{"paper":{"title":"Length filtration of the separable states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dragomir Z Djokovic, Lin Chen","submitted_at":"2016-02-17T02:42:19Z","abstract_excerpt":"We investigate the separable states $\\r$ of an arbitrary multipartite quantum system with Hilbert space $\\cH$ of dimensionin $d$. The length $L(\\r)$ of $\\r$ is defined as the smallest number of pure product states having $\\r$ as their mixture. The length filtration of the set of separable states, $\\cS$, is the increasing chain $\\emptyset\\subset\\cS'_1\\subseteq\\cS'_2\\subseteq\\cdots$, where $\\cS'_i=\\{\\r\\in\\cS:L(\\r)\\le i\\}$. We define the maximum length, $L_{\\rm max}=\\max_{\\r\\in\\cS} L(\\r)$, critical length, $L_{\\rm crit}$, and yet another special length, $L_c$, which was defined by a simple formul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05278","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"}