MultiLine Geometry of QubitQutrit and HigherOrder Pauli Operators
Abstract
The commutation relations of the generalized Pauli operators of a qubitqutrit system are discussed in the newly established graphtheoretic and finitegeometrical settings. The dual of the Pauli graph of this system is found to be isomorphic to the projective line over the product ring mathcal{Z}_{2}×mathcal{Z}_{3} . A “peculiar” feature in comparison with twoqubits is that two distinct points/operators can be joined by more than one line. The multiline property is shown to be also present in the graphs/geometries characterizing twoqutrit and threequbit Pauli operators’ space and surmised to be exhibited by any other higherlevel quantum system.
 Publication:

International Journal of Theoretical Physics
 Pub Date:
 April 2008
 DOI:
 10.1007/s1077300795419
 arXiv:
 arXiv:0705.2538
 Bibcode:
 2008IJTP...47.1127P
 Keywords:

 Generalized Pauli operators;
 Pauli graphs;
 Finite projective geometries;
 Quantum Physics;
 Mathematical Physics
 EPrint:
 8 pages, 6 figures. International Journal of Theoretical Physics (2007) accept\'e