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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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Contributor : Michel Planat <>
Submitted on : Tuesday, June 12, 2007 - 5:29:25 PM
Last modification on : Thursday, November 12, 2020 - 9:42:07 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 12:51:28 PM


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  • HAL Id : hal-00147435, version 2
  • ARXIV : 0705.2538


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



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