{"paper":{"title":"A remarkable representation of the Clifford group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ingemar Bengtsson","submitted_at":"2012-02-16T10:51:08Z","abstract_excerpt":"The finite Heisenberg group knows when the dimension of Hilbert space is a square number. Remarkably, it then admits a representation such that the entire Clifford group --- the automorphism group of the Heisenberg group --- is represented by monomial phase-permutation matrices. This has a beneficial influence on the amount of calculation that must be done to find Symmetric Informationally Complete POVMs. I make some comments on the equations obeyed by the absolute values of the components of the SIC vectors, and on the fact that the representation partly suggests a preferred tensor product st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3559","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"}