Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators

Details Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators

2007-05-17

arxiv.org/abs/0705.2538v2

International Journal of Theoretical Physics 47 (2008) 1127-1135

Physics

Quantum Physics

8 pages, 6 figures. International Journal of Theoretical Physics (2007) accept\'e

Scientific paper

10.1007/s10773-007-9541-9

The commutation relations of the generalized Pauli operators of a qubit-qutrit system are discussed in the newly established graph-theoretic and finite-geometrical settings. The dual of the Pauli graph of this system is found to be isomorphic to the projective line over the product ring Z2xZ3. A "peculiar" feature in comparison with two-qubits is that two distinct points/operators can be joined by more than one line. The multi-line property is shown to be also present in the graphs/geometries characterizing two-qutrit and three-qubit Pauli operators' space and surmised to be exhibited by any other higher-level quantum system.

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