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Topological Quantum Computing Quantum Simulation Entanglement Theory Quantum Correlations

Projective Ring Line of a Specific Qudit

arXiv
Authors: Hans Havlicek, Metod Saniga

Year

2007

Paper ID

49205

Status

Preprint

Abstract Read

~2 min

Abstract Words

133

Citations

N/A

Abstract

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 bZd is established, where the integer exponents of the generating shift (X) and clock (Z) operators are associated with submodules of bZ2d. Under this correspondence, the set of operators commuting with a given one - a perp-set - represents a bZd-submodule of bZ2d. A crucial novel feature here is that the operators are also represented by {\it non}-admissible pairs of bZ2d. 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.

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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0708.4333 [2] arXiv https://arxiv.org/abs/0708.4333 [3] Publisher https://arxiv.org/abs/0708.4333

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