{"paper":{"title":"Optimal reducibility of all Stochastic Local Operation and Classical Communication equivalent W states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Preeti Parashar, Swapan Rana","submitted_at":"2011-10-20T18:11:34Z","abstract_excerpt":"We show that all multipartite pure states that are SLOCC equivalent to the $N$-qubit $W$ state, can be uniquely determined (among arbitrary states) from their bipartite marginals. We also prove that only $(N-1)$ of the bipartite marginals are sufficient and this is also the optimal number. Thus, contrary to the $GHZ$ class, $W$-type states preserve their reducibility under SLOCC. We also study the optimal reducibility of some larger classes of states. The generic Dicke states $|GD_N^\\ell\\ran$ are shown to be optimally determined by their ($\\ell+1$)-partite marginals. The class of `$G$' states "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4597","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"}