{"paper":{"title":"Constructions of Unextendible Maximally Entangled Bases in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Gui-Jun Zhang, Shao-Ming Fei, Xin-Lei Yong, Yi-Fan Han, Yuan-hong Tao","submitted_at":"2018-02-21T14:51:32Z","abstract_excerpt":"We study unextendible maximally entangled bases (UMEBs) in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\) ($d<d'$). An operational method to construct UMEBs containing $d(d^{\\prime}-1)$ maximally entangled vectors is established, and two UMEBs in \\(\\mathbb {C}^{5}\\otimes \\mathbb {C}^{6}\\) and \\(\\mathbb {C}^{5}\\otimes \\mathbb {C}^{12}\\) are given as examples. Furthermore, a systematic way of constructing UMEBs containing $d(d^{\\prime}-r)$ maximally entangled vectors in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\) is presented for $r=1,2,\\cdots, d-1$. Correspondingly, two UMEBs in \\("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07594","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"}