Projective Ring Line of a Specific Qudit

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dc.creatorHavlicek, Hans
dc.creatorSaniga, Metod
dc.date2007-08-31
dc.date2007-12-27
dc.date.accessioned2026-07-07T08:51:02Z
dc.date.available2026-07-07T08:51:02Z
dc.descriptionA 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 $\bZ_{d}$ is established, where the integer exponents of the generating shift ($X$) and clock ($Z$) operators are associated with submodules of $\bZ^{2}_{d}$. Under this correspondence, the set of operators commuting with a given one -- a perp-set -- represents a $\bZ_{d}$-submodule of $\bZ^{2}_{d}$. A crucial novel feature here is that the operators are also represented by {\it non}-admissible pairs of $\bZ^{2}_{d}$. This additional degree of freedom makes it possible to view any perp-set as a {\it set-theoretic} union of the corresponding points of the associated projective line.
dc.identifierhttps://arxiv.org/abs/0708.4333
dc.identifierhttp://arxiv.org/abs/0708.4333
dc.identifierJournal of Physics A Mathematical and Theoretical 40 (2007) F943-F952
dc.identifierdoi:10.1088/1751-8113/40/43/F03
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144803
dc.subjectQuantum Physics
dc.subjectMathematical Physics
dc.titleProjective Ring Line of a Specific Qudit
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