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arXiv · 0705.2538

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

Michel R. P. Planat·Anne-Céline Baboin·Metod Saniga
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Abstract

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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Michel R. P. Planat, Anne-Céline Baboin, Metod Saniga. 2007-06-12. Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators. https://doi.org/10.1007/s10773-007-9541-9

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