper":{"title":"Characterization of linear maps on $M_n$ whose multiplicity maps have maximal norm, with an application in quantum information","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Daniel Puzzuoli","submitted_at":"2017-10-09T19:38:21Z","abstract_excerpt":"Given a linear map $\\Phi : M_n \\rightarrow M_m$, its multiplicity maps are defined as the family of linear maps $\\Phi \\otimes \\text{id}_k : M_n \\otimes M_k \\rightarrow M_m \\otimes M_k$, where $\\text{id}_k$ denotes the identity on $M_k$. Let $\\|\\cdot\\|_1$ denote the trace-norm on matrices, as well as the induced trace-norm on linear maps of matrices, i.e. $\\|\\Phi\\|_1 = \\max\\{\\|\\Phi(X)\\|_1 : X \\in M_n, \\|X\\|_1 = 1\\}$. A fact of fundamental importance in both operator algebras and quantum information is that $\\|\\Phi \\otimes \\text{id}_k\\|_1$ can grow with $k$. In general, the rate of growth is bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03281","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"}