A deformation quantization on the sphere for qubits is defined via Stratonovich-Weyl correspondence, with the star product reproducing complex quaternion algebra and enabling phase-space propagators.
Girard,Quaternions, Clifford Algebras and Relativistic Physics(Birkhauser, 2004)
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Star product for qubit states in phase space and star exponentials
A deformation quantization on the sphere for qubits is defined via Stratonovich-Weyl correspondence, with the star product reproducing complex quaternion algebra and enabling phase-space propagators.