{"paper":{"title":"A Notable Relation between $N$-Qubit and $2^{N-1}$-Qubit Pauli Groups via Binary ${\\rm LGr}(N,2N)$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.CO","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Fr\\'ed\\'eric Holweck, Metod Saniga, P\\'eter L\\'evay","submitted_at":"2013-11-11T10:27:11Z","abstract_excerpt":"Employing the fact that the geometry of the $N$-qubit ($N \\geq 2$) Pauli group is embodied in the structure of the symplectic polar space $\\mathcal{W}(2N-1,2)$ and using properties of the Lagrangian Grassmannian ${\\rm LGr}(N,2N)$ defined over the smallest Galois field, it is demonstrated that there exists a bijection between the set of maximum sets of mutually commuting elements of the $N$-qubit Pauli group and a certain subset of elements of the $2^{N-1}$-qubit Pauli group. In order to reveal finer traits of this correspondence, the cases $N=3$ (also addressed recently by L\\'evay, Planat and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2408","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"}