{"paper":{"title":"Necessary and sufficient condition of separability for D-symmetric diagonal states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Adam Rutkowski, Marcin Marciniak, Michal Banacki","submitted_at":"2018-10-12T13:57:08Z","abstract_excerpt":"For multipartite states we consider a notion of D-symmetry. For a system of $N$ qubits it concides with usual permutational symmetry. In case of $N$ qudits ($d\\geq 3$) the D-symmetry is stronger than the permutational one. For the space of all D-symmetric vectors in $(\\mathbb{C}^d)^{\\otimes N}$ we define a basis composed of vectors $\\{|R_{N,d;k}\\rangle: \\,0\\leq k\\leq N(d-1)\\}$ which are analog for Dicke states. The aim of this paper is to discuss the problem of separability of D-symmetric states which are diagonal in the basis $\\{|R_{N,d;k}\\rangle\\}$. We show that if $N$ is even and $d\\geq 2$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05522","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"}