Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators - Archive ouverte HAL Access content directly
Journal Articles International Journal of Theoretical Physics Year : 2008

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

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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Dates and versions

hal-00147435 , version 1 (17-05-2007)
hal-00147435 , version 2 (12-06-2007)

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Michel R. P. Planat, Anne-Céline Baboin, Metod Saniga. Multi-Line Geometry of Qubit-Qutrit and Higher-Order Pauli Operators. International Journal of Theoretical Physics, 2008, 47, pp.1127-1135. ⟨hal-00147435v2⟩
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