{"paper":{"title":"On discrete Wigner transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jianfeng Lu, Kevin Stubbs, Zhenning Cai","submitted_at":"2018-02-16T04:38:02Z","abstract_excerpt":"In this work, we derive a discrete analog of the Wigner transform over the space $(\\mathbb{C}^p)^{\\otimes N}$ for any prime $p$ and any positive integer $N$. We show that the Wigner transform over this space can be constructed as the inverse Fourier transform of the standard Pauli matrices for $p=2$ or more generally of the Heisenberg-Weyl group elements for $p > 2$. We connect our work to a previous construction by Wootters of a discrete Wigner transform by showing that for all $p$, Wootters' construction corresponds to taking the inverse symplectic Fourier transform instead of the inverse Fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.05834","kind":"arxiv","version":2},"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"}