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.

8 pages, 6 figures. International Journal of Theoretical Physics (2007) accepté

References in corpus (4)

• Multiple Qubits as Symplectic Polar Spaces of Order Two
• Projective Ring Line Encompassing Two-Qubits
• The Projective Line Over the Finite Quotient Ring GF(2)[$x$]/$<x^3-x>$ and Quantum Entanglement II. The Mermin "Magic" Square/Pentagram
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• Projective Ring Line of a Specific Qudit
• SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
• A Sequence of Qubit-Qudit Pauli Groups as a Nested Structure of Doilies
• Generalized spin bases for quantum chemistry and quantum information