{"paper":{"title":"Hermitian unitary matrices with modular permutation symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Ondrej Turek, Taksu Cheon","submitted_at":"2011-04-03T17:18:08Z","abstract_excerpt":"We study Hermitian unitary matrices $\\mathcal{S}\\in\\mathbb{C}^{n,n}$ with the following property: There exist $r\\geq0$ and $t>0$ such that the entries of $\\mathcal{S}$ satisfy $|\\mathcal{S}_{jj}|=r$ and $|\\mathcal{S}_{jk}|=t$ for all $j,k=1,\\ldots,n$, $j\\neq k$. We derive necessary conditions on the ratio $d:=r/t$ and show that these conditions are very restrictive except for the case when $n$ is even and the sum of the diagonal elements of $\\S$ is zero. Examples of families of matrices $\\mathcal{S}$ are constructed for $d$ belonging to certain intervals. The case of real matrices $\\mathcal{S}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0408","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"}