{"paper":{"title":"The stabilizer for $n$-qubit symmetric states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"quant-ph","authors_text":"Xian Shi","submitted_at":"2018-06-06T02:49:44Z","abstract_excerpt":"The stabilizer group for an $n$-qubit state $\\ket{\\phi}$ is the set of all invertible local operators (ILO) $g=g_1\\otimes g_2\\otimes \\cdots\\otimes g_n,$ $ g_i\\in \\mathcal{GL}(2,\\mathbb{C})$ such that $\\ket{\\phi}=g\\ket{\\phi}.$ Recently, G. Gour $et$ $al.$ \\cite{GKW} presented that almost all $n$-qubit state $\\ket{\\psi}$ own a trivial stabilizer group when $n\\ge 5.$ In this article, we consider the case when the stabilizer group of an $n$-qubit symmetric pure state $\\ket{\\psi}$ is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state $\\ket{\\phi}$ is nontrivial when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01991","kind":"arxiv","version":4},"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"}