{"paper":{"title":"Embeddings of spaces of quregisters into special linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dalia Cervantes, Guillermo Morales-Luna","submitted_at":"2016-04-26T02:52:16Z","abstract_excerpt":"We study embeddings of the unit sphere of complex Hilbert spaces of dimension a power $2^n$ into the corresponding groups of non-singular linear transformations. For the case of $n=1$, the sphere $S_2$ of qubits is identified with $\\mbox{SU}(2)$ and the algebraic structure of this last group is carried into $S_2$. Hence it is natural to analyse whether is it possible, for $n\\geq 2$, to carry the structure of the symmetry group $\\mbox{SU}(2^n)$ into the unit sphere $S_{2^n}$. For $n=2$ the embeddings of $S_{2^2}$ into $\\mbox{GL}(2^2)$, obtained as tensor products of the above embedding, fails t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07498","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"}