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Open Quantum Systems Decoherence
Qudits of composite dimension, mutually unbiased bases and projective ring geometry
arXiv
Authors: Michel Planat, Anne-Céline Baboin
Year
2007
Paper ID
49061
Status
Preprint
Abstract Read
~2 min
Abstract Words
99
Citations
N/A
Abstract
The d2 Pauli operators attached to a composite qudit in dimension d may be mapped to the vectors of the symplectic module mathcal{Z}d2 $mathcal{Z}d$ the modular ring. As a result, perpendicular vectors correspond to commuting operators, a free cyclic submodule to a maximal commuting set, and disjoint such sets to mutually unbiased bases. For dimensions d=6, 10, 15, 12, and 18, the fine structure and the incidence between maximal commuting sets is found to reproduce the projective line over the rings mathcal{Z}6, mathcal{Z}10, mathcal{Z}15, mathcal{Z}6 times mathbf{F}4 and mathcal{Z}6 times mathcal{Z}3, respectively.
Why This Paper Matters
- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
- It adds a 2007 reference point for readers tracking recent quantum research.
- The d^2 Pauli operators attached to a composite qudit in dimension d may be mapped to the vectors of the symplectic module mathcalZd^2 mathcalZd the modular ring.
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