{"paper":{"title":"Constructing $2\\times2\\times4$ and $4\\times4$ unextendible product bases and positive-partial-transpose entangled states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kai Wang, Lijun Zhao, Lin Chen, Yi Shen, Yize Sun","submitted_at":"2018-10-21T12:30:38Z","abstract_excerpt":"The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in $\\cH=\\bbC^2\\ox\\bbC^2\\ox\\bbC^4$, three UPBs of size $9$ in $\\cK=\\bbC^4\\ox\\bbC^4$, and no UPB of size $7$ in $\\cH$ and $\\cK$. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state $\\r$ of rank seven, and show that it is also a PPT entangled state in $\\cH$ and $\\cK$, respectively. We analytically derive the geometric measure of entanglement of a spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08932","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"}