{"paper":{"title":"An infinite family of strongly unextendible mutually unbiased bases in $\\mathbb{C}^{2^{2h}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jonathan Jedwab, Lily Yen","submitted_at":"2016-04-16T21:05:51Z","abstract_excerpt":"A set of $b$ mutually unbiased bases (MUBs) in $\\mathbb{C}^d$ (for $d > 1$) comprises $bd$ vectors in $\\mathbb{C}^d$, partitioned into $b$ orthogonal bases for $\\mathbb{C}^d$ such that the pairwise angle between all vectors from distinct bases is $\\arccos(1/\\sqrt{d})$. The largest number $\\mu(d)$ of MUBs that can exist in $\\mathbb{C}^d$ is at most $d+1$, but constructions attaining this bound are known only when $d$ is a prime power. A set of $b$ MUBs in $\\mathbb{C}^d$ that cannot be enlarged, even by the first vector of a potential $(b+1)$-th MUB, is called strongly unextendible. Until now, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04797","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"}