2007/08/31 by Hans Havlicek, Metod Saniga, Метод Санига · 24 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics #Computer science #Connection (principal bundle) #Degree (music) #Discrete mathematics #Geometry #Integer (computer science) #Line (geometry) #Magnetism in coordination complexes #Mathematics #Physics #Product (mathematics) #Projective line #Projective space #Projective test #Pure mathematics #Ring (chemistry) #Set (abstract data type) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/40/43/f03
published in Journal of Physics A Mathematical and Theoretical 40(43), F943-F952 (Institute of Physics)
openalex publication_date 2007/10/09 · arxiv created 2007/12/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A very particular connection between the commutation relations of the elements of the generalized Pauli group of a d -dimensional qudit, d being a product of distinct primes, and the structure of the projective line over the (modular) ring is established, where the integer exponents of the generating shift ( X ) and clock ( Z ) operators are associated with submodules of . Under this correspondence, the set of operators commuting with a given one—a perp-set—represents a submodule of . A crucial novel feature here is that the operators are also represented by non -admissible pairs of . This additional degree of freedom makes it possible to view any perp-set as a set-theoretic union of the corresponding points of the associated projective line.