{"ID":23595660,"CreatedAt":"2026-09-18T05:42:42.291333095Z","UpdatedAt":"2026-09-18T05:42:42.291333095Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20161","arxiv_id":"2609.20161","title":"Quantum expanders and dimension-free commutator bounds","abstract":"We prove that every traceless real or complex matrix $A$ can be written as $A=BC-CB$, with factors of the same size and over the same field satisfying $\\|B\\|\\,\\|C\\|\\le K\\|A\\|$, where $K$ is an absolute constant. The proof combines an approximate-rank dichotomy with stable commutator representations obtained from quantum expansion.","short_abstract":"We prove that every traceless real or complex matrix $A$ can be written as $A=BC-CB$, with factors of the same size and over the same field satisfying $\\|B\\|\\,\\|C\\|\\le K\\|A\\|$, where $K$ is an absolute constant. The proof combines an approximate-rank dichotomy with stable commutator representations obtained from quantu...","url_abs":"https://arxiv.org/abs/2609.20161","url_pdf":"https://arxiv.org/pdf/2609.20161v1","authors":"[\"Tuan Tran\"]","published":"2026-09-17T12:50:25Z","proceeding":"math.FA","tasks":"[\"math.FA\",\"math.OA\"]","methods":"[]","has_code":false}