{"paper":{"title":"Sufficient and Necessary Condition of Separability for Generalized Werner States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dong-Ling Deng, Jing-Ling Chen","submitted_at":"2008-08-08T03:07:14Z","abstract_excerpt":"We introduce a sufficient and necessary condition for the separability of a specific class of $N$ $d$-dimensional system (qudits) states, namely special generalized Werner state (SGWS): $W^{[d^N]}(v)=(1-v)\\frac{I^{(N)}}{d^N}+v|\\psi _d^N><\\psi_d^N|$, where $ |\\psi_d^N>=\\sum_{i=0}^{d-1}\\alpha_i|i... i>$ is an entangled pure state of $N$ qudits system and $\\alpha_i$ satisfys two restrictions: (i) $\\sum_{i=0}^{d-1}\\alpha_i\\alpha_i^*=1$; (ii) Matrix $\\frac{1}{d}(I^{(1)}+\\mathcal{T}\\sum_{i\\neq j}\\alpha_i|i>< j|\\alpha_j^*)$, where $\\mathcal{T}=\\texttt{Min}_{i\\neq j}\\{1/|\\alpha_i\\alpha_j|\\}$, is a den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1147","kind":"arxiv","version":1},"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"}