{"paper":{"title":"Unextendible entangled bases with fixed Schmidt number","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Shengjun Wu, Yu Guo","submitted_at":"2014-07-16T16:08:53Z","abstract_excerpt":"The unextendible product basis (UPB) is generalized to the unextendible entangled basis with any arbitrarily given Schmidt number $k$ (UEBk) for any bipartite system $\\mathbb{C}^d\\otimes\\mathbb{C}^{d'}$ ($2\\leq k<d\\leq d'$), which can also be regarded as a generalization of the unextendible maximally entangled basis (UMEB). A general way of constructing such a basis with arbitrary $d$ and $d'$ is proposed. Consequently, it is shown that there are at least $k-r$ (here $r=d$ mod $k$, or $r=d'$ mod $k$) sets of UEBk when $d$ or $d'$ is not the multiple of $k$, while there are at least $2(k-1)$ se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4362","kind":"arxiv","version":3},"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"}